NDA/NA(I) Exam 2015 General Ability Test Previous Year Paper

NDA/NA(I) Exam 2015 General Ability Test

Q. 1 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

Unless you stop making noise at once, I will have no option but to bring the matter to the attention of the police.

A. Unless you stop to make noise at once,

B. I will have no option but to

C. bring the matter to the attention of the police.

D. No error

 

Q. 2 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

He couldn’t but help shed tears at the plight of the villagers rendered homeless by a

devastating cyclone.

A. He couldn’t but help

B. shed tears at the plight of the villagers

C. rendered homeless by a devastating cyclone.

D. No error

 

Q. 3 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

Since it was his first election campaign, the candidate was confused; none could clearly understand either the principles he stood for or the benefits he promised.

A. Since it was his first election campaign, the candidate was confused;

B. none could clearly understand

C. either the principles he stood for or the benefits he promised.

D. No error

 

Q. 4 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

It is an established fact that the transcendental American poets and philosophers, who

lived in the latter half of the nineteenth century, were more influenced by Indian philosophy, in particular by Upanishadic Philosophy.

A. It is an established fact that the transcendental American poets and philosophers,

B. who lived in the latter half of the nineteenth century,

C. were more influenced by Indian philosophy, in particular by Upanishadic Philosophy.

D. No error

 

Q. 5 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

No sooner did I open the door when the rain, heavy and stormy, rushed in making us shiver from head to foot.

A. No sooner did I open the door

B. when the rain, heavy and stormy, rushed in

C. making us shiver from head to foot.

D. No error

 

Q. 6 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

After opening the door we entered into the room next to the kitchen.

A. After opening the door

B. we entered into the room

C. next to the kitchen.

D. No error

 

Q. 7 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

When the dentist came in my tooth was stopped aching out of feat that I might lose my tooth.

A. When the dentist came in

B. my tooth was stopped aching

C. out of fear that I might lose my tooth.

D. No error

 

Q. 8 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

Emphasis on equality of life ensures for the health and happiness of every individual.

A. Emphasis on equality of life ensures

B. for the health and happiness

C. of every individual.

D. No error

 

Q. 9 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

The students were awaiting for the arrival of the chief guest.

A. The students were

B. awaiting for

C. the arrival of the chief guest.

D. No error

 

Q. 10 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

You will come to my party tomorrow, isn’t it?

A. You will come

B. to my party tomorrow,

C. isn’t it?

D. No error

 

Q. 11 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

Having read a number of stories about space travel his dream now is about to visit the

Moon.

A. Having read a number of stories

B. about space travel

C. his dream now is about to visit the moon.

D. No error

 

Q. 12 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

The meeting adjourned abruptly by the Chairman after about three hours of deliberation.

A. The meeting adjourned abruptly

B. by the Chairman after

C. about three hours of deliberation.

D. No error

 

Q. 13 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

Not one of the hundreds of striking workers were allowed o go near the factory.

A. Not one of the hundreds

B. of striking workers

C. were allowed to go near the factory.

D. No error

 

Q. 14 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

If I had known this earlier I will have helped him.

A. If I had known

B. this earlier

C. I will have helped him.

D. No error

 

Q. 15 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

Mr. Smith was accused for murder but the court found him not guilty and acquitted him.

A. Mr. Smith was accused for murder

B. but the court found him not guilty

C. and acquitted him.

D. No error

 

Q. 16 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

Although India is still ‘by far’ a poor country, it can become rich if its natural and human resources are fully utilized.

A. few and far between

B. by and large

C. by and by

D. No improvement

 

Q. 17 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet. Thus, a ‘No improvement’ response will be signified by the letter (d). ‘The more they earn, more they spend.’

A. More they earn, more they spend

B. More they earn, the more they spend

C. The more they earn, the more they spend

D. No improvement

 

Q. 18 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

But in all these cases conversion from one scale to another is easy because scales ‘have well-formulated.’

A. can be well-formulated

B. are well-formulated

C. well-formulated

D. No improvement

 

Q. 19 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

Five years ago on this date, I ‘am sitting’ in a small Japanese car, driving across Poland towards Berlin.

A. was sitting

B. sat

C. have been sitting

D. No improvement

 

Q. 20 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

The old man felled some trees in the garden with ‘hardly no effort’ at all. 

A. hard effort

B. hardly any effort

C. a hardly any effort

D. No improvement

 

Q. 21 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

She says she’s already paid me back, but I can’t remember, so I’ll have ‘to take her word.’

A. to take her word true

B. to take her at word

C. to take her for word it

D. No improvement

 

Q. 22 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

The workers are ‘hell burnt at getting’ what is due to them.

A. hell burnt on getting

B. hell burnt for getting

C. hell burnt to getting

D. No improvement

 

Q. 23 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

You are warned ‘against committing’ the same mistake again.

A. to commit

B. for committing

C. against to commit

D. No improvement

 

Q. 24 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet. 

Thus, a ‘No improvement’ response will be signified by the letter (d).

While we would like ‘that all Indian children’ to go to school, we need to ponder why they do not.

A. that all the Indian children

B. if all the children of India

C. all Indian children

D. No improvement

 

Q. 25 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet. 

Thus, a ‘No improvement’ response will be signified by the letter (d).

‘Due to these reasons’ we are all in favor of universal compulsory education.

A. Out of these reasons

B. For these reasons

C. By these reasons

D. No improvement

 

Q. 26 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

When it was feared that the serfs might go too far and gain their freedom from serfdom, the Protestant leaders joined the princes ‘at crushing’ them.

A. into crushing

B. in crushing

C. without crushing

D. No improvement

 

Q. 27 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

In India, today many of our intellectuals still talk in terms of the French revolution and the Rights of Man, not appreciating that ‘much has happened’ since then.

A. much has been happening

B. much had happened

C. much might happen

D. No improvement

 

Q. 28 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

Taxpayers ‘are to’ be conscious of their privileges.

A. have to

B. need

C. ought to

D. No improvement

 

Q. 29 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

I would have waited for you at the station if ‘I knew’ that you would come

A. had known

B. was knowing

C. have known

D. No improvement

 

Q. 30 Look at the quoted part of the sentence. Below it are given three possible substitutions for the quoted part. If one of them, (a), (b) or (c), is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet.

Thus, a ‘No improvement’ response will be signified by the letter (d).

No one could explain how a calm and balanced person like him could ‘penetrate’ such a mindless act on his friends.

A. perpetuate

B. perpetrate

C. precipitate

D. No improvement

 

Q. 31 The given passage consists of six sentences. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences have been removed and jumbled up. These are labeled P, Q, R, and S. You are required to find out the proper order for the four sentences and mark accordingly on the Answer Sheet.

S1: At the roadside the driver will be asked to blow through a small glass tube into a plastic bag.

S6: The driver will be asked to go to the police station.

P: And if the color change does not reach the line the diver cannot be punished under the new law.

Q: Inside the tube are chemically treated crystals which change color if the driver has

alcohol on his breath.

R: But if the color change does reach the line then the test has proved positive.

S: If the color change goes beyond a certain line marked on the tube this indicates that the driver is probably over the specified limit.

The proper sequence should be

A. PSQR

B. SQRP

C. RPSQ

D. QSPR

 

Q. 32 The given passage consists of six sentences. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences have been removed and jumbled up. These are labeled P, Q, R, and S. You are required to find out the proper order for the four sentences and mark accordingly on the Answer Sheet.

S1: Hope springs eternally in the heart of man.

S6: This is the central idea of the poem.

P: But hope is everlasting.

Q: Love, friendship and youth perish.

R: It is nursed by the glorious elements of nature.

S: Man derives hope from nature in his gallant struggle after some noble ideal.

The proper sequence should be

A. QPRS

B. SRQP

C. RSQP

D. QPSR

 

Q. 33 The given passage consists of six sentences. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences have been removed and jumbled up. These are labeled P, Q, R, and S. You are required to find out the proper order for the four sentences and mark accordingly on the Answer Sheet.

S1: Mr. Sherlock Holmes and Doctor Watson were spending a weekend in a University town.

S6: It was clear that something very unusual happened.

P: One evening they received a visit from an acquaintance, Mr. Hilton Soames.

Q: On that occasion he was in a state of great agitation.

R: They were staying in furnished rooms, close to the library.

S: Mr. Soames was a tall, thin man of a nervous and excitable nature.

The proper sequence should be

A. PRSQ

B. RPSQ

C. PQRS

D. RPQS

 

Q. 34 The given passage consists of six sentences. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences have been removed and jumbled up. These are labeled P, Q, R, and S. You are required to find out the proper order for the four sentences and mark accordingly on the Answer Sheet. 

S1: The machines that drive modern civilization derive their power from coal and oil.

S6: Nuclear energy may also be effectively used in this respect.

P: But they are not inexhaustible.

Q: These sources may not be exhausted very soon.

R: A time may come when some other sources have to be tapped and utilized.

S: Power may, of course, be obtained in future from forests, water, wind and withered

vegetables.

The proper sequence should be

A. PQRS

B. QPRS

C. SRQP

D. SPQR

 

Q. 35 The given passage consists of six sentences. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences have been removed and jumbled up. These are labeled P, Q, R, and S. You are required to find out the proper order for the four sentences and mark accordingly on the Answer Sheet.

S1: The body can never stop.

S6: It comes from food.

P: To support this endless activity, the body needs all the fuel for action.

Q: Sometimes it is more active than at other times, but it is always moving.

R: Even in the deepest sleep we must breathe.

S: The fuel must come from somewhere.

The proper sequence should be

A. PQRS

B. PRQS

C. QRPS

D. SRQP

 

Q. 36 The given passage consists of six sentences. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences have been removed and jumbled up. These are labeled P, Q, R, and S. You are required to find out the proper order for the four sentences and mark accordingly on the Answer Sheet.

S1: American idealism is essentially a belief in the idea of progress.

S6: This sense they have inherited from the English.

P: Therefore, he believes that, because of human effort, the future will be better than the past.

Q: But if Americans are usually optimistic, they are not wholly unrealistic.

R: The American tends to view history as a record of human achievement.

S: They have some common sense practicality.

The proper sequence should be

A. PQRS

B. PQSR

C. RPQS

D. PRQS

 

Questions: 37 – 42

After having slept for an hour, Bond Decided to go out into the city and try to find his contact . After changing his suit, he carefully locked his room and steeped out of the hotel . No one was around. But he had walked only for a few minutes when it suddenly (37)” ” that he was being (38) ” ” by someone. There was really no (39)” ” for it except a very slight (40) ” ” of footsteps. He was ow walking (41) ” ” the main street , which was crowded (42) ” ” with people. He became extremely aware of the danger of people threatening him.  

Q. 37 Choose the word which best suits the space quoted in (37) 

A. felt

B. occured

C. happened

 

Q. 38 Choose the word which best suits the space quoted in (38)

A. Followed

B. Shot

C. Looked

 

Q. 39 Choose the word which best suits the space quoted in (39)

A. reason

B. cause

C. evidence

 

Q. 40 Choose the word which best suits the space quoted in (40)

A. weight

B. Sound

C. Hurting

 

Q. 41 Choose the word which best suits the space quoted in (41)

A. from

B. down

C. over

 

Q. 42 Choose the word which best suits the space quoted in (42)

A. with

B. by

C. in

 

Q. 43 The given sentence consists of a quoted word followed by four words or group of words. Select the word or group of words that is most similar in meaning to the quoted word.

He was ‘fired’ for negligence on duty.

A. relieved of his job

B. scolded

C. rebuked

D. attacked

 

Q. 44 The given sentence consists of a quoted word followed by four words or group of words. Select the word or group of words that is most similar in meaning to the quoted word. Democracy is not the standardizing of everyone so as to ‘obliterate’ all peculiarity.

A. demolish

B. extinguish

C. erase

D. change

 

Q. 45 The given sentence consists of a quoted word followed by four words or group of words. Select the word or group of words that is most similar in meaning to the quoted word. Divine grace is truly ‘ineffable.’

A. that which cannot be rubbed out

B. incapable of being understood

C. that which is too great to be expressed in words

D. too powerful to be defeated

 

Q. 46 The given sentence consists of a quoted word followed by four words or group of words. Select the word or group of words that is most similar in meaning to the quoted word.

The convocation address was very ‘edifying.’

A. tedious

B. in need of editing

C. instructive

D. exciting

 

Q. 47 The given sentence consists of a quoted word followed by four words or group of words. Select the word or group of words that is most nearly opposite in meaning to the quoted word.

John is always ‘shabbily’ dressed.

A. decently

B. beautifully

C. extravagently

D. scantily

 

Q. 48 The given sentence consists of a quoted word followed by four words or group of words. Select the word or group of words that is most nearly opposite in meaning to the quoted word.

The new manager of the Bank is ‘urbane’ in his manners.

A. civilized

B. slow

C. rude

D. foolish

 

Q. 49 The given sentence consists of a quoted word followed by four words or group of words. Select the word or group of words that is most nearly opposite in meaning to the quoted word.

It is necessary to develop ‘thrifty’ habits to be able to lead a comfortable life.

A. expensive

B. extravagant

C. economical

D. good

 

Q. 50 The given sentence consists of a quoted word followed by four words or group of words. Select the word or group of words that is most nearly opposite in meaning to the quoted word.

Many people suffer because of ‘pride.’

A. lowliness

B. submission

C. humility

D. obedience

 

Q. 51 Consider the following two statements & answer below.

Statement I: Growth of plants is smooth with a complete fertilizer.

Statement II: A complete fertilizer always contains N, P, K.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 52 Consider the following two statements & answer below.

Statement I: The granules of modern gunpowder (also called black powder) are typically coated with Graphite.

Statement II: Graphite prevents the build-up of electrostatic charge.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 53 Consider the following two statements & answer below.

Statement I: Color of nitrogen dioxide changes to colorless at low temperature.

Statement II: At low-temperature Nitrogen tetroxide (N2O4) is formed which is colorless.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct

explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 54 Consider the following two statements & answer below.

Statement I: Diamond is very bright

Statement II: Diamond has very low refractive index.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 55 Consider the following two statements & answer below.

Statement I: Oxygen gas is easily produced at a faster rate by heating a mixture of

potassium chlorate and manganese dioxide than heating potassium chlorate alone.

Statement II: Manganese dioxide acts as a negative catalyst.

A. Both the statements are individually true but Statement II is the correct explanation

of Statement I

B. Both the Statements are individually true but Statement II is not the correct

explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 56 Consider the following two statements & answer below.

Statement I: A body weighs less on a hilltop than on earth’s surface even though its mass remains unchanged.

Statement II: The acceleration due to gravity of the earth decreases with height.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 57 Consider the following two statements & answer below.

Statement I: While putting clothes for drying up, we spread them out.

Statement II: The rate of evaporation increases with an increase in surface area.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 58 Consider the following two statements & answer below.

Statement I: Due to diffused or irregular reflection of light, a closed room gets light even if no direct sunlight falls inside the room.

Statement II: Irregular reflection, where the reflected rays are not parallel, does not follow the laws of reflection.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the Statements are individually true but Statement II is not the correct explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 59 Ultrasonic waves of frequency 3 x 10⁵ Hz are passed through a medium where the speed of sound is 10 times that in the air (speed of sound in air is 300m/s). The wavelength of this wave in that medium will be of the order or

A. 1cm

B. 10cm

C. 100cm

D. 0.1cm

 

Q. 60 If radius of the earth were to shrink by 1%, its mass remaining the same, g would decrease by nearly

A. 1%

B. 2%

C. 3%

D. 4%

 

Q. 61 The displacement-time graph of a particle acted upon by a constant force is

A. a straight line

B. a circle

C. a parabola

D. any curve depending upon initial conditions

 

Q. 62 Which one of the following is not a result of surface tension?

A. nearly spherical drop of rain

B. capillary rise

C. removal of dirt by soap or detergent

D. flow of a liquid

 

Q. 63 Match List I with List II and select the correct answer using the code given below the Lists: 

List I List II

(Compound) (Nature)

A. Sodium hydroxide 1. Strong acid

B. Calcium oxide 2. Alkali

C. Acetic acid 3. Weak acid

D. Hydrochloric acid 4. Base

Code: 

A. A(2), B(3), C(4), D(1)

B. A(2), B(4), C(3), D(1)

C. A(1), B(4), C(3), D(2)

D. A(1), B(3), C(4), D(2)

 

Q. 64 Which one of the following statements is not correct?

A. Kerala is the largest producer of natural rubber in India

B. Neyveli is an important thermal power generating area of Tamil Nadu

C. Ratnagiri Bauxite mining area is located in Karnataka

D. Assam is the largest tea producing state in India

 

Q. 65 Match List I with List II and select the correct answer using the code given below the Lists:

List I List II

(Paper industry center) (State)

A. Kamptee 1. Karnataka

B. Rajahmundry 2. Maharashtra

C. Shahdol 3. Andhra Pradesh

D. Belagola 4. Madhya Pradesh

A. A(1), B(4), C(3), D(2)

B. A(2), B(3), C(4), D(1)

C. A(1), B(3), C(4), D(2)

D. A(2), B(4), C(3), D(1)

 

Q. 66 The newly formed state of Telangana is surrounded by

A. 5 states

B. 4 states

C. 6 states

D. 3 states

 

Q. 67 Energy is required for maintenance of life. It is obtained by a process called

A. Metabolism

B. Phagocytosis

C. Photorespiration

D. Decomposition

 

Q. 68 All life forms contain “molecules of life”. These are

A. Carbohydrates

B. Proteins

C. Nucleic acids

D. All of the above

 

Q. 69 If a charged particle (+q) is projected with certain velocity parallel to the magnetic field, then it will

A. trace helical path

B. trace circular path

C. continue its motion without any change

D. come to rest instantly

 

Q. 70 Optical fibers, through heat bent in any manner, allows light to pass through. What is the inference that one can draw from it?

A. The concept that light travels in straight path is wrong

B. Light can flow through the optical fibers

C. Light can travel through the fibers because of their ductility

D. Light can travel through the fibers due to multiple total internal reflections

 

Q. 71 Which one among the following happens when a swing rises to a certain height from its resting position?

A. Its potential energy decreases while kinetic energy increases

B. Its kinetic energy decreases while potential energy increases

C. Both potential and kinetic energy decrease

D. Both potential and kinetic energy increase

 

Q. 72 Which one among the following is used in making gunpowder?

A. Magnesium sulphate

B. Potassium nitrate

C. Sodium stearate

D. Calcium sulphate

 

Q. 73 The cleaning action of soap and detergent in water is due to the formation of

A. Micelle

B. salt

C. Base

D. Acid

 

Q. 74 The chemical used as a fixer/developer in photography is

A. Sodium sulphate

B. Sodium sulphide

C. Sodium thiosulphate

D. Sodium sulphite

 

Q. 75 Rainshadow effect is associated with

A. Cyclonic rainfall

B. Orographic rainfall

C. Convectional rainfall

D. Frontal rainfall

 

Q. 76 Match List I with List II and select the correct answer using the code given below the Lists:

List I List II

(Place) (Industry)

A. Jabalpur 1. Petro-chemical industry

B. Bengaluru 2. IT Industry

C. Mathura 3. Paper Industry

D. Ballarpur 4. Automobile Industry

Code:

A. A(4), B(1), C(2), D(3)

B. A(3), B(2), C(1), D(4)

C. A(4), B(2), C(1), D(3)

D. A(3), B(1), C(2), D(4)

 

Q. 77 Which one of the following irrigation canals is the most important in terms of area coverage in Haryana?

A. Bhakra canal

B. The Western Yamuna canal

C. Jawaharlal Nehru canal

D. Gurgaon canal

 

Q. 78 Which one of the following is the smallest unit showing the properties of life such as the capacity for metabolism, response to the environment, growth, and reproduction?

A. Gene

B. Chromosome

C. Nucleus

D. Cell

 

Q. 79 In plants, which one of the following gases is released during Photosynthesis?

A. Carbon dioxide

B. Oxygen

C. Hydrogen

D. Methane

 

Q. 80 Match List I with List II and select the correct answer using the code given below the Lists: 

List I List II

(Physical quantity) (Unit)

A. Distance 1. Mole

B. Amount of material 2. Coulomb

C. Amount of electrical charge 3. Lightyear

D. Energy 4. Watt-hour

Code:

A. A(3), B(1), C(2), D(4)

B. A(3), B(2), C(1), D(4)

C. A(4), B(2), C(1), D(3)

D. A(4), B(1), C(2), D(3)

 

Q. 81 A ray of light when refracted suffers a change in velocity. In this context, which one among the following statements is correct?

A. Velocity increases as the ray passes from a rarer to a denser medium

B. Velocity decreases as the ray passes from a denser to a rarer medium

C. Velocity decreases as the ray passes from a rarer to a denser medium

D. Change of velocity does not depend on the nature of medium

 

Q. 82 An object is placed 10 cm in front of a convex lens of focal length 15 cm. The image produced will be

A. Real and magnified

B. Virtual and magnified

C. Virtual and reduced in size

D. Real and reduced in size

 

Q. 83 Why is Graphite used in electrolytic cells?

A. Graphite is soft and can be easily moulded into electrodes

B. Graphite is made of layers of carbon atoms which can slide

C. Graphite is inert to most of the chemicals and remains intact in electrolytic cells

D. Graphite is a good conductor of electricity

 

Q. 84 Washing Soda is the common name for

A. Calcium Carbonate

B. Magnesium Carbonate

C. Sodium Carbonate

D. Potassium Carbonate

 

Q. 85 Which one of the following Indian states has the highest proportion of area under forest cover?

A. Madhya Pradesh

B. Sikkim

C. Meghalaya

D. Mizoram

 

Q. 86 Match List I with List II and select the correct answer using the code given below the Lists:

List I List II

(National Park/ (State)

Wildlife Sanctuary)

A. Chandra Prabha 1. Uttarakhand

B. Silent Valley 2. Chhattisgarh

C. Valley of flowers 3. Uttar Pradesh

D. Indravati 4. Kerala

Code:

A. A(2), B(1), C(4), D(3)

B. A(3), B(4), C(1), D(2)

C. A(2), B(4), C(1), D(3)

D. A(3), B(1), C(4), D(2)

 

Q. 87 To a perpendicular to the plane of the ecliptic, Earth’s axis of rotation makes an angle of 23½ degrees. Had this angle been zero degrees, which one among the following would result?

A. There would have been no season

B. The length of day and night would have been the same throughout the year

C. The length of the day and night would have been the same all over the earth

D. All of the above

 

Q. 88 Gametophytes of sexually reproducing flowering plants are

A. Haploid

B. Diploid

C. Tetraploid

D. Polyploid

 

Q. 89 The seeds of flowering plants are made up of

A. ovary and ovary wall

B. embryo, food reserves and coat

C. cotyledons

D. zygotes

 

Q. 90 A person stands on his two feet over a surface and experiences a pressure P. Now the person stands on only one foot. He would experience a pressure of magnitude

A. 4P

B. P

C. ½P

D. 2P

 

Q. 91 A solid is melted and allowed to cool and solidify again. The temperature is measured at equal intervals of time. The graph in the figure shows the change of temperature with time. 

The part of the curve that is practically horizontal is due to

A. latent heat given away by liquid

B. specific heat given away by liquid

C. thermal capacity increases with time keeping temperature constant

D. change in density during transformation

 

Q. 92 A deep sea driver may hurt his eardrum during diving because of

A. lack of oxygen

B. high atmospheric pressure

C. high water pressure

D. all of the above

 

Q. 93 When you walk on a woolen carpet and bring your finger near the metallic handle of a door, an electric shock is produced. 

This is because

A. charge is transferred from your body to the handle

B. a chemical reaction occurs when you touch the handle

C. the temperature of the human body is higher than that of the handle

D. the human body and the handle arrive at thermal equilibrium by the process

 

Q. 94 Which among the following does not wet the walls of the glass vessel in which it is kept? 

A. water

B. alcohol

C. mercury

D. phenol

 

Q. 95 Permanent hardness of water is due to the presence of

A. sulphates of sodium and potassium

B. sulphates of magnesium and calcium

C. carbonates of sodium and magnesium

D. bicarbonates of magnesium and calcium

 

Q. 96 In the reaction ZnO + C→Zn + CO, ‘C’ acts as

A. an acid

B. a base

C. an oxidizing agent

D. a reducing agent

 

Q. 97 Which of the following are the characteristics of organic farming?

1. Use of chemical fertilizers to improve soil fertility.

2. Frequent decomposing and fallowing.

3. Use of herbs to control pests.

4. Higher productivity per hectare.

Select the correct answer using the code given below:

A. 1 and 4 only

B. 1, 3 and 4

C. 2 and 3 only

D. 2, 3 and 4

 

Q. 98 ‘Yakuts’ are the nomadic herders of

A. Gobi

B. Sahara

C. Tundra

D. Kalahari

 

Q. 99 A farmer in a semi-arid area claims that his farming practice is very environment-friendly. Which of the following practices on his farm can justify his claim?

1. Planting a tree belt.

2. Practising crop rotation.

3. Carrying out a large scale irrigation system.

4. Using organic fertilizers.

Select the correct answer using the code given below:

A. 3 and 4 only

B. 1, 2 and 4

C. 1, 3 and 4

D. 1 and 2 only

 

Q. 100 The luxuriant growth of natural vegetation in tropical rainforest is due to

1. fertile soil

2. hot and wet climate throughout the year

3. intense sunlight for photosynthesis

4. seasonal change to facilitate nutrient absorption

Select the correct answer using the code given below:

A. 1 and 4 only

B. 2 and 3 only

C. 1, 2 and 3 only

D. 1, 2, 3 and 4

 

Q. 101 Which endocrine gland requires iodine to synthesize a particular hormone whose deficiency may cause goitre disease?

A. Hypothalamus

B. Pancreas

C. Thymus

D. Thyroid gland

 

Q. 102 Which one of the following is not a part of nerves?

A. Axons

B. Connective tissues

C. Schwann cells

D. Smooth muscles

 

Q. 103 The product of conductivity and resistivity of a conductor

A. depends on pressure applied

B. depends on current flowing through conductor

C. is the same for all conductors

D. varies from conductor to conductor

 

Q. 104 We use CFL to save electrical energy and to provide sufficient light. The full form of CFL is

A. Condensed filament light

B. Compact filament lamp

C. Condensed fluorescent lamp

D. Compact fluorescent lamp

 

Q. 105 When the sun is 30° above the horizon, the shadow of one tree is 17.3m long. What is the height of this tree?

A. 20m

B. 17.30m

C. 10m

D. 1.73m

 

Q. 106 When heat rays are reflected from Earth, gases like Carbon dioxide, Nitrous oxide do not allow them to escape back to space causing our planet to heat up. These gases are known as

A. noble gas

B. green-house gas

C. hot gas

D. blue gas

 

Q. 107 A spring can be used to determine the mass m of an object in two ways: (i) by measuring the extension in the spring due to the object; and (ii) by measuring the oscillation period for the given mass. Which of these methods can be used in a space-station orbiting Earth?

A. Both

B. Only the extension method

C. Only the oscillation method

D. Neither

 

Q. 108 Match List I with List II and select the correct answer using the code given below the Lists: 

List I List II

(Region) (Vegetation)

A. Selvas 1. Conifers

B. Savannas 2. Mosses and Lichens

C. Taiga 3. Epiphytes

D. Tundra 4. Grasses and trees

Code:

A. A(4), B(1), C(2), D(3)

B. A(3), B(2), C(1), D(4)

C. A(3), B(4), C(1), D(2)

D. A(4), B(2), C(1), D(3)

 

Q. 109 Which of the following statements with regard to the western coastal plain of India are correct?

1. It is a narrow belt

2. It is an example of submerged coastal plain

3. It provides natural conditions for development of ports

4. It has well-developed deltas

Select the correct answer using the code given below:

A. 1, 2 and 3 only

B. 1 and 2 only

C. 1, 2, 3 and 4

D. 3 and 4 only

 

Q. 110 Which one of the following weather conditions indicates a sudden fall in barometer reading?

A. stormy weather

B. calm weather

C. cold and dry weather

D. hot and sunny weather

 

Q. 111 Match List I with List II and select the correct answer using the code given below the Lists: 

List I List II

(Island) (Location)

A. Continental island 1. Mauritius

B. Coral island 2. Madagascar

C. Volcanic island 3. Andaman & Nicobar Islands

D. Mountain island 4. Maldives

Code:

A. A(2), B(4), C(1), D(3)

B. A(2), B(1), C(4), D(3)

C. A(3), B(1), C(4), D(2)

D. A(3), B(4), C(1), D(2)

 

Q. 112 Consider the following diagram

In which one among the following lettered areas of diagram would erosion most likely change the shape of riverbed ?

A. A

B. B

C. C

D. D

 

Q. 113 Match List I with List II and select the correct answer using the code given below the Lists:

List I List II

(Cloud) (Characteristic)

A. Cirrus 1. Rain giving

B. Stratus 2. Feathery appearance

C. Nimbus 3. Vertically growing

D. Cumulus 4. Horizontally spreading

Code:

A. Match List I with List II and select the correct answer using the code given below the Lists: List I List II (Island) (Location) A. Continental island 1. Mauritius B. Coral island 2. Madagascar C. Volcanic island 3. Andaman & Nicobar Islands D. Mountain island 4. Maldives A(3), B(1), C(4), D(2)

B. Match List I with List II and select the correct answer using the code given below the Lists: List I List II (Island) (Location) A. Continental island 1. Mauritius B. Coral island 2. Madagascar C. Volcanic island 3. Andaman & Nicobar Islands D. Mountain island 4. Maldives A(3), B(4), C(1), D(2)

C. Match List I with List II and select the correct answer using the code given below the Lists: List I List II (Island) (Location) A. Continental island 1. Mauritius B. Coral island 2. Madagascar C. Volcanic island 3. Andaman & Nicobar Islands D. Mountain island 4. Maldives A(2), B(4), C(1), D(3)

D. Match List I with List II and select the correct answer using the code given below the Lists: List I List II (Island) (Location) A. Continental island 1. Mauritius B. Coral island 2. Madagascar C. Volcanic island 3. Andaman & Nicobar Islands D. Mountain island 4. Maldives A(2), B(1), C(4), D(3)

 

Q. 114 The concept of demographic transition provides a model for

A. analyzing government responses to changing pattern of population growth

B. explaining major patterns of global population movement throughout the history

C. analyzing spatial variations in the distribution, growth and movement of population

over time

D. examining the relationship between economic development and natural population

change. 

 

Q. 115 The precursor of which one of the following vitamins comes from β-carotene?

A. Vitamin A

B. Vitamin C

C. Vitamin D

D. Vitamin K

 

Q. 116 ‘Lub-dup’ sound is produced due to action of

A. large intestine

B. lungs

C. heart

D. oesophagus

 

Q. 117 The Sun is observed to be reddish when it is near the horizon, i.e., in the morning and the evening. This is because

A. red light is least scattered by atmosphere

B. red light is most scattered by atmosphere

C. it is the color of the Sun in the morning and evening

D. Earth’s atmosphere emits red light

 

Q. 118 Thermal conductivity of aluminum, copper, and stainless steel increases in the order 

A. Copper<Aluminium<Stainless steel

B. Stainless steel<aluminium<copper

C. Aluminium<Copper<Stainless steel

D. Copper<Stainless steel<Aluminium

 

Q. 119 Perspiration cools the body because

A. presence of water on the skin is cooling

B. evaporation requires latent heat

C. water has a high specific heat

D. water is a poor conductor of heat

 

Q. 120 The radius of the Moon is about one-fourth that of the Earth and acceleration due to gravity on the Moon is about one-sixth that on the Earth. From this, we can conclude that the ratio of the mass of Earth to the mass of the Moon is about

A. 10

B. 100

C. 1,000

D. 10,000

 

Q. 121 Which of the following country/countries successfully inserted a spacecraft into Mars’ orbit by maiden attempt?

A. USA

B. USA and Russia

C. India

D. China

 

Q. 122 The European Space Agency (ESA) successfully landed a spacecraft on a speeding comet that lies 310 million miles away from the Earth. As a result, the scientists may find out 

A. the age of the Sun

B. the age of the Universe

C. new fundamental atomic particles

D. the role of the comets in bringing organic matter and water to Earth

 

Q. 123 Who among the following Nobel laureates has recently announced to put his Nobel Medal under auction?

A. Kailash Satyarthi

B. J D Watson

C. Mikhail Gorbachev

D. Jody Williams

 

Q. 124 Which one among the following statements with regard to a climate deal adopted between USA and China in November 2014 is not correct?

A. China committed to cap its output of carbon pollution by the year 2030 or earlier

B. China committed to increase its use of zero emission energy to 20% by the year 2030

C. USA agreed to reduce its emissions by 26%-28% below its year 2005 levels in the year 2025

D. Both the countries agreed to completely phase out coal technologies by the year 2020

 

Q. 125 Which one among the following books is centered around ‘environment’?

A. The Late, Great Planet Earth

B. Silent Spring

C. Here I Stand

D. And Then One Day

 

Q. 126 Who among the following cricket players has not died while playing a match?

A. Wasim Raja

B. Phillip Hughes

C. Raman Lamba

D. Vijay Hazare

 

Q. 127 Which one among the following films was conferred the ‘Golden Peacock’ award in the 45th International Film Festival of India (2014)?

A. Ek Hazarachi Note

B. A Short Story

C. Leviathan

D. Ajeyo

 

Q. 128 Which one among the following films was awarded the best motion picture (Drama) at the 72nd Golden Globe Awards?

A. The Theory of Everything

B. Boyhood

C. Still Alice

D. Birdman

 

Q. 129 East Zone won the prestigious Deodhar Trophy cricket tournament 2014-15 by defeating 

A. South Zone

B. Central Zone

C. West Zone

D. North Zone

 

Q. 130 Which one among the following books won the Man Booker Prize 2014?

A. History of the Rain

B. The Lives of Others

C. The Narrow Road to the Deep North

D. How to be Both

 

Q. 131 The Second Five Year Plan that called for the establishment of Socialist pattern of society was commonly referred to as the

A. Harrod-Domar Plan

B. Mahalanobis Plan

C. Nehru Plan

D. Peoples Plan

 

Q. 132 Harappan crafts display an amazing degree of standardization. According to Kenoyer, what was the possible reason for such an achievement?

A. availability of raw materials at local level

B. centralized markets for crafts

C. specialized training centers for craftsmen

D. state control

 

Q. 133 Consider the following statements about Ashokan rock edicts:

1. Major Rock Edict XIII records Ashoka’s remorse at the sufferings caused by his Kalinga campaign.

2. Major Rock Edict X records Ashoka’s visit to Lumbini.

3. Major Rock Edict XII refers to Dhamma Mahamattas as a new category of officers

instituted by Ashoka.

4. Major Rock Edict XII speaks about showing tolerance towards all sects.

Which of the statements given above are correct?

A. 1 and 4 only

B. 2 and 3

C. 3 and 4 only

D. 1, 3 and 4

 

Q. 134 Which one of the following is the common element among Rajagriha, Vaishali, and Pataliputra?

A. Pali canon of the Sthaviravadins was compiled there

B. Ashokan Major Rock Edicts were found there

C. Places where Buddhist Councils were held

D. Places associated with the compilation of Buddhist canons of the Mahasanghikas

 

Q. 135 Which one among the following sects was associated with Gosala Maskariputra? 

A. Vajrayana

B. Ajivikas

C. Sthaviravadins

D. Mahasanghikas

 

Q. 136 Consider the following statements about the early modern technology in India:

1. The Portuguese brought European movable metal types to Goa in 1550.

2. The first Indian script of which types were prepared was Tamil.

3. The English Company’s first experiment with printing press was at Calcutta.

4. The English Company imported printing press to India in 1674-75 at the request of Bhimji Parak.

Which of the statements given above are correct?

A. 1 and 2 only

B. 2 and 3

C. 3 and 4

D. 1, 2 and 4

 

Q. 137 Which of the following statement(s) is/are true for Olympe de Gouges?

1. She was one of the most important politically active women in revolutionary France.

2. She was one of the members of the Committee that drafted the Declaration of Rights of Man and Citizen.

3. She wrote the Declaration of the Rights of Woman and Citizen.

Select the correct answer using the code given below:

A. 1 only

B. 2 only

C. 1 and 2

D. 1 and 3

 

Q. 138 Arrange the following inventions in the field of cotton industry in chronological order (starting with the earliest):

1. James Hargreave’s Spinning Jenny

2. John Kay’s Lying Shuttle

3. Samuel Crompton’s Mule

4. Richard Arkwright’s Water Frame

Select the correct answer using the code given below:

A. 1, 3, 4, 2

B. 2, 1, 4, 3

C. 4, 1, 3, 2

D. 2, 4, 1, 3

 

Q. 139 While opposing the Public Safety Bill 1928 who among the following said that it was ‘a direct attack on Indian Nationalism, on the Indian National Congress’ and as ‘the Slavery of India, Bill No. 1’?

A. Motilal Nehru

B. Lala Lajpat Rai

C. T Prakasam

D. Diwan Chaman Lal

 

Q. 140 Soon after the formation of the Indian National Congress, the British became suspicious of nationalists. Who among the following called Congress representing only the elite-‘a microscopic minority’?

A. Lord Napier

B. Lord Dufferin

C. Lord Ripon

D. Lord Lytton

 

Q. 141 What is the common element among Ram Prasad Bismil, Roshan Singh, and Rajendra Lahiri?

A. They threw a bomb in the Central Legislative Assembly on 8 April 1929

B. They were the founder members of Swaraj Party

C. They were the founders of Hindustan Republican Association

D. They were associated with Kakori Conspiracy case

 

Q. 142 Which among the following is/are not fundamental right(s) under the Constitution of India? 

1. right to education

2. right to work

3. right to form associations

4. rights to practice any profession

Select the correct answer using the code given below:

A. 1 and 2

B. 2 and 4

C. 2 only

D. 1 and 3

 

Q. 143 Mahatma Gandhi’s Hind Swaraj is essentially

A. a critique o Western modernity

B. an outline of his philosophy of Satyagraha

C. an innovation to Indians to free themselves from the British

D. a blueprint of Gram Swaraj

 

Q. 144 The Seventeenth Schedule of the Constitution of India contains

A. provisions regarding the administration of tribal areas

B. the Union list, the State list, and the Concurrent list

C. a list of recognized languages

D. provisions about the disqualification of Members of Legislatures on grounds of

defection

 

Q. 145 Pochampally in Nalgonda district of Telangana became famous in April 1951 because 

A. the Bhoodan movement was launched there by Vinoba Bhave

B. the landless peasants rose up in arms against the landlords

C. it witnessed violent anti-Hindi agitation

D. Silk weavers’ cooperative was formed for the first time in India

 

Q. 146 Who among the following was not associated with the Sarvodaya movement?

A. Jaya Prakash Narayan

B. Acharya Vinoba Bhave

C. Dhirendra Mazumdar

D. GV Apparao

 

Q. 147 Article 368 of the Constitution of India deals with

A. the powers of the Parliament of India to amend the Constitution

B. financial emergency

C. reservation of seats for Scheduled Castes and Scheduled Tribes in the Lok Sabha

D. Official language of the Union of India

 

Q. 148 Which among the following is not a basic feature of the Constitution of India?

A. fundamental rights

B. independence of judiciary

C. federalism

D. the unquestioned right of the parliament to amend any part of the constitution

 

Q. 149 Which among the following is not a fundamental duty?

A. to abide by the Constitution of India and respect the national flag and national

anthem

B. to safeguard public property

C. to protect the Sovereignty, Unity, and Integrity of India

D. to render compulsory military service

 

Q. 150 Which of the following are the basic features of the Constitution (73rd Amendment) Act?

1. Provides for a three-tier structure of panchayats in the village, intermediary, and district levels.

2. Reservation of seats for Scheduled Castes and Scheduled Tribes and women in all the tiers of panchayats.

3. Election to panchayats under the supervision of the State Election Commission.

4. Introduction of the 11th Schedule to the Constitution.

Select the correct answer using the code given below:

A. 1, 2 and 3 only

B. 3 and 4 only

C. 1, 2, 3 and 4

D. 2 and 4 only

 

Answer Sheet 
Question 1 2 3 4 5 6 7 8 9 10
Answer A A D C B B B B B C
Question 11 12 13 14 15 16 17 18 19 20
Answer C A C C A B C B A B
Question 21 22 23 24 25 26 27 28 29 30
Answer C A D C B B D C A B
Question 31 32 33 34 35 36 37 38 39 40
Answer D A B B C C B A C B
Question 41 42 43 44 45 46 47 48 49 50
Answer B A A C C C A C B C
Question 51 52 53 54 55 56 57 58 59 60
Answer A A A C C A A C A B
Question 61 62 63 64 65 66 67 68 69 70
Answer C D B C B A A D C D
Question 71 72 73 74 75 76 77 78 79 80
Answer B B A C B C B D B A
Question 81 82 83 84 85 86 87 88 89 90
Answer C B D C D B A A B D
Question 91 92 93 94 95 96 97 98 99 100
Answer A C A C B D C C B B
Question  101 102 103 104 105 106 107 108 109 110
Answer D D C D C B C C A A
Question  111 112 113 114 115 116 117 118 119 120
Answer A B C D A C A B B B
Question  111 112 113 114 115 116 117 118 119 120
Answer A B C D A C A B B B
Question 121 122 123 124 125 126 127 128 129 130
Answer C D B D B D C B C C
Question 131 132 133 134 135 136 137 138 139 140
Answer B D D C B D D B A B
Question 141 142 143 144 145 146 147 148 149 150
Answer D C A B A D A D D C

NDA/NA(II) Exam 2014 General Ability Test Previous Year Paper

NDA/NA(II) Exam 2014 General Ability Test

Q. 1 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

It was nearly thirty years ago, since this magazine was first published.

A. It was nearly thirty years ago,

B. since this magazine

C. was first published.

D. No error

 

Q. 2 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

Ten years ago he was having an income of over ten thousand rupees a month; he must

indeed be a wealthy man by now.

A. Ten years ago he was having an income

B. of over ten thousand rupees a month;

C. he must indeed be a wealthy man by now.

D. No error

 

Q. 3 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

In spite of the fact that the meeting was about to end, he insisted to ask several questions.

A. In spite of the fact

B. that the meeting was about to end,

C. he insisted to ask several questions.

D. No error

 

Q. 4 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

Hardly had he entered into the room and taken his seat, when the girls began to giggle.

A. Hardly had he entered into the room

B. and taken his seat,

C. when the girls began to giggle.

D. No error

 

Q. 5 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

I was disappointed when I came for seeing you last evening but could not find you at home.

A. I was disappointed

B. when I came for seeing you last evening

C. but could not find you at home.

D. No error

 

Q. 6 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

The number of jobs that would be satisfactory in all respects are small.

A. The number of jobs

B. that would be satisfactory in all respects

C. are small.

D. No error

 

Q. 7 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

I have found the man who I know is the thief.

A. I have found the man

B. whom I know

C. is the thief

D. No error

 

Q. 8 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

There is no reason why he should not come since he is in town and is free.

A. There is no reason

B. why he should not come

C. since he is in town and is free.

D. No error

 

Q. 9 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

It is high time we cried a half to the existing corrupt practices followed in the educational sphere.

A. It is high time

B. we cried a halt to the existing corrupt practices

C. followed in the educational sphere.

D. No error

 

Q. 10 The sentence given below has three parts labeled (a), (b) and (c). Read it to find out whether there is an error in any of the labeled parts and indicate your response in the Answer Sheet against the corresponding letter, i.e., (a) or (b) or (c). If you find ‘No error’, your response should be indicated as (d).

The situation is perilous but if we are prepared promptly to act, there is still one chance of escape.

A. The situation is perilous

B. but if we are prepared promptly to act,

C. there is still one chance of escape.

D. No error

 

Q. 11 Given below is a sentence comprising of a quoted part. For each part, there are four words listed. Choose the nearest in meaning to the quoted part and indicate your response in the Answer Sheet.

We should always try to maintain and promote communal ‘amity’.

A. bondage

B. contention

C. friendship

D. understanding

 

Q. 12 Given below is a sentence comprising of a quoted part. For each part, there are four words listed. Choose the nearest in meaning to the quoted part and indicate your response in the Answer Sheet.

Many species of animals have become ‘extinct’ during the last hundred years.

A. aggressive

B. non-existent

C. scattered

D. feeble

 

Q. 13 Given below is a sentence comprising of a quoted part. For each part, there are four words listed. Choose the nearest in meaning to the quoted part and indicate your response in the Answer Sheet.

True religion does not require one to ‘proselytize’ through guile or force.

A. translate

B. hypnotize

C. attack

D. convert

 

Q. 14 Given below is a sentence comprising of a quoted part. For each part, there are four words listed. Choose the nearest in meaning to the quoted part and indicate your response in the Answer Sheet.

That the plan is both inhuman and ‘preposterous’ needs no further proof.

A. heartless

B. impractical

C. absurd

D. abnormal

 

Q. 15 Given below is a sentence comprising of a quoted part. For each part, there are four words listed. Choose the nearest in meaning to the quoted part and indicate your response in the Answer Sheet.

The attitude of the Western countries towards the third-world countries is rather ‘callous’ to say the least.

A. passive

B. unkind

C. cursed

D. unfeeling

 

Q. 16 Given below is a sentence comprising of a quoted part. For each part, there are four words listed. Choose the nearest in meaning to the quoted part and indicate your response in the Answer Sheet.

Whatever the ‘verdict’ of history may be, Chaplin will occupy a unique place in its pages.

A. judgement

B. voice

C. outcome

D. prediction

 

Q. 17 Given below is a sentence comprising of a quoted part. For each part, there are four words listed. Choose the nearest in meaning to the quoted part and indicate your response in the Answer Sheet.

He ‘corroborated’ the statement of his brother.

A. confirmed

B. disproved

C. condemned

D. seconded

 

Q. 18 Given below is a sentence comprising of a quoted part. For each part, there are four words listed. Choose the nearest in meaning to the quoted part and indicate your response in the Answer Sheet.

Whatever opinion he gives is ‘sane.’

A. rational

B. obscure

C. wild

D. arrogant

 

Q. 19 Given below is a sentence comprising of a quoted part. For each part, there are four words listed. Choose the nearest in meaning to the quoted part and indicate your response in the Answer Sheet.

The story is too fantastic to be ‘credible.’

A. believable

B. false

C. readable

D. praiseworthy

 

Q. 20 Given below is a sentence comprising of a quoted part. For each part, there are four words listed. Choose the nearest in meaning to the quoted part and indicate your response in the Answer Sheet.

Catching snakes can be ‘hazardous’ for people untrained in the art.

A. tricky

B. harmful

C. difficult

D. dangerous

 

Q. 21 Read the given sentence with a quoted word. It is followed by four words, one of which is closest to the opposite in meaning of the quoted word. Choose the word and indicate your response in the Answer Sheet.

His short but pointed speech was ‘applauded’ by all sections of the audience.

A. disapproved

B. misunderstood

C. praised

D. welcomed

 

Q. 22 Read the given sentence with a quoted word. It is followed by four words, one of which is closest to the opposite in meaning of the quoted word. Choose the word and indicate your response in the Answer Sheet.

In ancient India, scholars had no interest in political power or ‘material’ growth.

A. internal

B. spiritual

C. psychic

D. celestial

 

Q. 23 Read the given sentence with a quoted word. It is followed by four words, one of which is closest to the opposite in meaning of the quoted word. Choose the word and indicate your response in the Answer Sheet.

A ‘friendly’ dog met us at the farm gate.

A. helpful

B. understanding

C. quiet

D. hostile

 

Q. 24 Read the given sentence with a quoted word. It is followed by four words, one of which is closest to the opposite in meaning of the quoted word. Choose the word and indicate your response in the Answer Sheet.

He is extremely ‘intelligent’ but proud.

A. dull

B. weak

C. ignorant

D. arrogant

 

Q. 25 Read the given sentence with a quoted word. It is followed by four words, one of which is closest to the opposite in meaning of the quoted word. Choose the word and indicate your response in the Answer Sheet.

The young leader was ‘reluctant’ to shoulder the responsibilities of the ministerial office.

A. wanting

B. willing

C. anxious

D. eager

 

Q. 26 Read the given sentence with a quoted word. It is followed by four words, one of which is closest to the opposite in meaning of the quoted word. Choose the word and indicate your response in the Answer Sheet.

He ‘abandoned’ his family.

A. supported

B. encouraged

C. pleased

D. saved

 

Q. 27 Read the given sentence with a quoted word. It is followed by four words, one of which is closest to the opposite in meaning of the quoted word. Choose the word and indicate your response in the Answer Sheet.

History ‘abounds’ in instances of courage.

A. shines

B. lacks

C. suffices

D. fails

 

Q. 28 Read the given sentence with a quoted word. It is followed by four words, one of which is closest to the opposite in meaning of the quoted word. Choose the word and indicate your response in the Answer Sheet.

‘Adversity’ teaches man to be humble and self-reliant.

A. Sincerity

B. Animosity

C. Curiosity

D. Prosperity

 

Q. 29 Read the given sentence with a quoted word. It is followed by four words, one of which is closest to the opposite in meaning of the quoted word. Choose the word and indicate your response in the Answer Sheet.

Life poverty, ‘affluence’ can sometimes create its own problems.

A. indigence

B. opulence

C. sorrow

D. exuberance

 

Q. 30 Read the given sentence with a quoted word. It is followed by four words, one of which is closest to the opposite in meaning of the quoted word. Choose the word and indicate your response in the Answer Sheet.

The habit of ‘squandering’ money should not be encouraged.

A. discarding

B. hoarding

C. donating

D. stealing

 

Q. 31 The given sentence has a blank space and four words given after it. Select whichever word you consider the most appropriate for the blank space and indicate your response on the Answer Sheet.

You haven’t had your lunch yet, ________ you?

A. are

B. aren’t

C. have

D. haven’t

 

Q. 32 The given sentence has a blank space and four words given after it. Select whichever word you consider the most appropriate for the blank space and indicate your response on the Answer Sheet.

Life is to death as pleasure is to ____________.

A. poverty

B. suffering

C. anguish

D. pain

 

Q. 33 The given sentence has a blank space and four words given after it. Select whichever word you consider the most appropriate for the blank space and indicate your response on the Answer Sheet.

The French _________ reputed to have a very good sense of humour.

A. is

B. was

C. are

D. will be

 

Q. 34 The given sentence has a blank space and four words given after it. Select whichever word you consider the most appropriate for the blank space and indicate your response on the Answer Sheet.

‘Please’ and ‘Thank you’ are the little courtesies by which we keep the ________ of life oiled and running smoothly.

A. path

B. machine

C. garden

D. river

 

Q. 35 The given sentence has a blank space and four words given after it. Select whichever word you consider the most appropriate for the blank space and indicate your response on the Answer Sheet.

Many of the advances of civilization have been conceived by young people just on the

_________ of adulthood.

A. boundary

B. threshold

C. peak

D. horizon

 

Q. 36 The given sentence has a blank space and four words given after it. Select whichever word you consider the most appropriate for the blank space and indicate your response on the Answer Sheet.

The more your action and thought are allied and ________, the happier you grow.

A. divergent

B. unraveled

C. integrated

D. invincible

 

Q. 37 The given sentence has a blank space and four words given after it. Select whichever word you consider the most appropriate for the blank space and indicate your response on the Answer Sheet.

He ________ in wearing the old-fashioned coat in spite of his wife’s disapproval.

A. insists

B. persists

C. desists

D. resists

 

Q. 38 The given sentence has a blank space and four words given after it. Select whichever word you consider the most appropriate for the blank space and indicate your response on the Answer Sheet.

It is not what you say that ________, but what you do.

A. matches

B. implies

C. matters

D. moves

 

Q. 39 The given sentence has a blank space and four words given after it. Select whichever word you consider the most appropriate for the blank space and indicate your response on the Answer Sheet.

Physically we are now all neighbors, but psychologically we are ________ to each other.

A. primitives

B. complementary

C. strangers

D. cowards

 

Q. 40 The given sentence has a blank space and four words given after it. Select whichever word you consider the most appropriate for the blank space and indicate your response on the Answer Sheet.

The old ‘Nature’ versus _______ debate regarding crime continues even today.

A. ‘Man’

B. ‘Universe’

C. ‘Culture’

D. ‘Nurture’

 

Q. 41 The given sentence has a quoted part. Below the sentence are given three possible substitutions for the part. If one of them. i.e., (a), (b) or (c) is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter (a), (b), or (c).

If none of the substitutions improve the sentence, indicate (d) as your response on the

Answer Sheet. Thus, a ‘No improvement’ response will be signified by the letter (d). As the parties failed to reach any agreement, the meeting ‘broke through.’

A. broke out

B. broke away

C. broke up

D. No improvement

 

Q. 42 The given sentence has a quoted part. Below the sentence are given three possible substitutions for the part. If one of them. i.e., (a), (b) or (c) is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter (a), (b), or (c).

If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet. Thus, a ‘No improvement’ response will be signified by the letter (d). If I ‘have reached’ there by this time tomorrow, I will write to you immediately. 

A. reached

B. reach

C. am reaching

D. No improvement

 

Q. 43 The given sentence has a quoted part. Below the sentence are given three possible substitutions for the part. If one of them. i.e., (a), (b) or (c) is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter (a), (b), or (c).

If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet. Thus, a ‘No improvement’ response will be signified by the letter (d). My friend met me, unexpectedly, when I ‘looked’ for a taxi, desperately.

A. had looked

B. was looking

C. had been looking

D. No improvement

 

Q. 44 The given sentence has a quoted part. Below the sentence are given three possible substitutions for the part. If one of them. i.e., (a), (b) or (c) is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter (a), (b), or (c). If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet. Thus, a ‘No improvement’ response will be signified by the letter (d).

Her learning makes up ‘towards’ her want of beauty.

A. for

B. to

C. against

D. No improvement

 

Q. 45 The given sentence has a quoted part. Below the sentence are given three possible substitutions for the part. If one of them. i.e., (a), (b) or (c) is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter (a), (b), or (c). If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet. Thus, a ‘No improvement’ response will be signified by the letter (d). 

If he ‘got’ his enemy in his hand, he would have crushed him to death.

A. has got

B. was getting

C. had got

D. No improvement

 

Q. 46 The given sentence has a quoted part. Below the sentence are given three possible substitutions for the part. If one of them. i.e., (a), (b) or (c) is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter (a), (b), or (c). If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet. Thus, a ‘No improvement’ response will be signified by the letter (d). Please ask your son to turn ‘off’ the radio so that is is not quite so loud.

A. in

B. back

C. down

D. No improvement

 

Q. 47 The given sentence has a quoted part. Below the sentence are given three possible substitutions for the part. If one of them. i.e., (a), (b) or (c) is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter (a), (b), or (c). 

If none of the substitutions improve the sentence, indicate (d) as your response on the

Answer Sheet. Thus, a ‘No improvement’ response will be signified by the letter (d). He said that when I ‘have worked’ for him for six months I would get a pay rise.

A. had worked

B. have had worked

C. did work

D. No improvement

 

Q. 48 The given sentence has a quoted part. Below the sentence are given three possible substitutions for the part. If one of them. i.e., (a), (b) or (c) is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter (a), (b), or (c). If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet. Thus, a ‘No improvement’ response will be signified by the letter (d). 

I am looking forward to ‘joining’ your organization.

A. join

B. join in

C. having joined

D. No improvement

 

Q. 49 The given sentence has a quoted part. Below the sentence are given three possible substitutions for the part. If one of them. i.e., (a), (b) or (c) is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter (a), (b), or (c).

If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet. Thus, a ‘No improvement’ response will be signified by the letter (d). I am not sure why ‘she is wanting’ to see him.

A. she wants

B. is she wanting

C. she want

D. No improvement

 

Q. 50 The given sentence has a quoted part. Below the sentence are given three possible substitutions for the part. If one of them. i.e., (a), (b) or (c) is better than the quoted part, indicate your response on the Answer Sheet against the corresponding letter (a), (b), or (c). 

If none of the substitutions improve the sentence, indicate (d) as your response on the

Answer Sheet. Thus, a ‘No improvement’ response will be signified by the letter (d). Everbody who ‘finished’ writing can go home.

A. had finished

B. have finished

C. has finished

D. No improvement

 

Q. 51 Consider the following two statements & answer below.

Statement I: Grand banks are one of the major fishing grounds of the world due to the

presence of a vast continental shelf.

Statement II: Planktons grow in the shallow waters.

A. Both the statements are individually true and statement II is the correct explanation

of Statement I

B. Both the statements are individually true but Statement II is not the correct

explanation of Statement I

C. Statement I is the true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 52 Consider the following two statements & answer below.

Statement I: Amoeba is a unicellular organism and the single cell performs all functions of a living organism.

Statement II: Cell is the fundamental unit of a living organism.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 53 Consider the following two statements & answer below.

Statement I: The first coins to bear the names and images of rulers were issued by the

Kushanas.

Statement II: The first gold coins were issued by the Kushanas.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct

explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 54 Consider the following two statements & answer below.

Statement I: Jahandar Sah’s reign came to an early end in January 1713

Statement II: He was defeated at Agra by Farrukhsiyar, his nephew.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct

explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 55 Consider the following two statements and answer below.

Statement 1: The defects of the Regulating Act and the exigencies of British politics

necessitated the passing of the Pitt’s India Act.

Statement II: The Pitt’s India Act gave the British Government supreme control over the Company’s affairs and its administration in India.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct

explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 56 Consider the following two statements and answer below.

Statement I: It is not necessary that every bar magnet has one North Pole and one South Pole.

Statement II: Magnetic poles occur in pair.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct

explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 57 Consider the following two statements and answer below.

Statement I: A body moving in a circular path is acted upon by the centripetal force.

Statement II: Centripetal force acting on the body is doing work to keep it rotating in the circular path.

A. Both the statements are individually true and Statement II is the correct explanation of Statement I

B. Both the statements are individually true but Statement II is not the correct

explanation of Statement I

C. Statement I is true but Statement II is false

D. Statement I is false but Statement II is true

 

Q. 58 Which of the following statements is/are correct?

1. The tropical cyclones of China Sea are called typhoons.

2. The tropical cyclones of the West Indies are called tornadoes.

3. The tropical cyclones of Australia are called willy-willies.

4. Formation of an anticyclone results in stormy weather condition.

Select the correct answer using the code given below.

A. 1, 2, 3 and 4

B. 1, 2 and 4 only

C. 1 and 3 only

D. 3 only

 

Q. 59 Which one of the following is not an ASEAN member?

A. Cambodia

B. Laos

C. Myanmar

D. Taiwan

 

Q. 60 Heat given to a body which raises its temperature by 1°C is known as

A. water equivalent

B. thermal capacity

C. specific heat

D. temperature gradient

 

Q. 61 Consider the following reaction :

xAs₂S₃+yO₂→zAs₂O₃+wSO₂

What is y(the coefficient for O₂) when the equation is balanced using whole number

coefficients?

A. 5

B. 7

C. 9

D. 11

 

Q. 62 Growth and repair of damaged tissue involve

A. mitotic cell division only

B. both mitotic and meiotic cell divisions

C. meiotic cell division only

D. amitotic cell division only

 

Q. 63 Rotterdam of Netherlands is largely famous for

A. textiles

B. dairying

C. shipbuilding

D. paper industry

 

Q. 64 If the motion of an object is represented by a straight line parallel to the time axis in a distance-time graph, then the object undergoes

A. an accelerated motion

B. a decelerated motion

C. a uniform non-zero velocity motion

D. a zero velocity motion

 

Q. 65 How many grams of MgCO₃ contain 24.00 g of oxygen? (The molar mass of MgCO₃ is 84.30 g mo⁻¹)

A. 42.15 g

B. 84.30 g

C. 126.00 g

D. 154.00 g

 

Q. 66 Which one of the following is not a function of the liver?

A. Conversion of glucose into glycogen

B. Production of urea

C. Destruction of dead and worn-out red blood cells

D. Absorption of food and excess water from the undigested food

 

Q. 67 Which one of the following is the correct sequence of economic sectors in terms of their contribution to the GDP of India in decreasing order?

A. Service-Industry-Agriculture

B. Agriculture-Industry-Service

C. Industry-Service-Agriculture

D. Agriculture-Service-Industry

 

Q. 68 A force F⃗, acting on an electric charge q, in presence of an electromagnetic field, moves the charge parallel to the magnetic field with velocity v⃗. Then F⃗ is equal to *where E⃗ and B⃗ are electric field and magnetic field respectively)

A. qE⃗

B. q(v⃗xB⃗)

C. q(v⃗xE⃗)

D. qB⃗

 

Q. 69 What is the oxidizing agent in the following equation?

HAsO₂(aq)+Sn²⁺(aq)+H⁺(aq)→As(s)+Sn⁴⁺(aq)+H₂O(l)

A. HAsO₂(aq)

B. Sn²⁺(aq)

C. H¬⁺(aq)

D. Sn⁴⁺(aq)

 

Q. 70 Which one of the following is not a part of the female reproductive system?

A. Fallopian tube

B. Cervix

C. Urethra

D. Vagina

 

Q. 71 If a news is broadcast from London at 1:45 pm on Monday, at what time and on what day will it be heard at Dhaka (90°E)?

A. 7:45 pm on Monday

B. 7:45 am on Monday

C. 7:45 pm on Tuesday

D. 7:45 am on Sunday

 

Q. 72 Which of the following are the correct parameters for the common domestic power supply in India?

A. 220 V, 110 Hz

B. 220 V, 50 Hz

C. 110 V, 220 Hz

D. 110 V, 50 Hz

 

Q. 73 Which one o the following substances is most likely to be used as soap?

A. CH₃(CH₂)₁₂COOCH₃

B. CH₃(CH₂)₅O(CH₂)₅CH₃

C. CH₃(CH₂)₁₂COONa

D. CH₃(CH₂)₁₂CHCl₂

 

Q. 74 Which one of the following animals is cold-blooded?

A. Dolphin

B. Shark

C. Whale

D. Porpoise

 

Q. 75 Match List-I with List-II and select the correct answer using the code given below the Lists:

List-I List-II

(Geographical Feature) (Type of Geographical process)

A. Cirque 1. Erosional feature of wind

B. Yardang 2. Depositional feature of glacier

C. Barkhan 3. Depositional feature of wind

D. Drumlin 4. Erosional feature of glacier

Code:

A. A(4), B(1), C(3), D(2)

B. A(4), B(3), C(1), D(2)

C. A(2), B(3), C(1), D(4)

D. A(2), B(1), C(3), D(4)

 

Q. 76 A ray of light travels from a medium refractive index n₁ to a medium refractive index n₂. If angle of incidence is i and angle of refraction is r, then sin i/sin r is equal to

A. n₁

B. n₂

C. n₂/n₁

D. n₁/n₂

 

Q. 77 A sample of gas is to be identified by means of its behaviour in the presence of a glowing splint. Which of the following gases will neither itself burn not cause the splint to burn?

A. Oxygen

B. Nitrogen

C. Hydrogen

D. Methane

 

Q. 78 Leprosy is caused by

A. virus

B. bacteria

C. protozoa

D. retrovirus

 

Q. 79 A topographical map with scale 1:50000 indicates 1 cm to

A. 50 km

B. 500 m

C. 50 m

D. 5 km

 

Q. 80 Light waves projected on oil surface show even colours due to the phenomenon of

A. polarization

B. refraction

C. reflection

D. interference

 

Q. 81 A monatomic species that has 18 electrons and a net charge of 2⁻ has

A. The same number of electrons as a neutral argon atom

B. More protons than electrons

C. 2 unpaired electrons

D. 20 protons

 

Q. 82 Which among the following is a plant hormone?

A. Insulin

B. Thyroxin

C. Gibberellin

D. Estrogen

 

Q. 83 Quartzite is metamorphosed from

A. limestone

B. plutonic rock

C. sandstone

D. shale

 

Q. 84 Which one of the following processes explains the splitting of a beam of white light into its constituent colours?

A. Dispersion

B. Reflection

C. Diffraction

D. Polarization

 

Q. 85 The very high heat of vaporization of water is mainly a result of

A. van der Waals forces

B. covalent bonds

C. interionic attraction

D. hydrogen bonding

 

Q. 86 Which of the following groups of plants can be used as indicators of SO2 pollution of air? 

A. Ferns

B. Mentha

C. Lichens

D. Hornworts

 

Q. 87 The permanent wind that blows from the horse latitude to the equatorial region is known as

A. westerly

B. trade wind

C. doldrum

D. easterly

 

Q. 88 Two bodies A and B having masses m and 4 m respectively are moving with equal linear momentum. The ratio of kinetic energies between A and B is

A. 1:4

B. 4:1

C. 1:1

D. 1:2

 

Q. 89 Optical glass used in the construction of spectacles is made by

A. flint glass

B. crookes glass

C. quartz glass

D. hard glass

 

Q. 90 Which one of the following cell organelles is absent in animal cell?

A. cell membrane

B. endoplasmic reticulum

C. cell wall

D. mitochondria

 

Q. 91 Which one of the following is a warm ocean current?

A. labrador current

B. kuroshio current

C. peru current

D. benguela current

 

Q. 92 A force applied on a body is represented as –

F⃗ = 6î-8ĵ+10k̂

and accelerates it at 1 m/s². The mass of the body is

A. 10 kg

B. 10√2 kg

C. 2√10 kg

D. 8 kg

 

Q. 93 The burning sensation of a bee sting can be stopped by rubbing the affected area with soap. This is because

A. a bee sting is acidic and soap, an alkali, neutralizes it

B. a bee sting is alkaline and soap, an acid, neutralizes it

C. soap cleans the affected area and removes the sting

D. soap acts as an anesthetic and dulls the sensation

 

Q. 94 Consider the following statements:

1. Carbohydrates are the only source of energy to humans.

2. Fats give maximum energy on oxidation as compared to other foods.

Which of the statements given above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 95 The place located at the confluence of Alaknanda and Bhagirathi rivers is

A. Badrinath

B. Rishikesh

C. Rudraprayag

D. Devprayag

 

Q. 96 Light waves are

A. electro-mechanical waves

B. electro-magnetic waves

C. electro-optical waves

D. magneto-optical waves

 

Q. 97 A sample of carbon dioxide that undergoes a transformation from solid to liquid and then to gas would undergo

A. a change in mass

B. a change in density

C. a change in composition

D. no change in physical properties

 

Q. 98 Which one of the following pairs of power projects is not correctly matched?

A. Papanasam-Hydropower

B. Neyveli-Hydropower

C. Ukai-Thermal power

D. Rana Pratap Sagar-Hydropower

 

Q. 99 A particle is moving in a circular path of radius r at a constant speed v. Which one of the following graphs correctly represents its acceleration a?

A. I

B. II

C. III

D. IV

 

Q. 100 Which of the following element combinations will form ionic compounds?

1. Ca (Z=20) and Ti (Z=22)

2. Si (Z=14) and Br (Z=35)

3. Mg (Z=12) and Cl (Z=17)

Select the correct answer using the code given below.

A. 2 only

B. 3 only

C. 2 and 3 only

D. 1, 2 and 3

 

Q. 101 In the term GIS, ‘G’ stands for

A. Global

B. Geographic

C. Goodness

D. Geological

 

Q. 102 A thermodynamic process where no heat is exchanged with the surroundings is

A. isothermal

B. adiabatic

C. isobaric

D. isotropic

 

Q. 103 A compound of X₂O₃ contains 31.58% oxygen by weight. The atomic mass of X is

A. 34.66 g mol⁻¹

B. 45.01 g mol⁻¹

C. 52.00 g mol⁻¹

D. 104.00 g mol⁻¹

 

Q. 104 Which one of the following is the correct sequence of oil refineries in India in respect of their time of establishment (starting from the earliest)?

A. Barauni-Haldia-Guwahati-Mathura

B. Barauni-Mathura-Guwahati-Haldia

C. Guwahati-Haldia-Mathura-Barauni

D. Guwahati-Barauni-Haldia-Mathura

 

Q. 105 Which one of the following circuit elements is an active component?

A. Resistor

B. Transistor

C. Inductor

D. Capacitor

 

Q. 106 Which one among the following contains the most neutrons?

A. ⁵⁹₂₆Fe

B. ⁶¹₂₉Cu

C. ⁶¹₃₀Zn

D. ⁶⁰₃₀Zn²⁺

 

Q. 107 Movements of tides are mostly determined by

A. albedo effect

B. wind velocity

C. rotation of the Earth

D. revolution of the Earth

 

Q. 108 Fahrenheit and Celsius are the two scales used for measuring temperature. It the numerical value of a temperature recorded in both the scales is found to be same, what is the temperature?

A. -40°

B. +40°

C. +72°

D. -72°

 

Q. 109 Turpentine oil in paints is used as a

A. pigment

B. film-forming material

C. thinner

D. drier

 

Q. 110 Match List-I with List-II and select the correct answer using the code given below the Lists:

List-I List-II

(Textile industry) (Place)

A. Woolen textile 1. Sualkuchi

B. Cotton textile 2. Rishra

C. Silk textile 3. Ludhiana

D. Jute textile 4. Devangere

Code:

A. A(3), B(4), C(1), D(2)

B. A(2), B(1), C(4), D(3)

C. A(2), B(4), C(1), D(3)

D. A(3), B(1), C(4), D(2)

 

Q. 111 Kerosene oil rises in a wick of lantern because of

A. buoyancy of air

B. diffusion of the oil through the wick

C. capillary action in the wick

D. gravitational pull of the wick

 

Q. 112 If the reaction of 1.0 mol NH₃(g) and 1.0 mol O₂(g)

4NH₃(g)+5O₂(g)→4NO(g)+6H₂O(l)

is carried to completion, then

A. all the O₂(g) is consumed

B. 4.0 mol NO(g) is produced

C. 1.5 mol H₂O(l) is produced

D. All the NH₃(g) is consumed

 

Q. 113 Which of the following sequences is correct for rainfall?

A. Slow ascent of air-slow condensation-heavy downpour

B. Rapid ascent of air-large raindrops-heavy downpour

C. Pressure decreased-air compressed-heavy downpour

D. Descent of air-air warmed-heavy downpour

 

Q. 114 The working of a microwave oven involves

A. absorption of microwaves by matter

B. reception of microwaves by optical fibre

C. microwave amplification by stimulated emission of radiation

D. transmission of microwaves through a metal

 

Q. 115 What would be the total population at the end of the year if the population at the beginning of the year is 5000 and population changed during the year is-birth 250, death 60, immigration 30 and emigration 15?

A. 5205

B. 5235

C. 5310

D. 5180

 

Q. 116 Two cars A and B have masses mA and mB respectively, with mA>mB. Both the cars are moving in the same direction with equal kinetic energy. If equal braking force is applied on both, then before coming to rest

A. A will cover a greater distance

B. B will cover a greater distance

C. Both will cover the same distance

D. Distance covered by them will depend on their respective velocities

 

Q. 117 If the length of the Equator is about 40000 km and the velocity of rotation is about 1700 km per hour, what would be the velocity of rotation at the Pole?

A. Zero

B. 850 km/hr

C. 1700 km/hr

D. 3400 km/hr

 

Q. 118 A bullet is fired vertically up from a 400m tall tower with a speed 80m/s. If g is taken as 10m/s², the time taken by the bullet to reach the ground will be

A. 8s

B. 16s

C. 20s

D. 24s

 

Q. 119 A cyclotron accelerates particles of mass m and chage q. The energy of particles emerging is proportional to

A. q²/m

B. q/m²

C. q²/m²

D. q

 

Q. 120 The electric field inside a perfectly conducting hollow object is

A. 4π

B. infinite

C. zero

D. dependent upon the shape of the object

 

Q. 121 The densities of three liquids are D, 2D and 3D. What will be the density of the resulting mixture if equal volumes of the three liquids are mixed?

A. 6D

B. 1.4D

C. 2D

D. 3D

 

Q. 122 A particle is moving with uniform acceleration along a straight line ABC, where AB=BC. The average velocity of the particle from A to B is 10m/s and from B to C is 15m/s. The average velocity for the whole journey from A to C in m/s is

A. 12

B. 12.5

C. 13

D. 13.5

 

Q. 123 The dimension of ‘impulse’ is the same as that of

A. pressure

B. angular momentum

C. work

D. linear momentum

 

Q. 124 Consider the following statements:

1. China won both Thomas Cup and Uber Cup Badminton Tournaments 2014.

2. The Uber Cup is the World Team Championship for women and the Thomas Cup is for men.

Which of the statements given above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 125 Consider the following statements about Drishti system:

1. It is a sophisticated instrument to assess the runway visual range.

2. This system is developed by Airports Authority of India.

Which of the statements given above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 126 Which of the following about Malavath Poorna is correct?

A. First Indian swimmer to cross Suez Canal

B. Youngest woman to scale Everest

C. First Indian to win FIDE World Junior Championship

D. Winner of Young Scientist Award, 2014

 

Q. 127 Which one among the following countries was the top contributor to India’s FDI for the year 2013-14?

A. Mauritius

B. Singapore

C. USA

D. Japan

 

Q. 128 Which of the following statements about SIMBEX 14 is/are correct?

1. It was a bilateral naval exercise between Indian Navy and Sri Lankan Navy.

2. It was the 21st in the series.

3. It was conducted in the Andaman Sea.

Select the correct answer using the code given below.

A. 1, 2 and 3

B. 2 and 3 only

C. 2 only

D. 1 and 3 only

 

Q. 129 Consider the following statements:

1. Mobile Seva, the National Mobile Governance Initiative of Department of Electronics and Information Technology of India, has won the United Nations Public Service Award, 2014.

2. The innovative initiative is aimed at mainstreaming mobile governance in the country.

Which of the statements given above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 130 Consider the following statements about Prithvi-II Missile:

1. It is a nuclear-capable ballistic missile.

2. It has a maximum range of 100km.

3. It is India’s first native made the ballistic missile.

Which of the statements given above is/are correct?

A. 1, 2 and 3

B. 1 only

C. 1 and 3 only

D. 2 and 3 only

 

Q. 131 Consider the following statements about Indian Regional Navigation Satellite System (IRNSS):

1. IRNSS is a constellation of five satellites, which were launched by PSLV.

2. It is an independent regional navigation satellite system designed to provide position information in the Indian region.

Which of the statements given above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 132 The National Defence Academy has foreign cadets from which of the following countries?

1. Bhutan

2. Bangladesh

3. Nepal

4. Afghanistan

Select the correct answer using the code given below.

A. 1, 2, 3 and 4

B. 1, 3 and 4

C. 3 and 4 only

D. 1 and 2 only

 

Q. 133 From which one among the following countries has India recently (May 2014) recalled its troops, who went for a joint combat exercise in the country?

A. Malaysia

B. Thailand

C. Egypt

D. Singapore

 

Q. 134 Who among the following was associated with the formulation of the basic ideas of the Mahayana Buddhism?

A. Nagarjuna

B. Kashyapa Matanga

C. Menander

D. Kanishka

 

Q. 135 Consider the following statements about Harappan Culture:

1. The Harappan Culture matured in Sindh and Punjab.

2. It spread from there to Southwards and Eastwards.

3. The area, where it spread, was bigger than Egypt and Mesopotamia.

Which of the statements given above is/are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 3 only

D. 1, 2 and 3

 

Q. 136 Megasthenes was a

A. Greek ambassador to the court of Chandragupta Maurya

B. Greek trader during Ashoka’s time

C. Greek trader in the Gupta period

D. Chinese pilgrim during Harsha’s time

 

Q. 137 By the late 19th century, India was one of the largest producers and exporters of

A. cotton yard and wheat

B. sugar and rice

C. sugar and alcohol

D. iron and steel

 

Q. 138 Which one of the following is the correct sequence of appearance of the poet-saints of the Bhakti-Sufi tradition?

A. Basavanna-Appar-Mira Bai-Lal Ded

B. Appar-Mira Bai-Lal Ded-Basavanna

C. Appar-Basavanna-Lal Ded-Mira Bai

D. Basavanna-Mira Bai-Lal Ded-Appar

 

Q. 139 Who among the following did not bring trading ships to the port of Surat in pre-British times?

A. Portuguese and English

B. Russian and German

C. English and Arab

D. French and Arab

 

Q. 140 The Factory Act of 1891 in India was enacted to

A. improve the condition of labor in India

B. ensure greater governmental control over industry in India

C. provide a level playing field for English manufacturers

D. enable greater political control over Indian industry

 

Q. 141 Which of the following statements is correct?

A. The Presiding Officer of the Rajya Sabha is elected every year

B. The Presiding Officer of the Rajya Sabha is elected for a term of 5 years

C. The Presiding Officer of the Rajya Sabha is elected for a term of 6 years

D. The Vice President of India is the Ex Officio Presiding Officer of the Rajya Sabha

 

Q. 142 Who among the following was not a member of the Drafting Committee of the Constitution of India?

A. B.R.Ambedkar

B. K.M.Munshi

C. Krishnaswamy Iyer

D. M.K.Gandhi

 

Q. 143 Who among the following was not a member of the ‘Big Four’ in the Congress of Vienna (1815)?

A. Great Britain

B. Russia

C. Austria

D. France

 

Q. 144 The Stamp Act Congress consisting of delegates from nine of the thirteen colonies met in 1765 at

A. Philadelphia

B. New York City

C. Boston

D. Providence

 

Q. 145 Which of the following American colonies did not attend the first Continental Congress held in Philadelphia?

A. Rhode Island

B. Connecticut

C. Georgia

D. Maryland

 

Q. 146 The Bolshevik Revolution started in Russia during the reign of

A. Czar Alexander I

B. Czar Alexander II

C. Czar Alexander III

D. Czar Nicholas II

 

Q. 147 Which of the following is/are not related to fundamental duties?

1. To cherish and follow the noble ideals which inspired our national struggle for freedom.

2. To value and preserve the rich heritage of our composite culture.

3. To promote the educational and economic interests of the weaker sections of the people, especially the Scheduled Castes and Scheduled Tribes

4. To protect all monuments of historic interest and national importance

Select the correct answer using the code given below.

A. 1 and 2

B. 2 and 3

C. 3 and 4

D. 4 only

 

Q. 148 Joint sittings of the two Houses of Indian Parliament are held to

A. elect the President of India

B. elect the Vice President of India

C. adopt a Constitution Amendment Bill

D. consider and pass a Bill on which the two Houses disagree

 

Q. 149 The President of India can issue proclamation of Emergency

A. on the advice of the Prime Minister

B. on the advice of the Council of Ministers

C. in his own discretion

D. when the decision of the Union Cabinet for the issue of such proclamation has been communicated to him in writing

 

Q. 150 Which of the following statements is/are correct about the working of the Permanent Settlement in Bengal?

1. The traditional Zamindars lost their lands.

2. The reason for the Zamindars’ inability to pay up land revenues was that the Ryots

defaulted on payment of revenue.

3. A new group of farmers-the Jotedars-became influential.

4. The Collector replaced the Zamindars as the alternative focus of authority.

Select the correct answer using the code given below.

A. 1 only

B. 1 and 4 only

C. 2 and 3 only

D. 1, 2, 3 and 4

 

Answer Sheet 
Question 1 2 3 4 5 6 7 8 9 10
Answer B A C A B C B D D B
Question 11 12 13 14 15 16 17 18 19 20
Answer C B D C D A A A A D
Question 21 22 23 24 25 26 27 28 29 30
Answer A B D A B A B D A B
Question 31 32 33 34 35 36 37 38 39 40
Answer C D C B B C B C C D
Question 41 42 43 44 45 46 47 48 49 50
Answer C B B A C C A D A C
Question 51 52 53 54 55 56 57 58 59 60
Answer A B D A A D C C D B
Question 61 62 63 64 65 66 67 68 69 70
Answer C A C D A D A A A C
Question 71 72 73 74 75 76 77 78 79 80
Answer A B C B A C B B B D
Question 81 82 83 84 85 86 87 88 89 90
Answer A C C A D C B B A C
Question 91 92 93 94 95 96 97 98 99 100
Answer B B A B D B B B D B
Question  101 102 103 104 105 106 107 108 109 110
Answer B B C D B A C A C A
Question  111 112 113 114 115 116 117 118 119 120
Answer C A B A A C A B A C
Question 121 122 123 124 125 126 127 128 129 130
Answer C A D B A B B B C C
Question 131 132 133 134 135 136 137 138 139 140
Answer B B B A D A A C B C
Question 141 142 143 144 145 146 147 148 149 150
Answer D D D B C D C D D D

NDA/NA(II) Exam 2014 Mathematics Previous Year Paper

NDA/NA(II) Exam 2014 Mathematic

Q. 1 Every quadratic equation ax²+bx+ c=0 where a,b,c ∈ ℝ and a ≠ 0

A. exactly one real root

B. at least one real root

C. at least two real roots

D. at most two real roots

 

Q. 2 the relation S is defined for a set of integers Z as xSy if integer x divides integer y. Then

A. S is an equivalence relation

B. S is only reflexive and symmetric

C. S is only reflexive and transitive

D. S is only symmetric and transitive

 

Q. 3 If a not equal to b not equal to c are all positive, then the value of determinant is

A. non -negative

B. non-positive

C. negative

D. positive

 

Q. 4 let A and B be two matrices such that AB=A and BA=B. Which of the following statements are correct

1) A²=A

2) B²=B

3) (AB)²= AB

Select the answer using the code given below .

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2and 3

 

Q. 5 What is (1001)₂ equal to ?

A. (5)₁₀

B. (9)₁₀

C. (17)₁₀

D. (11)₁₀

 

Q. 6 What is{(√3 + i) / (√3 – i)}⁶ equal to if i= √-1

A. 1

B. 1/6

C. 6

D. 2

 

Q. 7 Let z be a complex number such that ∣z∣ =4 and arg z=5π/6.What is Z equal to ?

A. 2√3+2i

B. 2√3-2i

C. -2√3+2i

D. -√3+i

 

Q. 8 If given value in the figure, where i =√-1 then what is x equal to?

A. 3

B. 2

C. 1

D. 0

 

Q. 9 If α and β are the roots of ax²+bx+c=0 and α+h and β+h are the roots of px²+qx+r=0 , then what is the value of h?

A. (b/a – q/p)/2

B. (-b/a + q/p)/2

C. (b/p + q/a)/2

D. (-b/p + q/a)/2

 

Q. 10 If the matrix A is shown in figure. What is A equal to ?

A. a

B. b

C. c

D. d

 

Q. 11 Consider the following statements

1) The determinant is the square matrix

2) The determinant is the number associated with a square matrix

Which of the above statements is correct

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 12 If A is an invertible matrix .then what is det (A⁻¹) eqaul to ?

A. det A

B. 1/det A

C. 1

D. none of the above

 

Q. 13 From the matrix equation AB=BC, where A,B,C are are the square matrices of same order, we can conclude B=C Provided .

A. A is nonsingular

B. A is singular

C. A is symmetric

D. A is skew symmetric

 

Q. 14 If the given value is symmetric ,then what is X eqaul to ?

A. 2

B. 3

C. -1

D. 5

 

Q. 15 If the given value is , then which one of the following statements is correct ?

A. a/b is one of he cube roots of unity

B. a/b is one of he cube roots of -1

C. a is one of he cube roots of unity

D. b is one of he cube roots of unity

 

Q. 16 If function f:N –> N , N being the set of natural numbers defined by f(x)=2x+3 is :

A. Injective and surjective

B. Injective but not surjective

C. not Injective but surjective

D. neither Injective nor surjective

 

Q. 17 What is the value of the given equation , where n is the natural number and i =√-1 ?

A. 2

B. 2i

C. -2i

D. i

 

Q. 18 What is the number of ways in which one can post 5 letters in 7 letter boxes?

A. 7⁵

B. 3⁵

C. 5⁷

D. 2520

 

Q. 19 What is the number of ways that a cricket team of 11 players can be made out of 15 players?

A. 364

B. 1001

C. 1365

D. 32760

 

Q. 20 A and B are two sets having 3 elements in common. If n(A) = 5, n(B) = 4, then what is n( A x B) equal to ?

A. 0

B. 9

C. 15

D. 20

 

Q. 21 If f(x)=ax+b and g(x)= cx+d such that f(g(x)) and g(f(x)), then which of the following is correct ?

A. f(c)=g(a)

B. f(a)=g(c)

C. f(c)=g(d)

D. f(d)=g(b)

 

Q. 22  If A and B are square matrices of second order such that ∣A∣ = – 1 and ∣B∣ = 3, then what is ∣3AB∣ equal to?

A. 3

B. -9

C. -27

D. none of the above

 

Questions: 23 – 25

Consider the function

Q. 23 What is f(x) + 1/f(x) -1 = x equal to ?

A. 0

B. 1

C. 2x

D. 4x

 

Q. 24 What is f(2x) equal to ?

A. f(x) + 1/f(x) + 3

B. f(x) + 1/3 f(x) + 1

C. 3 f(x) + 1/ f(x) + 3

D. f(x) + 3/3 f(x) +1

 

Q. 25 What is f(f(x)) equal to ?

A. x

B. -x

C. -1/x

D. None of the above

 

Questions: 26 – 30

For the next 5 questions that follow

Consider the expansion (x²+1/x)¹⁵

Q. 26 what is the independent term in the given equation ?

A. 2103

B. 3003

C. 4503

D. none of the above

 

Q. 27 What is the coefficient of x¹⁵ to the term independent of x in the given expansion ?

A. 1

B. 1/2

C. 2/3

D. 3/4

 

Q. 28 Consider the following statements :

1 .There are 15 terms in the given expansion

2. the coefficinet x¹²of is equal to that of x³

Which of the above statements is correct

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 29 Consider the following statements :

1. The term containing x² does not exist in the given expansion

2.The sum of the coefficients of all the given terms in the given expansion 2¹⁵

which of the above sentences is correct ?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 30 What is the sum of coeffcieents of the middle terms in the given expansion ?

A. C ( 15 , 9 )

B. C ( 16 , 9 )

C. C ( 16 , 8 )

D. None of the above

 

Q. 31 What is √1+sin2θ equal to ?

A. Cos θ – Sin θ

B. Cos θ + Sin θ

C. 2 Cos θ + Sin θ

D. Cos θ + 2 Sin θ

 

Q. 32 A lamp post stands on a horizontal plane .From a point situated at a distance 150 m from its foot , the angle of elevation at the top is 30 deg .what is the height of the lamp post ?

A. 50 m

B. 50√3 m

C. 50/√3 m

D. 100 m

 

Q. 33 IF cot A =2 and cot B= 3, then what is the value of A+B?

A. π/6

B. π

C. π/2

D. π/4

 

Q. 34 what is the value of Sin² 133/2° – Sin² 47/2° ?

A. Sin 47°

B. Co[s 47°

C. 2 Sin 47°

D. 2 Cos 47°

 

Q. 35 What is the value of Sin⁻¹ 3/5 + sin⁻¹ 4/5 ?

A. π/2

B. π/3

C. π/4

D. π/6

 

Q. 36 What is the value of (cos 7x – cos3x) / (sin 7x – 2 sin5x + sin 3x)?

A. tan x

B. cot x

C. tan 2x

D. cot 2x

 

Q. 37 In a triangle ABC, c= 2, A = 45° , a = 2√2 , then what is c equal to ?

A. 30°

B. 15°

C. 45°

D. None of the above

 

Q. 38 In a triangle sinA – cos B = cos C then what is B equal to?

A. π

B. π/3

C. π/2

D. π/4

 

Q. 39 what is the value of tanx/tany if given ?

A. b/a

B. a/b

C. ab

D. 1

 

Q. 40 If sin A sin(60 – A) sin (60 + A) = K sin 3A, then what is k equal to ?

A. 1/4

B. 1/2

C. 1

D. 4

 

Q. 41 The line y =√3 meets the graph y =tan x where x ε(0,π/2), in k points , what is k equal to ?

A. 1

B. 2

C. 3

D. infinity

 

Q. 42 Which one of the following is one of the solutions of the equations tan 2θ.tanθ=1?

A. π/12

B. π/6

C. π/4

D. π/3

 

Q. 43 Given that 16sin⁵x = p sin5x+qsin3x+rsinx

What is the value of p?

A. 1

B. 2

C. -1

D. -2

 

Q. 44 Given that 16sin⁵x = p sin5x+qsin3x+rsinx

What is the value of q?

A. 3

B. 5

C. 10

D. -5

 

Q. 45 Given that 16sin⁵x = p sin5x+qsin3x+rsinx

What is the value of r?

A. 5

B. 8

C. 10

D. -10

 

Questions: 46 – 48

Let Sn denote the sum of first n terms of an AP and 3Sn=S₂n

Q. 46 What is S₃n:Sn is equal to ?

A. 4:1

B. 6:1

C. 8:1

D. 10:1

 

Q. 47 What is S₃n:S₂n is equal to ?

A. 2:1

B. 3:1

C. 4:1

D. 5:1

 

Q. 48 What is the length of the lactus rectum of the eclipse 25x²+16y²=400

A. 25/2

B. 25/4

C. 16/5

D. 32/5

 

Questions: 49 – 50

Consider the circlels x²+y²+2ax +c =0 and x²+y²+2by +c=0

Q. 49 What is the differnece between the centre of the 2 circles ?

A. √(a²+b²)

B. a²+b²

C. a+b

D. 2(a+b)

 

Q. 50 Two circles touch each other

A. c= √(a²+b²)

B. 1/c = 1/a² + 1/b²

C. c = 1/a² + 1/b²

D. c = 1/a²+b²

 

Q. 51 A(3,4) and B(5,-2) are 2 points and P is a point such that PA=PB.If the area of triangle PABis 10 square unit.What are the co -ordinates of P?

A. (1,0 )only

B. (7,2 ) only

C. (1,0 ) and (7,2 )

D. neither (1,0) nor (7,2)

 

Q. 52 What is the product of the perpendiculars drawn from the points (±√(a² – b²), 0) upon the line bx cos α + ay sin α = ab?

A. a²

B. b²

C. a² + b²

D. a + b

 

Q. 53 Which of the following sentences is right in respect of the equations (x-1)/2 = (y-2)/3 and 2x+3y=5?

A. They reresent 2 lines which are parallel

B. They reresent 2 lines which are Perpendicular

C. They reresent 2 lines which are neither parallel nor perpendicular

D. The first equation does not represnt line

 

Questions: 54 – 56

For the following next 3 questions Consider a sphere passing through the origin and the points (2,1,-1) (1,5,-4) and (-2,4 ,-6)

Q. 54 What is the radius of the sphere ?

A. √12

B. √14

C. 12

D. 14

 

Q. 55 What is the centre of the sphere ?

A. (-1,2,-3)

B. (1,-2,3)

C. (1,2,-3)

D. (-1,-2,-3)

 

Q. 56 Consider the following statements

1 ) The sphere passes through the point (0,4,0)

2)The point (1,1,1) is at a distance of 1 unit from the centre of the plane .

Which one of the above statements is correct ?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Questions: 57 – 58

The line joining the points (2,1,3) and (4,-2,5) cuts the plane at 2x + y – z = 3

Q. 57 Where does the line cut the plane ?

A. (0,-4,-1)

B. (0,-4,1)

C. (1,4,0)

D. (0,4,1)

 

Q. 58 What is the ratio in which plane divides the line ?

A. 1:1

B. 2:3

C. 3:4

D. none of the above

 

Questions: 59 – 60

Compare the plane passing through the points

A(2,2,1), B(3,4,2) and C(7,0,6)

Q. 59 Which of the following points lies in the plane ?

A. (1,0,0)

B. (1,0,1)

C. (0,0,1)

D. None of the above

 

Q. 60 What are the direction ratios of the normal to the plane?

A. < 1, 0, 1 >

B. < 0, 1, 0 >

C. < 1, 0, -1 >

D. None of the above

 

Questions: 61 – 63

consider the function f(x) = { x²-5, x ≤3 √(x+13), x>3

Q. 61 what is the value of the limit (x-> 3) f(x) ?

A. 2

B. 4

C. 5

D. 13

 

Q. 62 Consider the following statements :

1. The function is continuous for x = 3

2. The function is not differentiable at x=0

Which of the above statements is/are correct ?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 63 What is the differential coefficient of f(x) at x = 12?

A. 5/2

B. 5

C. 1/5

D. 1/10

 

Questions: 64 – 66

For the next three items that follow.

The line 2y = 3x + 12 cuts the parabola by 4y = 3x²

Q. 64 where does the line cut the parabola?

A. At (-2,3) only

B. At (4,12) only

C. At both (-2,3) and (4,12)

D. neither (-2,3) nor (4,12)

 

Q. 65 What is the area enclosed by the parabola and the line?

A. 27 square unit

B. 36 square unit

C. 48 square unit

D. 54 square unit

 

Q. 66 What is the area enclosed by the parabola, the line and the y-axis in the first quardrant ?

A. 7 square unit

B. 14 square unit

C. 20 square unit

D. 21 square unit

 

Q. 67 Consider the function is given in the figure. What is the non-zero value of k for which the function is continuous at x = 0?

A. 1/4

B. 1/2

C. 1

D. 2

 

Q. 68 consider the following statements:

1. The function f(x) = [x], where [.] is the greatest integer function defined as R is continuous at all points except at x =0.

2. The function f(x) = sin IxI is continuous at all x ∈ R

which of the above statements is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Questions: 69 – 70

for the next two items that follow:

consider the curve x = a (cos θ + θ sin θ) and y = a(sin θ – θ cos θ).

Q. 69 what is dy/dx equal to?

A. tan θ

B. cot θ

C. sin 2θ

D. cos 2θ

 

Q. 70 What is d²y/dx² equal to?

A. sec² θ

B. -cosec² θ

C. sec³ θ/aθ

D. none of the above

 

Q. 71 What is the area of the parabola y² = 4bx bounded by its latus rectum?

A. 2b²/3 square unit

B. 4b²/3 square unit

C. b² square unit

D. 8b²/3 square unit

 

Q. 72 If y= n ln n + neⁿ, then what is the value of dy/dn at n = 1?

A. 1+e

B. 1-e

C. 1+2e

D. none of the above

 

Q. 73 What is the value of the limit (x->0) log₅(1+x)/x equal to ?

A. 1

B. logₑ5

C. log₅e

D. 5

 

Q. 74 What is it equal to ?

A. logₑ5

B. log₅e

C. 5

D. 1

 

Q. 75 what is the value of ?

A. 5

B. 2

C. 1

D. 0

 

Q. 76 Consider K = ⁱ ₀∫ xdx/(1 + sinx)

i = π

What is K equal to ?

A. -π

B. 0

C. π

D. 2π

 

Q. 77 Consider K = ⁱ ₀∫ xdx/(1 + sinx)

i = π

The value of the ⁱ ₀∫ (π-x)dx/(1 + sinx) is?

A. π

B. π/2

C. 0

D. 2π

 

Q. 78 Consider K = ⁱ ₀∫ xdx/(1 + sinx)

i = π

what is the value of the ⁱ ₀∫ dx/(1 + sinx)?

A. 1

B. 2

C. 4

D. -2

 

Questions: 79 – 80

If ∫x tan⁻¹ x dx = A(x²+1)tan⁻¹ x+Bx+C, where C is the constant of integration.

Q. 79 What is the value of A?

A. 1

B. 1/2

C. -1/2

D. 1/4

 

Q. 80 what is the value of B?

A. 1

B. 1/2

C. -1/2

D. 1/4

 

Q. 81 Consider the integral K = ₀²ⁱ ∫ ln(sinx) dx

i = π

what is the value of the integral ₀ⁱ∫ ln(sinx) dx ?

A. 4K

B. 2K

C. K

D. K/2

 

Q. 82 Consider the integral K = ₀²ⁱ ∫ ln(sinx) dx

i = π

what is the value of integral ₀ⁱ∫ ln(Cos x) dx?

A. K/2

B. K

C. 2K

D. 4K

 

Questions: 83 – 84

A rectangular box is to be made from a sheet of 24-inch length and 9-inch width cutting out identical squares of side length x from the four corners and turning up the sides.

Q. 83 what is the value of x for which the volume id maximum?

A. 1 inch

B. 1.5 inch

C. 2 inch

D. 2.5 inch

 

Q. 84 what is the maximum volume of the box?

A. 200 cubic inch

B. 400 cubic inch

C. 100 cubic inch

D. none of the above

 

Q. 85 What is the degree of the differential equation (d³y/dx³)^(3/2) = (d²y/dx²)² ?

A. 1

B. 2

C. 3

D. 4

 

Q. 86 what is the solution of the equation ln (dy/dn) + n = 0?

A. y + eⁿ = c

B. y – e⁻ⁿ = c

C. y + e⁻ⁿ = c

D. y – eⁿ = c

 

Q. 87 Eliminating the arbitrary constants B and C in the expression y = 2/3C(Cx-1)^3/2 + B , we get

A. x[1+(dy/dx)²] = d²y/dx²

B. 2x(dy/dx)d²y/dx² = 1+ (dy/dx)²

C. (dy/dx)d²y/dx² = 1

D. (dy/dx)² + 1 = d²y/dx²

 

Questions: 88 – 90

Let f(x) = ax²+bx+c such that f(1) = f(-1) and a,b,c are in arithmetic progression?

Q. 88 what is the value of b?

A. -1

B. 0

C. 1

D. cannot be determined due to insufficient data

 

Q. 89 f'(a),f'(b),f'(c) are in

A. A.P

B. G.P

C. H.P

D. arithmetico-geometric progression

 

Q. 90 f”(a),f”(b),f”(c) are

A. in A.P only

B. in G.P only

C. in both A.P and G.P

D. neither in A.P nor in G.P

 

Q. 91 if |a̅| = 2, |b̅| = 5 and |a̅ x b̅| = 8, then what is a̅ . b̅ equal to ?

a̅ = a is vector

b̅ = b is vector

A. 6

B. 7

C. 8

D. 9

 

Q. 92 If | a̅ + b̅ | = | a̅ – b̅ |, then which one of the following is correct ?

a̅ = a is vector

b̅ = b is vector

A. | a̅ | = | b̅ |

B. a̅ is parallel to b̅

C. a̅ is perpendicular to b̅

D. a̅ is a unit vector

 

Q. 93 what is the area of the triangle OAB where O̅A̅ = 3î – ĵ + k̂ and O̅B̅ = 2î + ĵ – 3k̂ ? 

O̅A̅ is a vector

O̅B̅ is a vector

A. 5√6

B. 5√6/2

C. √6

D. √30

 

Q. 94 Which of the following is the unit vector perpendicular to both a̅ = î + ĵ + k̂ and b̅ = î – ĵ + k̂

A. (î + ĵ) / √2

B. k̂

C. (î + ĵ)/ √2

D. (î – ĵ)/ √2

 

Q. 95 what is the interior acute angle of the parallelogram whose sides are represented by the vectors 1/√2 1̂ + 1/√2 ĵ + k̂ ?

A. 60°

B. 45°

C. 30°

D. 15°

 

Q. 96 For what value of λ are the vectors λ î + (1 + λ) ĵ + (1 + 2λ) k̂ and (1 – λ) 1̂ + λ ĵ + 2 k̂ perpendicular ?

A. -1//3

B. 1/3

C. 2/3

D. 1

 

Questions: 97 – 100

a̅ + b̅ + c̅ = 0̅ such that |a̅| = 3, |b̅| = 5 and |c̅| = 7

a̅ is a vector

b̅ is a vector

c̅ is a vector

 

Q. 97 What is the angle between a̅ and b̅ ?

A. π/6

B. π/4

C. π/3

D. π/2

 

Q. 98 what is a̅ . b̅ + b̅ . c̅ + c̅ . a̅ equal to ?

A. -83

B. -83/2

C. 75

D. -75/2

 

Q. 99 What is the cosine of angle between b̅ and c̅ ?

A. 11/12

B. 13/14

C. -11/12

D. -13/14

 

Q. 100 What is | a̅ + b̅ | equal to ?

A. 7

B. 8

C. 10

D. 11

 

Q. 101 what is the value of the integral?

A. 2ab

B. 2πab

C. π/2ab

D. π/ab

 

Q. 102 A cylindrical is inscribed in a sphere of radius r.

what is the height of the cylinder of maximum volume?

A. 2r/√3

B. r/√3

C. 2r

D. √3 r

 

Q. 103 A cylindrical is inscribed in a sphere of radius r.

what is the radius of the cylinder of maximum volume?

A. 2r/√3

B. √2r/√3

C. r

D. √3 r

 

Questions: 104 – 105

for the next two items that follow

consider the function f”(x) = sec⁴ x + 4 with f(0) = 0 and f'(0) = 0

Q. 104 what is f'(x) equal to?

A. tan x-(tan³ x/4)+4x

B. tan x +(tan³ x/4) +4x

C. tan x +(sec³ x/3)+4x

D. -tan x-(tan³ x/3)+4x

 

Q. 105 what is f(x) equal to?

A. (2 ln sec x/3) +(tan² x/6)+2x²

B. (3 ln sec x/2)+(cot² x/6)+2x²

C. (4 ln sec x/3)+(sec² x/6)+2x²

D. ln sec x+(tan⁴ x/12)+2x²

 

Q. 106 suppose A and B are two events. Events B has occurred and it is known that P(B)<1.What is P(A I Bⁱ ) equal to?

i = compliment

A. [P(A)-P(B)]/(1-P(B))

B. [P(A)-P(B)]/(1-P(B))

C. [P(A)+P(B)]/(1-P(Bⁱ ))

D. none of the above

 

Questions: 107 – 110

consider events A,B,C,D,E of the sample space S = {n : n is an integer such that 10≤ n ≤20}given by :

A is the set of all even number.

B is the set of all prime numbers C={15}

D is the set of all integers ≤ 16

E is the set of all double digit numbers expressible as a power of 2.

Q. 107 A,B and D are

A. mutually exclusive events but not exhaustive events.

B. exhaustive events but not mutually exclusive events

C. mutually exclusive and exhaustive events

D. elementary events

 

Q. 108 A,B and C are

A. mutually exclusive events but not exhaustive events

B. exhaustive events but not mutually exclusive events

C. mutually exclusive and exhaustive events

D. elementary events

 

Q. 109 B and C are

A. mutually exclusive events but not exhaustive events

B. compound events

C. mutually exclusive and exhaustive events

D. elementary events

 

Q. 110 C and E are

A. mutually exclusive events but not elementary events

B. exhaustive events but not mutually exclusive events

C. mutually exclusive and exhaustive evnts

D. elementary and mutually exclusive events

 

Q. 111 consider the following statements in respect of histogram:

1. The histogram is a suitable representation of a frequency distribution of a continuous variable.

2. The area included under the whole histogram is the total frequency.

which of the above statements is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 112 The regression lines will be perpendicular to each other if the coefficient of correlation r is equal to

A. 1 only

B. 1 or -1

C. -1 only

D. 0

 

Q. 113 For any two events A and B, which one of the following holds?

A. P(A⋂B) ≤ P(A) ≤ P(A⋃B) ≤ P(A)+P(B)

B. P(A⋃B) ≤ P(A) ≤ P(A⋂B) ≤ P(A)+P(B)

C. P(A⋃B) ≤ P(B) ≤ P(A⋂B) ≤ P(A)+P(B)

D. P(A⋂B) ≤ P(B) ≤ P(A) ≤ P(B) ≤ P(A⋃B)

 

Q. 114 The probability that in a random arrangement of the letters of the word ‘UNIVERSITY’, the two I’s do not come together is

A. 4/5

B. 1/5

C. 1/10

D. 9/10

 

Q. 115 There are 4 white and 3 black balls in a box. In another box, there are three white and four black balls. An unbiased dices is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the second box, otherwise from the first box. If the ball drawn is black, then the probability that the ball was drawn from the first box is

A. 1/2

B. 6/7

C. 4/7

D. 3/7

 

Q. 116 If x̅ and y̅ are the means of two distributions such that x̅ < y̅ and z̅ is the mean of the combines distribution, then which one of the following statements is correct?

A. x̅ < y̅ < z̅

B. x̅ > y̅ > z̅

C. z̅ = (x̅ + y̅)/2

D. x̅ < z̅ < y̅

 

Q. 117 What is the mean deviation about the mean for the data 4,7,8,9,10,12,13,17?

A. 2.5

B. 3

C. 3.5

D. 4

 

Q. 118 The variance of 20 observations is 5. If each observation is multiplied by 2, then what is the new variance of the resulting observations?

A. 5

B. 10

C. 20

D. 40

 

Q. 119 Two students X and Y appeared in an examination. The probability that X will qualify the examination is 0.05 and Y will be qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. What is the probability that only one of them will qualify the examination?

A. 0.15

B. 0.14

C. 0.12

D. 0.11

 

Q. 120  A fair coin is tossed four times. What is the probability that at most three tails occur? 

A. 7/8

B. 15/16

C. 13/16

D. 3/4

Answer Sheet 
Question123456 78910
AnswerBCDDAACCAA
Question11121314151617181920
AnswerCBADBAAACD
Question21222324252627282930
AnswerDCACBABCCC
Question31323334353637383940
AnswerBBDBABACBA
Question41424344454647484950
AnswerABBBCBADAC
Question51525354555657585960
AnswerDABBAADDAB
Question61626364656667686970
AnswerBBDCBBBBAC
Question71727374757677787980
AnswerDCBADCABBC
Question81828384858687888990
AnswerCACACCBBAC
Question919293949596979899100
AnswerACBABACBDB
Question 101102103104105106107108109110
AnswerCACBABCCAD
Question 111112113114115116117118119120
AnswerCBDACDBCDB

NDA/NA(I) Exam 2014 Mathematics Previous Year Paper

NDA/NA(I) Exam 2014 Mathematics

Q. 1 Let x be the set of all citizens of India . Elements x, y in X are said to be related if the difference of their age is 5 years. Which one of the following is correct?

A. The relation is an equivalence relation on x

B. The relation is symmetric but neither reflexive nor transitive

C. The relation is reflexive but neither symmetric nor transitive

D. None of above

 

Q. 2 Consider the following relation from A to B where A = {u, v, w, x, y, z} and B = {p, q, r, s}

1. {(u,p), (v,p) (w,p) (x,q), (y,q), (z,q)}

2. {(u,p), (v,q), (w,r), (z,s)}

3. {(u,s), (v,r), (w,q), (u,p), (v,q), (z,q)}

4. {(u,q), (v,p), (w,s), (x,r), (y,q), (z,s)}

Which of the above relation are not function?

A. 1 and 2

B. 1 and 4

C. 2 and 3

D. 3 and 4

 

Q. 3 If α and β are the roots of the equation ax² + bx + c = 0, where a ≠ 0, then (aα + b)(aβ + b) is equal to :

A. ab

B. bc

C. ca

D. abc

 

Q. 4 Let S denote set of all integers. Define a relation R on S as ‘aRb if ab ≥ where a, b ∈ S’. Then R is:

A. Reflexive but neither symmetric nor transitive relation

B. Reflexive, symmetric but not transitive relation

C. An equivalence relation

D. Symmetric but reflexive nor transitive relation

 

Q. 5 The roots of the equation 2a²x² – 2abx + b² = 0 when a < 0 and b > 0 are:

A. Sometimes complex

B. Always irrational

C. Always complex

D. Always real

 

Q. 6 What is the sum of the two numbers (11110)₂ and (1010)₂?

A. (101000)₂

B. (110000)₂

C. (100100)₂

D. (101100)₂

 

Q. 7 Let N denote the set of all non-negative integers and Z denote the set of all integers. The function f : Z → N given by f(x) = |x| is:

A. One – one but not onto

B. Onto but not one – one

C. Both one – one and onto

D. Neither one – one nor onto

 

Q. 8 If P and Q are two complex numbers, then the modulus of the quotient of P and Q is: 

A. Greater than the quotient of their moduli

B. Less than the quotient of their moduli

C. Less than or equal to the quotient of their moduli

D. Equal to the quotient of their moduli

 

Q. 9 Let z = x + iy where x, y are real variables and i = √- 1. If |2z – 1| = |z – 2|, then the point z describes:

A. A circle

B. An ellipse

C. A hyperbola

D. A parabola

 

Q. 10 The sum of an infinite GP is x and the common ratio r is such that |r| < 1. If the first term of the GP is 2, then which one of the following is correct?

A. -1 < x < 1

B. -∞ < x < 1

C. 1 < x < ∞

D. None of the above

 

Q. 11 A box contains 3 white and 2 black balls. Two balls are drawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black? 

A. 2/5

B. 1/5

C. 1/10

D. None of the above

 

Q. 12 For two variables x and y, the two regression coefficients are bᵧₓ = -3/2 and bₓᵧ = -1/6. The correlation coefficient between x and y is:

A. -1/4

B. 1/4

C. -1/2

D. 1/2

 

Q. 13 The variance of numbers x₁, x₂, x₃……..xᵤ is V. Consider the following statements : 

1. If every x₁ is increased by 2, the variance of the new set of numbers is V.

2. If the number x₁ is squared, the variance of the new set is V².

Which of the following statements is/are correct ?

A. 1 only

B. 2 only

C. both 1 and 2

D. Neither 1 and 2

 

Q. 14 What is the mean of the squares of the first 20 natural numbers?

A. 151.5

B. 143.5

C. 65

D. 72

 

Q. 15 p, q , r, s, t are five numbers such that the average of p, q and r is 5 and that of s and t is 10. What is the average of all five numbers?

A. 7.75

B. 7.5

C. 7

D. 5

 

Q. 16 The cumulative frequency of the largest observed value must always be:

A. Less than the total number of observations

B. Greater than the total number of observation

C. Equal to total number of observations

D. Equal to mid point of the last class interval

 

Q. 17 It has been found that if A and B play a game 12 times, A wins 6 times, B wins 4 times and they draw twice. A and B take part in a series of 3 games. The probability that they win alternatively, is:

A. 5/12

B. 5/36

C. 19/27

D. 5/27

 

Q. 18 Out of the 7 consonants and 4 vowels, words are to be formed by involving 3 consonants and 2 vowels. The number of such words formed is:

A. 25200

B. 22500

C. 10080

D. 5040

 

Q. 19 Let X denote the number of scores which exceed 4 in 18 tosses of a symmetrical die. Consider the following statements:

1. The arithmetic mean of X is 6.

2. The standard deviation of X is 2.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 20 How many different words can be formed by taking four letters out of the letters of the word ‘AGAIN’ if each word has to be start with A?

A. 6

B. 12

C. 24

D. None of the above

 

Q. 21 The sum of the series formed by the sequence 3, √3, ….. upto infinity is:

A. 3√3(√3 + 1)/2

B. 3√3(√3 – 1)/2

C. 3(√3 + 1)/2

D. 3(√3 – 1)/2

 

Q. 22 If |z + z̅| = |z – z̅|, then the locus of z is:

A. A part of straight lines

B. A lines

C. A set of four straight lines

D. A circles

 

Q. 23 The number 251 in decimal system is expressed in binary system by:

A. 11110111

B. 11111011

C. 11111101

D. 11111110

 

Q. 24 What is the argument of the complex number (1 + i)(2 + i)/(3 – i) where i = √-1?

A. 0

B. π/4

C. -π/4

D. π/2

 

Q. 25 Consider the following statements in respect of the matrix A given in figure

1. The matrix A is skew-symmetric.

2. The matrix A is symmetric.

3. The matrix A is invertible.

Which of the above statements is/are correct?

A. 1 only

B. 3 only

C. 1 and 3

D. 2 and 3

 

Q. 26 Consider two matrices A and B given in the figure. Which one of the following is correct?

A. B is the right inverse of A

B. B is the left inverse of A

C. B is the both sided inverse of A

D. None of the above

 

Q. 27 One of the roots of the matrix shown in figure

A. abc

B. a + b + c

C. -(a + b + c)

D. -abc

 

Q. 28 If A is any matrix , then the product AA is defined only when AA is defined only when A is a matrix of order m x n where:

A. m > n

B. m < n

C. m = n

D. m ≤ n

 

Q. 29 The determinant of an odd order skew symmetric matrix is always:

A. Zero

B. One

C. Negative

D. Depends on the matrix.

 

Q. 30 If any two adjacent rows or columns of a determinant are interchanged in position, the value of the determinant:

A. Becomes zero

B. Remains the same

C. Changed its sign

D. Is doubled

 

Questions: 31 – 33

In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.

Q. 31 The number of students who had taken only Physics is:

A. 2

B. 3

C. 5

D. 6

 

Q. 32 The number of students who had taken only two subjects is:

A. 7

B. 8

C. 9

D. 10

 

Q. 33 Consider the following statements:

1. The number of students who had taken only one subject is equal to the number of students who had taken only two subjects.

2. The number of students who had taken at least two subjects is four times the number of students who had taken all the three subjects.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Questions: 34 – 36

In the expansion of (x³ – 1/x²)ⁿ where n is a positive integer, the sum of the coefficients of x⁵ and x¹⁰ is 0.

Q. 34 What is n equal to?

A. 5

B. 10

C. 15

D. None of the above

 

Q. 35 What is the value of the independent term?

A. 5005

B. 7200

C. -5005

D. -7200

 

Q. 36 What is the sum of the coefficients of the two middle terms?

A. 0

B. 1

C. -1

D. None of the above

 

Questions: 37 – 39

Given that C(n, r) : C(n, r + 1) = 1 : 2 and C(n, r + 1) : C(n, r + 2) = 2 : 3. 

Q. 37 What is n equal to?

A. 11

B. 12

C. 13

D. 14

 

Q. 38 What is r equal to?

A. 2

B. 3

C. 4

D. 5

 

Q. 39 What is P(n, r) : C(n, r) equal to?

A. 6

B. 24

C. 120

D. 720

 

Q. 40 The complete solution of 3 tan²x = 1 is given by :

n ⋳ Z

A. x = nπ ± π/3

B. x = nπ ± π/3 only

C. x = nπ ± π/6

D. x = nπ ± π/3 only

 

Q. 41 What is the value of cos 36°?

A. (√5 – 1)/4

B. (√5 + 1)/4

C. √(10 + 2√5)/4

D. √(10 – 2√5)/4

 

Q. 42 Consider the following statements:

1. Value of sin θ oscillates between -1 and 1.

2. Value of cos θ oscillates between 0 and 1.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 43 If x and y are positive and xy > 1, then what is tan⁻¹ x + tan⁻¹ y equal to?

A. tan⁻¹ (x + y)/(1 – xy)

B. π + tan⁻¹ (x + y)/(1 – xy)

C. π – tan⁻¹ (x + y)/(1 – xy)

D. tan⁻¹ (x – y)/(1 + xy)

 

Q. 44 Consider the following statements:

1. n(sin² 67(1/2)° – sin²22(1/2)°) > 1 for all positive integers n ≥2.

2. If x is any positive real number, then nx > 1 for all positive integers n ≥ 2.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 45 Consider the following statements:

1. If 3θ is an acute angle such that sin 3θ = cos 2θ, then the measurement of θ in radian equals to π/10.

2. One radian is the angle subtended at the centre of a circle by an arc of the same circle whose length is equal to the diameter of that circle.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 46 From an aeroplane above a straight road the angles of depression of two positions at a distance 20 m apart on the road are observed to be 30° and 45°. The height of the aeroplane above the ground is:

A. 10√3 m

B. 10(√3 – 1) m

C. 10(√3 + 1) m

D. 20 m

 

Q. 47 Consider the following statements:

1. There exists no triangle ABC for which sin A + sin B = sin C.

2. If the angles of a triangle are in the ratio 1 : 2 : 3, then its sides will be in the ratio 1 : √3 : 2. Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 48 Consider the following statements:

1. sin |x| + cos |x| is always positive.

2. sin(x²) + cos(x²) is always positive.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 49 What is (1 + sin A)/(1 – sin A) – (1 – sin A)/(1 + sin A) equal to?

A. sec A – tan A

B. 2 sec A . tan A

C. 4 sec A . tan A

D. 4 cosec A . cot A

 

Q. 50 What is (cot 224° – cot 134°)/(cot 226° + cot 316°) equal to?

A. -cosec 88°

B. -cosec 2°

C. -cosec 44°

D. -cosec 46°

 

Q. 51 Consider the following statements:

1. tan⁻¹ 1 + tan⁻¹ (0.5) = π/2

2. sin⁻¹ (1/3) + cos⁻¹ (1/3) = π/2

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 52 If A + B + C = π, then what is cos(A + B) + cos C equal to?

A. 0

B. 2 cos C

C. cos C – sin C

D. 2 sin C

 

Q. 53 What is cos 20° + cos 100° + cos 140° equal to?

A. 2

B. 1

C. 1/2

D. 0

 

Q. 54 What is sin⁻¹ sin 3π/5 equal to?

A. 3π/5

B. 2π/5

C. π/5

D. None of the above

 

Q. 55 What is sin²(3π) + cos²(4π) + tan²(5π) equal to?

A. 0

B. 1

C. 2

D. 3

 

Q. 56 Consider the following points:

1. (0, 5)

2. (2, -1)

3. (3, -4)

Which of the above lie on the line 3x + y = 5 and at a distance √10 from (1, 2)?

A. 1 only

B. 2 only

C. 1 and 2 only

D. 1, 2 and 3

 

Q. 57 What is the equation of the line through (1, 2) so that the segment of the line intercepted between the axes is bisected at this point?

A. 2x – y = 4

B. 2x – y + 4 = 0

C. 2x + y = 4

D. 2x + y + 4 = 0

 

Q. 58 What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes?

A. x + y = 7

B. 3x + 4y = 7

C. x – y = 1

D. None of the above

 

Q. 59 What is the equation of the line midway between the lines 3x – 4y + 12 = 0 and 3x – 4y = 6 

A. 3x – 4y – 9 = 0

B. 3x – 4y + 9 = 0

C. 3x – 4y – 3 = 0

D. 3x – 4y + 3 = 0

 

Q. 60 What is the sum of the major and minor axes of the ellipse whose eccentricity is 4/5 and length of latus rectum is 14.4 unit?

A. 32 unit

B. 48 unit

C. 64 unit

D. None of the above

 

Questions: 61 – 63

A straight line passes through (1, -2, 3) and perpendicular to the plane 2x + 3y – z = 7.

Q. 61 What are the direction ratios of normal to plane?

A. ⟨2, 3, -1⟩

B. ⟨2, 3, 1⟩

C. ⟨-1, 2, 3⟩

D. None of the above

 

Q. 62 Where does the line meet the plane?

A. (2, 3, -1)

B. (1, 2, 3)

C. (2, 1, 3)

D. (3, 1, 2)

 

Q. 63 What is the image of the point (1, -2, 3) in the plane?

A. (2, -1, 5)

B. (-1, 2, -3)

C. (5, 4, 1)

D. None of the above

 

Questions: 64 – 65

Consider the spheres x² + y² + z² – 4y + 3 = 0 and x² + y² + z² + 2x + 4z – 4 = 0 

Q. 64 What is the distance between the centres of the two spheres?

A. 5 units

B. 4 units

C. 3 units

D. 2 units

 

Q. 65 Consider the following statements:

1. The two spheres intersect each other.

2. The radius of first sphere is less than that of second sphere.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Questions: 66 – 68

The vertices of a triangle ABC are A(2, 3, 1), B(-2, 2, 0) and C(0, 1, -1)

Q. 66 What is the cosine of angle ABC?

A. 1/√3

B. 1/√2

C. 2/√6

D. None of the above

 

Q. 67 What is the area of the triangle?

A. 6√2 square unit

B. 3√2 square unit

C. 10√3 square unit

D. None of the above

 

Q. 68 What is the magnitude of the line joining mid points of the sides AC and BC?

A. 1/√2 unit

B. 1 unit

C. 3/√2 unit

D. 2 unit

 

Q. 69 Consider the vectors a̅ = î – 2ĵ + k̂ and b̅ = 4î – 4ĵ + 7k̂.

What is the scaler projection of a̅ on b̅?

A. 1

B. 19/9

C. 17/9

D. 23/9

 

Q. 70 Consider the vectors a̅ = î – 2ĵ + k̂ and b̅ = 4î – 4ĵ + 7k̂.

What is the vector perpendicular to both the vectors?

A. -10î – 3ĵ + 4k̂

B. -10î + 3ĵ + 4k̂

C. 10î – 3ĵ + 4k̂

D. None of the above

 

Q. 71 Let a vector r makes angles 60°, 30° with x and y-axes respectively.

What angle does r vector make with z – axis?

A. 30°

B. 60°

C. 90°

D. 120°

 

Q. 72 Let a vector r makes angles 60°, 30° with x and y-axes respectively.

What are the direction cosines of r vector ?

A. ⟨1/2, √3/2, 0⟩

B. ⟨1/2, -√3/2, 0⟩

C. ⟨1/√2, 1/√2, 0⟩

D. ⟨-1/2, √3/2, 0⟩

 

Q. 73 Let |a̅ | = 7, |b̅| = 11, |a̅ + b̅| = 10√3, where ̅ denotes to vector

What is |a̅ – b̅| equal to?

A. 2√2

B. 2√10

C. 5

D. 10

 

Q. 74 Let |a̅ | = 7, |b̅| = 11, |a̅ + b̅| = 10√3, where ̅ denotes to vector

What is the angle between (a̅ + b̅) and (a̅ – b̅) ?

A. π/2

B. π/3

C. π/6

D. None of the above

 

Q. 75 A line passes through the points (6, -7, -1) and (2, -3, 1). What are the direction ratios of the line?

A. ⟨4, -4, 2⟩

B. ⟨4, 4, 2⟩

C. ⟨-4, 4, 2⟩

D. ⟨2, 1, 1⟩

 

Q. 76 What is lim(x → 0) {(1 +x)ⁿ – 1}/x equal to?

A. 0

B. 1

C. n

D. n – 1

 

Q. 77 What is lim(x → 0) x/√(1 – cos x) equal to?

A. √2

B. -√2

C. -1/√2

D. Limit does not exist

 

Q. 78 What is the derivative of √(1 + cos x)/(1 – cos x)?

A. 1/2 sec² x/2

B. -1/2 cosec² x/2

C. -cosec² x/2

D. None of the above

 

Q. 79 What is the value of the equation given in figure ?

A. eπ/⁴ – 1

B. eπ/⁴ + 1

C. e – 1

D. e

 

Q. 80 What is the slope of the tangent to the curve y = sin⁻¹(sin²ˣ) at x = 0?

A. 0

B. 1

C. 2

D. None of the above

 

Q. 81 The solution of dy/dx = |x| is, where c is an arbitrary constant.

A. y = x|x|/2 + c

B. y = |x|/2 + c

C. y = x²/2 + c

D. y = x³/2 + c

 

Q. 82 What is the solution of dy/dx + 2y = 1 satisfying y(0) = 0?

A. y = (1 – e⁻²ˣ)/2

B. y = (1 + e⁻²ˣ)/2

C. y = 1 + eˣ

D. y = (1 + eˣ)/2

 

Q. 83 Consider the curve y = e²ˣ

What is the slope of the tangent to the curve at (0, 1)?

A. 0

B. 1

C. 2

D. 4

 

Q. 84 Consider the curve y = e²ˣ

Where does the tangent to the curve at (0, 1) meet the x – axis?

A. (1, 0)

B. (2, 0)

C. (-1/2, 0)

D. (1/2, 0)

 

Q. 85 Consider an ellipse x²/a² + y²/b² = 1.

What is the area of the greatest rectangle that can be inscribed in the ellipse?

A. ab

B. 2 ab

C. ab/2

D. √ab

 

Q. 86 Consider an ellipse x²/a² + y²/b² = 1.

What is the area included between the ellipse and the greatest rectangle inscribed in the ellipse?

A. ab(π – 1)

B. 2ab(π – 1)

C. ab(π – 1)

D. None of the above

 

Questions: 87 – 88

Consider the integrals as shown in figure

Q. 87 What is I₁ – I₂ equal to ?

A. 0

B. 2I₁

C. π

D. None of the above

 

Q. 88 what is I₁ equal to ?

A. π/24

B. π/18

C. π/12

D. π/6

 

Questions: 89 – 90

Consider the function f(x) = (1 – sin x)/(π – 2x)² where x ≠ π/2 and f(π/2) = λ 

Q. 89 What is lim(x → π/2) equals to?

A. 1

B. 1/2

C. 1/4

D. 1/8

 

Q. 90 What is the value of if the function is continuous at x = π/2?

A. 1/8

B. 1/4

C. 1/2

D. 1

 

Q. 91 If f(9) = 9 and f′(9) = 4 then what is the value of the expression shown in figure

A. 36

B. 9

C. 4

D. None of the above

 

Q. 92 What is ∫(π/2 → -π/2) x sin x dx equal to?

A. 0

B. 2

C. -2

D. π

 

Q. 93 What is the general solution of the differential equation x dy – y dx = y² ?

(where c is an arbitrary constant)

A. x = cy

B. y² = cx

C. x + xy – cy = 0

D. None of the above

 

Q. 94 Consider the following statements :

1. The function f(x) = ∛x is continuous at all x except at x = 0

2. The function f(x) = [x] is continuous at x=2.99 where [.] is the bracket function

Which of the above statement is are correct ?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 95 Consider the following statements :

1. The function f(i) = |i| is not differentiable at i = 0

2. the function f(i) = eⁱ is differentiable at i = 0

Which of the above statement is are correct ?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 96 If z= f o f(x) where f(x) = x², then what is dz/dx equal to?

A. x³

B. 2x³

C. 4x³

D. 4x²

 

Q. 97 Consider the function f(x) = (x² – x + 1)/(x² + x + 1)

What is the maximum value of the function?

A. 1/2

B. 1/3

C. 2

D. 3

 

Q. 98 Consider the function f(x) = (x² – x + 1)/(x² + x + 1)

What is the minimum value of the function?

A. 1/2

B. 1/3

C. 2

D. 3

 

Questions: 99 – 101

Let f(x) be a function defined in 1 ≤ x < ∞ by f(x) given in figure (1).

Q. 99 Consider the following statements:

1. The function is continuous at every point in the interval [1, ∞).

2. The function is differentiable at x = 1.5.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 100 What is the differentiable coefficient of f(x) at x = 3?

A. 1

B. 2

C. -1

D. -3

 

Q. 101 Consider the following statements:

1. f(2 + 0) does not exist.

2. f(2 – 0) does not exist.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor

 

Q. 102 What is ∫(π/2 → 0) ln (tan x) dx equal to?

A. ln 2

B. -ln 2

C. 0

D. None of the above

 

Questions: 103 – 105

The general solution pf the differential equation (x² + x + 1)dy + (y² + y + 1)dx = 0 is (x + y + 1) = A(1 + Bx + Cy + Dxy) where B, C and D are constants and A is parameter.

Q. 103 What is B equal to?

A. -1

B. 1

C. 2

D. None of the above

 

Q. 104 What is C equal to?

A. 1

B. -1

C. 2

D. None of the above

 

Q. 105 What is D equal to?

A. -1

B. 1

C. -2

D. None of the above

 

Q. 106 Consider the following statements:

1. The functional f(x) = sin x decreases on the interval (0, π/2).

2. The function f(x) = cos x increases on the interval (0, π/2)

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 107 What is the number of arbitrary constants in the particular solution of differential equation of third order?

A. 0

B. 1

C. 2

D. 3

 

Q. 108 What is the equation of a curve passing through (0, 1) and whose differential equation is given by dy = y tan x dx?

A. y = cos x

B. y = sin x

C. y = sec x

D. y = cosec x

 

Q. 109 Consider the following statements in respect of the differential equation d²y/dx² + cos(dy/dx) = 0:

1. The degree of the differential equation is not defined.

2. The order of the differential equation is 2.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

 

Q. 110 What is the equation of parabola whose vertex is at (0, 0) and focus is at (0, -2)?

A. y² + 8x = 0

B. y2 – 8x = 0

C. x² + 8y = 0

D. x² – 8y = 0

 

Questions: 111 – 114

Number X is randomly selected from the set of odd numbers and Y is randomly

selected from the set of even numbers of the set {1, 2, 3, 4, 5, 6, 7}. Let Z = (X + Y).

Q. 111 What is P(Z = 5) equal to ?

A. 1/2

B. 1/3

C. 1/4

D. 1/6

 

Q. 112 What is P(Z = 10) equal to?

A. 0

B. 1/2

C. 1/3

D. 1/5

 

Q. 113 What is P(Z > 11) equal to ?

A. 0

B. 1/4

C. 1/6

D. 1/12

 

Q. 114 What is P(Z is the product of two prime numbers) equal to ?

A. 0

B. 1/2

C. 1/4

D. None of the above

 

Questions: 115 – 117

The number of telephone calls received in 245 successive one minute intervals at an exchange is given below in the frequency distribution given in figure

Q. 115 What is the mean of the distribution?

A. 3.76

B. 3.84

C. 3.96

D. 4.05

 

Q. 116 What is the median of the distribution?

A. 3.5

B. 4

C. 4.5

D. 5

 

Q. 117 What is the mode of the distribution?

A. 3

B. 4

C. 5

D. 6

 

Questions: 118 – 120

The mean and standard deviation of all 100 items are 50, 5 and that of 150 items are 40, 6 respectively.

Q. 118 What is the combined mean of the 250 items?

A. 43

B. 44

C. 45

D. 46

 

Q. 119 What is the combined standard deviation of all 250 items?

A. 7.1

B. 7.3

C. 7.5

D. 7.7

 

Q. 120 What is the variance of all the 250 items?

A. 50.6

B. 53.3

C. 55.6

D. 59.3

 

Answer Sheet 
Question 1 2 3 4 5 6 7 8 9 10
Answer B C C B C A B D A C
Question 11 12 13 14 15 16 17 18 19 20
Answer C C A B C C B A C C
Question 21 22 23 24 25 26 27 28 29 30
Answer A A B D A B C C A C
Question 31 32 33 34 35 36 37 38 39 40
Answer A C B C C A D C B C
Question 41 42 43 44 45 46 47 48 49 50
Answer B B B A A C C D C B
Question 51 52 53 54 55 56 57 58 59 60
Answer B A D B B C C A D C
Question 61 62 63 64 65 66 67 68 69 70
Answer A D C C C A B C B A
Question 71 72 73 74 75 76 77 78 79 80
Answer C A B D C C D B A A
Question 81 82 83 84 85 86 87 88 89 90
Answer A A C C B C A C D A
Question 91 92 93 94 95 96 97 98 99 100
Answer C B ABCD B B C D B B D
Question  101 102 103 104 105 106 107 108 109 110
Answer A C A B C D D C C C
Question  111 112 113 114 115 116 117 118 119 120
Answer D A D C A B B B C C

JEE Advanced 2018 Paper II Previous Year Paper

JEE Advanced 2018 Paper II 

Q. 1 A particle of mass ݉ is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as dK/dt = γ , where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

A. The force applied on the particle is constant

B. The speed of the particle is proportional to time

C. The distance of the particle from the origin increases linearly with time

D. The force is conservative

 

Q. 2 Consider a thin square plate floating on a viscous liquid in a large tank. The height ݄h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u₀ .Which of the following statements is (are) true?

A. The resistive force of liquid on the plate is inversely proportional to ݄h

B. The resistive force of liquid on the plate is independent of the area of the plate

C. The tangential (shear) stress on the floor of the tank increases with u₀

D. The tangential (shear) stress on the plate varies linearly with the viscosity η of the

liquid

 

Q. 3 An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge density λ. It pierces a thin non-conducting spherical shell of radius ܴ in such a way that the arc ܼܳܿPQ subtends an angle of 120° at the centre ܱO of the spherical shell, as shown in the figure. The permittivity of free space is ∈₀. Which of the following statements is (are) true?

A. The electric flux through the shell is √3 Rλ⁄ε₀

B. The Z- component of the electric field is zero at all the points on the surface of the

shell

C. The electric flux through the shell is √2 Rλ⁄ε₀

D. The electric field is normal to the surface of the shell at all points

 

Q. 4 A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length ݂, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

A. A

B. B

C. C

D. D

 

Q. 5 In a radioactive decay chain, ²³²₉₀Th nucleus decays to ²¹²₈₂Pb nucleus. Let ܰNα and ܰNβ be the number of α and β⁻ particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

A. N(α) = 5

B. N(α) = 6

C. N(β) = 2

D. N(β) = 4

 

Q. 6 In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube.Two successive resonances are heard at air columns of length 50.7݉ܿ cm and 83.9݉ܿ cm . Which of the following statements is (are) true?

A. The speed of sound determined from this experiment is 332 ݉m/s⁻¹

B. The end correction in this experiment is 0.9 ݉ܿcm

C. The wavelength of the sound wave is 66.4 ݉ܿcm

D. The resonance at 50.7݉ܿ cm corresponds to the fundamental harmonic

 

Q. 7 A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass m = 0.4kg ݇i݃ s at rest on this surface. An impulse of 1.0 N is applied to the block at time t= 0 so that it starts moving along the x- axis with a velocity v(t) = v₀e⁻ᵗ/ᵀ, where v₀ is a constant and τ = 4s.The displacement of the block, in ݁݉meters t = τ is_________.

Take e⁻¹ = 0.37

 

Q. 8 A ball is projected from the ground at an angle of 45° with the horizontal surface. It reaches a maximum height of 120 m and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of 30° with the horizontal surface. The maximum height it reaches after the bounce, in meters ,is

 

Q. 9 A particle, of mass 10⁻³ kg and charge 1.0 C ,is initially at rest. At time t=0, the particle comes under the influence of an electric field E̅=E₀sin ωtî, where Eₒ=1.0 N/C⁻¹ and ω=10³rad/s⁻¹. Consider the effect of only the electrical force on the particle. Then the maximum speed, in ݉m/s⁻¹ , attained by the particle at subsequent times is

 

Q. 10 A moving coil galvanometer has 50 turns and each turn has an area 2 x 10⁻⁴ m². The magnetic field produced by the magnet inside the galvanometer is 0.02 T. The torsional constant of the suspension wire is 10⁻⁴ N m rad⁻¹. When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 rad.݀ The resistance of the coil of the galvanometer is 50 Ω .This galvanometer is to be converted into an ammeter capable of measuring current in the range 0 – 1.0A .For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in Ω ,is __________.

 

Q. 11 A steel wire of diameter 0.5 ݉mm and Young’s modulus 2 x 10⁻¹¹ N m⁻² carries a load of mass ܯ .The length of the wire with the load is 1.0 ݉m A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count 1.0 mm is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by 1.2 ݇kg, the vernier scale division which coincides with a main scale division is __________. Take g = 10 ms⁻² and π = 3.2

 

Q. 12 One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100 K and the universal gas constant 8.0 J/mol⁻¹ K⁻¹, the decrease in its internal energy, in joule is__________.

 

Q. 13 In a photoelectric experiment a parallel beam of monochromatic light with power of 200 ܹ is incident on a perfectly absorbing cathode of work function 6.25 ܸ݁eV The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100%. A potential difference of 500 V is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force F= n x 10 N⁻⁴ due to the impact of the electrons. The value of ݊ is __________.Mass of the electron ݉9 x 10⁻³¹ kg and 1.0 eV = 1.6 x 10⁻¹⁹ J

 

Q. 14 Consider a hydrogen-like ionized atom with atomic number ܼ with a single electron. In the emission spectrum of this atom, the photon emitted in the n = 2 to n =1 transition has energy 74.8 eV higher than the photon emitted in the n = 3 to n = 2 transition. The ionization energy of the hydrogen atom is 13.6 ܸ݁eV The value of Z ܼ is __________

 

Q. 15 The electric field E is measured at a point ܼܿ(0, 0, ݀d) generated due to various charge distributions and the dependence of E on ݀d is found to be different for different charge distributions. List-I contains different relations between E and ݀d List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II.

A. A

B. B

C. C

D. D

 

Q. 16 A planet of mass M ,has two natural satellites with masses ݉m₁ and ݉m₂. The radii of their circular orbits are ܴR₁ and ܴR₂ respectively. Ignore the gravitational force between the satellites. Define v₁ , L₁ , K₁ and T₁ to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and v₂ , L₂ , K₂ and ܶT₂ to be the corresponding quantities of satellite 2. Given ݉m₁/m₂ = 2 and ܴR₁/R₂ = 1/4, match the ratios in List-I to the numbers in List-II.

A. A

B. B

C. C

D. D

 

Q. 17 One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the ܸܿPܼ V-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the corresponding statements in List-II.

A. A

B. B

C. C

D. D

 

Q. 18 In the List-I below, four different paths of a particle are given as functions of time. In these functions, α and β are positive constants of appropriate dimensions and α ≠ β .In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: p̅ is the linear momentum,L is the angular momentum about the origin, K is the kinetic energy, ܷU is the potential energy and E is the total energy. Match each path in List-I with those quantities in List-II, which are conserved for that path.

A. A

B. B

C. C

D. D

 

Q. 19 The correct option(s) regarding the complex [Co(en)(NH₃)₃(H₂O)]³⁺ (en = H₂NCH₂CH₂NH₂) is (are)

A. It has two geometrical isomers

B. It will have three geometrical isomers if bidentate ‘en’ is replaced be two cyanide

ligands.

C. It is paramagnetic

D. It absorbs light at longer wavelength as compared to [Co(en)(NH₃)₄]³⁺

 

Q. 20 The correct option(s) to distinguish nitrate salts of Mn⁺² and Cu⁺² taken separately is (are) 

A. Mn⁺² shows the characteristic green colour in the flame test

B. Only Cu⁺² shows the formation of precipitate by passing H₂S in acidic medium

C. Only Mn⁺² shows the formation of precipitate by passing H₂S in faintly basic medium

D. Cu⁺²/Cu has higher reduction potential than Mn⁺²/Mn (measured under similar

conditions)

 

Q. 21 Aniline reacts with mixed acid (conc. HNO₃ and conc. H₂SO₄) at 288 K to give P (51 %), Q (47%) and R (2%). The major product(s) of the following reaction sequence is (are) 

A. A

B. B

C. C

D. D

 

Q. 22 The Fischer presentation of D-glucose is given below. The correct structure(s) of β-

Lglucopyranose is (are)

A. A

B. B

C. C

D. D

 

Q. 23  For a first order reaction A(g) → 2B(g) + C(g) at constant volume and 300 K, the total pressure at the beginning (u=0) and at time u are ܼܿP₀ and ܼܿPᵤ, respectively. Initially, only A is present with concentration [A]₀, and t₁/₃ is the time required for the partial pressure of A to reach 1/3rd of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

A. A

B. B

C. C

D. D

 

Q. 24 For a reaction, A ⇌ P  the plots of [A] and [P] with time at temperatures T₁ and T₂ are given below.

If ܶT₂ > ܶT₁ , the correct statement(s) is (are)

A. A

B. B

C. C

D. D

 

Q. 25 The total number of compounds having at least one bridging oxo group among the molecules given below is ____.

N₂O₃, N₂O₅, P₄O₆, P₄O₇, H₄P₂O₅, H₅P₃O₁₀, H₂S₂O₃, H₂S₂O₅

 

Q. 26 Galena (an ore) is partially oxidized by passing air through it at high temperature. After some time, the passage of air is stopped, but the heating is continued in a closed furnace such that the contents undergo self-reduction. The weight (in kg) of Pb produced per kg of O2 consumed is ____.

(Atomic weights in g/mol: O = 16, S = 32, Pb = 207)

 

Q. 27 To measure the quantity of MnCl₂ dissolved in an aqueous solution, it was completely converted to KMnO₄ using the reaction, MnCl₂ + K₂S₂O₈ + H₂O —> KMnO₄ + H₂SO₄ + HCl (equation not balanced). Few drops of concentrated HCl were added to this solution and gently warmed. Further, oxalic acid (225 mg) was added in portions till the colour of the permanganate ion disappeared. The quantity of MnCl₂ (in mg) present in the initial solution is ____.

(Atomic weights in g/mol: Mn = 55, Cl = 35.5)

 

Q. 28 For the given compound X, the total number of optically active stereoisomers is ____.

 

Q. 29 In the following reaction sequence, the amount of D (in g) formed from 10 moles of acetophenone is ____.

(Atomic weights in g/mol : H = 1, C = 12, N = 14, O = 16, Br = 80. The yield (%)

corresponding to the product in each step is given in the parenthesis)

Q. 30 The surface of copper gets tarnished by the formation of copper oxide. N₂ gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the N₂ gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below: 2Cu(s) + H₂O(g) —> Cu₂O(s) + H₂(g), pH₂ is the minimum partial pressure of H₂ (in bar) needed to prevent the oxidation at 1250 K. The value of pH₂ is ____. 

(Given: total pressure = 1 bar, R (universal gas constant) = 8 J /K.mol , ln(10) = 2.3. Cu(s) and Cu₂O(s) are mutually immiscible.

 

Q. 31 Consider the following reversible reaction,

A(g) + B(g) ⇌ AB(g).

The activation energy of the backward reaction exceeds that of the forward reaction by 2ܴܶ ( in J/mol⁻¹ ). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of ΔGθ ( in J/mol⁻¹ ) for the reaction at 300 K is ____. (Given; ln(2) = 0.7, ܴܶ = 2500 J/mol⁻¹ at 300 K and G is the Gibbs energy)

 

Q. 32 Consider an electrochemical cell: A(s) | Aⁿ⁺ (aq, 2 M) || B²ⁿ⁺ (aq, 1 M) | B(s). The value of ΔH^Ɵ for the cell reaction is twice that of ΔG^Ɵ at 300 K. If the emf of the cell is zero, the ΔS^Ɵ (in J/K.mol⁻¹) of the cell reaction per mole of B formed at 300 K is ____.

(Given: ln(2) = 0.7, ܴ (universal gas constant) = 8.3 J/K⁻¹mol⁻¹. H, S and G are enthalpy,

entropy and Gibbs energy, respectively.)

 

Q. 33 Match each set of hybrid orbitals from LIST–I with complex(es) given in LIST–II.

A. A

B. B 

C. C

D. D

 

Q. 34 The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II.

(given, order of migratory aptitude: aryl > alkyl > hydrogen)

A. A

B. B

C. C

D. D

 

Q. 35 LIST-I contains reactions and LIST-II contains major products.

A. A

B. B

C. C

D. D

 

Q. 36 Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on [H⁺] are given in LIST-II. (Note: Degree of dissociation (α) of weak acid and weak base is << 1; degree of hydrolysis of salt <<1; [H⁺] represents the concentration of H⁺ ions)

A. A

B. B

C. C

D. D

 

Q. 37 For any positive integer ݊, define ݂f (n): (0, ∞) → R as Here, the inverse trigonometric function tan x assumes values in (-π/2, π/2)

Then, which of the following statement(s) is (are) TRUE?

A. A

B. B

C. C

D. D

 

Q. 38 Let ܶ be the line passing through the points ܼܿP(-2, 7) and ܳQ(2, -5). Let F be the set of all pairs of circles (S₁,S₂) such that ܶ is tangent to T at ܼܿ and tangent to ܵS₁ at P ܳ, and also such that ܵS₂ and ܵQ touch each other at a point, say, M .Let E₁ be the set representing the locus of M as the pair (S₁,S₂) varies in F₁. Let the set of all straight line segments joining a pair of distinct points of E₁ and passing through the point ܴR (1, 1) be F₂ Let E₂ be the set of the mid-points of the line segments in the set F₂ Then, which of the following statement(s) is (are) TRUE? 

A. The point (-2,7) lies in E₁

B. The point (4/5,7/5) does not lie in E₂

C. The point (1/2, 1) lie in E₂

D. The point (0,3/2) does not lie in E₂

 

Q. 39 Find the equation

A. A

B. B

C. C

D. D

 

Q. 40 Consider two straight lines, each of which is tangent to both the circle x² + y² = 1/2 and the parabola y² = 4x. Let these lines intersect at the point Q ܳ. Consider the ellipse whose center is at the origin ܱ(0,0) and whose semi-major axis is OQ ܱܳ. If the length of the minor axis of this ellipse is √2 , then which of the following statement(s) is (are) TRUE?

A. (A) For the ellipse, the eccentricity is 1/√2 and the length of the latus rectum is 1

B. (B) For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2

C. (C) The area of the region bounded by the ellipse between the lines x = 1/√2 and x = 1 is 1/4√2. (π-2)

D. (D) The area of the region bounded by the ellipse between the lines x = 1/√2 and x = 1 is 1/16 . (π-2)

 

Q. 41 Let s,t,r be non-zero complex numbers and L be the set of solutions z = xi + y where, x,y∈ R, ݅i =√-1 of the equation sz + tz̅+r = 0, where z̅ = x – iy .Then, which of the following statement(s) is (are) TRUE?

A. If L has exactly one element, then |sI ≠ ItI

B. If |sI = ItI then L has infinitely many elements

C. The number of elements in L ∩ {z : I z-i+1I = 5} is at most 2

D. If L has more than one element, then L has infinitely many elements

 

Q. 42 Let ݂f : (0,π) → R be a twice differentiable function such that

A. A

B. B

C. C

D. D

 

Q. 43 The value of the integral is_____________

 

Q. 44 Let ܼܿ be a matrix of order 3 x 3 such that all the entries in P are from the set {-1, 0, 1}. Then, the maximum possible value of the determinant of ܼܿP is _____ .

 

Q. 45 Let ܺX be a set with exactly 5 elements and ܻ be a set Y with exactly 7 elements. If α is the number of one-one functions from ܺX to Y ܻand β is the number of onto functions from ܻ to ܺ, then the value of 1/5!(β-α) is _____ .

 

Q. 46 Let ݂f: R—> R be a differentiable function with ݂f(0)=0. If y = f(x) satisfies the differential equation dy/dx = (2+5y)(5y-2) then the value of lim x–>∞ f(x) is _____.

 

Q. 47 Let f: R—> R be a differentiable function with ݂f(0)=1 and satisfying the equation f(x+y) = f(x).f'(y) + f'(x).f(y) Then, the value of log(e) f(4) is _____.

 

Q. 48 Let ܼܿ be a point P in the first octant, whose image ܳQ in the plane x+y=3 (that is, the line segment PQ ܼܳܿ is perpendicular to the plane x+y=3 and the mid-point of ܼܳܿ PQ lies in the plane x+y=3) lies on the z-axis. Let the distance of ܼܿP from the x-axis be 5. If R ܴ is the image of ܼܿR in the xy-plane, then the length of ܴܿ ܼ is _____

 

Q. 49 Consider the cube in the first octant with sides ܱܿOܼ P, OQ and ܱOܴ R of length 1, along the x-axis, y-axis and z-axis, respectively, where ܱO(0,0,0) is the origin. Let ܵS(1/2,1/2,1/2) be the centre of the cube and ܶ be the vertex of the cube opposite to the origin ܱ such that ܵ lies on the diagonal

 

Q. 50 Let 1(¹⁰C₁)² + 2(¹⁰C₂)² +….+10(¹⁰C₁₀)² where , ¹⁰Cᵣ , r ε {1, 2, ⋯ , 10} denote binomial coefficients. Then, the value of is _____ .

Q. 51 Match the following with the lists given below.

A. A

B. B

C. C

D. D

 

Q. 52 In a high school, a committee has to be formed from a group of 6 boys M₁, M₂, M₃, M₄, M₅ and M₆ and 5 girls G₁,G₂,G₃,G₄ and G₅

(i) Let α₁ be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls.

(ii) Let α₂ be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls.

(iii) Let α₃ be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls.

(iv) Let α₄ be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls and such that both M₁ and G₁ are NOT in the committee together.

A. A

B. B

C. C

D. D

 

Q. 53 Let H: x²/a² – y²/b² = 1, where a>b>0, be a hyperbola in the xy- plane whose conjugate ax is LM subtends an angle of 60° at one of its vertices N. Let the area of triangle LNM be 4√3. Match the correct option from List – 1 to List -2

A. P -> 4; Q -> 2; R -> 1; S-> 3

B. P -> 4; Q -> 3; R -> 1; S-> 2

C. P -> 4; Q -> 1; R -> 3; S-> 2

D. P -> 3; Q -> 4; R -> 2; S-> 1

 

Q. 54 Match them by observing the lists given in figure carefully. 

A. A

B. B

C. C

D. D

Answer Sheet 
Question 1 2 3 4 5 6 7 8 9 10
Answer ABD ACD AB B AC AC 6.30 30.00 3.00 5.55/5.56
Question 11 12 13 14 15 16 17 18 19 20
Answer 3.0 900.00 24.00 3.00 B B C A ABD BD
Question 21 22 23 24 25 26 27 28 29 30
Answer D D ACD BCD 6 6.47 126 7 495 -14.6
Question 31 32 33 34 35 36 37 38 39 40
Answer -8500 -11.62 C D B D ABD AD ACD ACD
Question 41 42 43 44 45 46 47 48 49 50
Answer ACD BCD 2 4 11 9 0.4 2 8 0.5 646
Question 51 52 53 54
Answer A C B D

JEE Advanced 2018 Paper I Previous Year Paper

JEE Advanced 2018 Paper I

Q. 1 The potential energy of a particle of mass m at a distance r from a fixed point 0 is given byV(r) = kr2/2, where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point 0. If is the speed of the particle and 0 is the magnitude of its angular momentum about 0, which of the following statements is (are) true?

A. v=(k/2m)R

B. v=(k/m)R

C. L=(mk)R2

D. v=[(mk)/2]R2

 

Q. 2 Consider a body of mass 1.0 kg at rest at the origin at time t = 0. A force F=(t i+ j) is applied on the body, where = 1.0 N/s and = 1.0 N. The torque acting on the body about the origin at time t = 1.0 s is . Which of the following statements is (are) true?

A. = 1/3 N m

B. The torque is in the direction of the unit vector + k

C. The velocity of the body at t = 1 s is v = 1/2 (i + 2 j) m/s

D. The magnitude of displacement of the body at t= 1 s is 1/6 m

 

Q. 3 A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height ℎ in the capillary tube above the water surface in the beaker. The surface tension of water is o. The angle of contact between water and the wall of the capillary tube is 8. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

A. For a given material of the capillary tube, ℎ decreases with increase in 􀀂

B. For a given material of the capillary tube, ℎ is independent of 􀀔

C. If this experiment is performed in a lift going up with a constant acceleration, then ℎ

decreases

D. ℎ is proportional to contact angle θ

 

Q. 4 In the figure below, the switches S₁ and S₂ are closed simultaneously at t = 0 and a current starts   to flow in the circuit. Both the batteries have the same magnitude of the electromotive  force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current  I in the middle wire reaches its maximum magnitude I(nax) at time t = v. Which of the following statements is (are) true?

A. I(nax) =V/2R

B. I(nax) =V/4R

C.  v = L/R ln 2

D. v = 2L/R ln 2

 

Question 5 This section contains SIX (06) questions.

Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s) is (are) correct option(s). For each question, choose the correct option(s) to answer the question. Answer to each question will be evaluated according to the following marking scheme:

Full Marks : +4 If only (all) the correct option(s) is (are) chosen.

Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.

Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct options.

Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option.

Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : −2 In all other cases.

For Example: If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all  the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option) ,without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in -2 marks.

 

Q. 5 Two infinitely long straight wires lie in the xy-plane along the lines x = ±R. The wire located at x = +R carries a constant current I1 and the wire located at x = −R carries a constant current I₂. A circular loop of radius R is suspended with its centre at (0, 0, √3R) and in a plane parallel to the xy-plane. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the +j true?

Direction. Which of the following statements regarding the magnetic field B⃗⃗ is (are)

A. If I₁ = I₂, then B cannot be equal to zero at the origin (0, 0, 0)

B. If I₁ > 0 and I₂ < 0, then Bcan be equal to zero at the origin (0, 0, 0)

C. If I₁ < 0 and I₂ > 0, thenB can be equal to zero at the origin (0, 0, 0)

D. If I₁ = I₂, then the z-component of the magnetic field at the centre of the loop is (−µ₀ I/2R)

 

Q. 6 One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where V is the volume and T is the temperature). Which of the statements below is (are) true?

A. Process I is an isochoric process

B. In process II, gas absorbs heat

C. In process IV, gas releases heat

D. Processes I and III are not isobaric

 

 

Q. 7 Two vectorsA and B are defined as A = a îand B = a (cos mtî+ sin mtĵ), where a is a constant and m = n/6 rad/s. If |A + B| = √3|A − B | at time t = v for the first time, the value of v, in seconds, is _______ 

 

Q. 8 Two  men are walking  along a horizontal  straight line in the  same direction. The man  in front walks at a speed 1.0 n/s and the man behind walks at a speed 2.0 n/s. A third man is standing  at a height 12 n above the same horizontal line such that all three men are in a vertical plane.  The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz. The  speed of sound in air is 330 n/s. At the instant, when the moving men are 10 n apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is   .

 

Q. 9 A  ring and  a disc are  initially at rest,  side by side, at the  top of an inclined plane  which makes an angle 60° with  the horizontal. They start to roll  without slipping at the same instant of time  along the shortest path. If the time difference  between their reaching the ground is (2 − √3) /√10  s, then the height of the top of the inclined plane,  in meters, is__________Take g = 10 n s⁻².

 

Q. 10  A spring-block  system is resting  on a frictionless floor  as shown in the figure. The  spring constant is 2.0 N/n and the  mass of the block is 2.0 kg. Ignore  the mass of the spring. Initially the spring is in an unstretched condition. Another block of mass 1.0 kg moving with a speed of 2.0 n/s collides elastically with the first block. The collision is such that the 2.0 kg block does not hit the wall. The distance, in meters, between the two blocks when the spring returns to its unstretched position for the first time after the collision is   .

 

Q. 11 Three identical capacitors C₁, C₂ and C₃ have a capacitance of 1.0 µF each and they are uncharged initially. They are connected in a circuit as shown in the figure and C₁ is then filled completely with a dielectric material of relative permittivity cᵣ . The cell electromotive force (emf) V₀ = 8 V. First the switch S₁ is closed while the switch S₂ is kept open. When the capacitor C₃ is fully charged, S₁ is opened and S₂ is closed simultaneously. When all the capacitors reach equilibrium, the charge on C₃ is found to be 5 µC. The value of cᵣ = ________

 

Q. 12 In the xy-plane, the region y > 0 has a uniform magnetic field B1k̂ and the region y < 0 has another  uniform magnetic field B₂k̂. A positively charged particle is projected from the origin along the positive y-axis with speed v₀ = n n/s at t = 0, as shown in the figure. Neglect gravity  in this problem. Let t = T be the time when the particle crosses the x-axis from below for the first time. If B₂ = 4B₁, the average speed of the particle, in n/s, along the x- axis in the time interval T is 

.

 

Q. 13 Sunlight of intensity 1.3 kW n⁻² is incident normally on a thin convex lens of focal length 20cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller  than its focal length. The average intensity of light, in kW n⁻² , at a distance 22 cn from the lens on the other side is _____.

 

Q. 14 Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures T₂ = 300 K and T₂ = 100 K, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are K₁ and K₂ respectively. If the temperature at the junction of the two cylinders in the steady state is 200 K, then K₁/K₂ = .

 

Questions: 15 – 16

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, [E] and [B] stand for dimensions of electric and magnetic fields respectively, while [c₀] and [µ₀] stand for dimensions of the permittivity and permeability of free space respectively. [L] and [T] are dimensions of length and time respectively. All the quantities are given in SI units. (There are two questions based on PARAGRAPH “X”, the question given below is one of them)

Q. 15 The relation between [E] and [B] is 

 

A. [E] = [B] [L] [T]

B.[E] = [B] [L]⁻¹[T]

C. [E] = [B] [L] [T]⁻¹

D. [E] = [B] [L]⁻¹[T]⁻

 

Q. 16 The relation between [c₀] and [µ₀] is

A.  [µ₀] = [c₀] [L]²[T]⁻²

B.  [µ₀] = [c₀] [L]⁻²[T]²

C.   [µ₀] = [c₀]⁻¹[L]²[T]⁻²

D.   [µ₀] = [c₀]⁻¹[L]⁻²[T]²

 

Questions: 17 – 18

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any  dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of  the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then z ± Δz = (x±Δx)/(y±Δy) =x/y (1 ± (Δx/x)) (1 ± (Δy/y))⁻¹.

The series expansion for (1 ± Δy/y)⁻¹, to first power in Δy/y, is 1 ∓ (Δy/y). The  relative errors in independent variables are always added. So the error in z will be  Δz = z (Δx/x + Δy/y). The above derivation makes the assumption that Δx/x ≪1, Δy/y ≪1. Therefore, the higher powers of these quantities are neglected.

(There are two questions based on PARAGRAPH “A”, the question given below is one of them)

 

Q. 17 Consider the ratio r =(1−a)/(1+a) to be determined by measuring a dimensionless quantity 

a. If the error in the measurement of a is Δa (Δa/a ≪ 1) , then what is the error Δr in determining r?

A. Δa/(1+a)²

B. 2Δa/(1+a)²

C. 2Δa/(1−a²)

D. 2aΔa/(1−a²)

 

Q. 18 In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000 ± 40 nuclei decayed in the first 1.0 s. For |x| ≪ 1, ln(1 + x) = x up to first power in x. The error Δh, in the determination of the decay constant h, in s⁻¹, is

A. 0.04

B. 0.03

C. 0.02

D. 0.01

 

Q. 19 The compound(s) which generate(s) N₂ gas upon thermal decomposition below 300⁰C is (are)

A. NH₄NO₃

B. (NH₄)₂Cr₂O₇

C. Ba(N₃)₂

D. Mg₃N₂

 

Q. 20 The correct statement(s) regarding the binary transition metal carbonyl compounds is

(are) (Atomic numbers: Fe = 26, Ni = 28)

A. Total number of valence shell electrons at metal centre in Fe(CO)₅ or Ni(CO)₄ is 16

B. These are predominantly low spin in nature

C. Metal–carbon bond strengthens when the oxidation state of the metal is lowered

D. The carbonyl C−O bond weakens when the oxidation state of the metal is increased

 

Q. 21 Based on the compounds of group 15 elements, the correct statement(s) is (are)

A. Bi₂O₅ is more basic than N₂O₅

B. NF₃ is more covalent than BiF₃

C. PH₃ boils at lower temperature than NH₃

D. The N−N single bond is stronger than the P−P single bond

 

Q. 22 In the following reaction sequence, the correct structure(s) of X is (are)

A. A

B. B

C. C

D. D

 

Q. 23 The reaction(s) leading to the formation of 1,3,5-trimethylbenzene is (are)

A. A

B. B

C. C

D. D

 

Q. 24 A reversible cyclic process for an ideal gas is shown below. Here, P, V, and T are pressure, volume and temperature, respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively. The correct option(s) is (are)

 

A. A

B. B

C. C

D. D

 

Q. 25 Among the species given below, the total number of diamagnetic species is ___.

H atom, NO₂ monomer, O₂⁻(superoxide), dimeric sulphur in vapour phase, Mn₃O₄, (NH₄)₂[FeCl₄], (NH₄)₂[NiCl₄], K₂MnO₄, K₂CrO₄

 

Q. 26 The ammonia prepared by treating ammonium sulphate with calcium hydroxide is

completely used by NiCl₂.6H₂O to form a stable coordination compound. Assume that both the reactions are 100% complete. If 1584 g of ammonium sulphate and 952 g of NiCl₂.6H₂O are used in the preparation, the combined weight (in grams) of gypsum and the nickel ammonia coordination compound thus produced is ____.(Atomic weights in g/mol : H = 1, N = 14, O = 16, S = 32, Cl = 35.5, Ca = 40, Ni = 59)

 

Q. 27 Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit cell is constructed from the unit cell of MX following the sequential instructions given below. Neglect the charge balance.

(i) Remove all the anions (X) except the central one

(ii) Replace all the face centered cations (M) by anions (X)

(iii) Remove all the corner cations (M)

(iv) Replace the central anion (X) with cation (M)

The value of (number of anions/number of cations) in Z is ____.

 

Q. 28 For the electrochemical cell, Mg(s) I Mg⁺² (aq, 1 M) II Cu⁺² (aq, 1 M) I Cu(s), the standard emf of the cell is 2.70 V at 300 K. When the concentration of Mg⁺² is changed to x M, the cell potential changes to 2.67 V at 300 K. The value of x is   . (given, F/R= 11500 K V⁻¹, where F is the Faraday constant and R is the gas constant, ln(10) = 2.30)

 

Q. 29 closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure 2), the volume (in m³ ) of the compartment A after the system attains equilibrium is ____.

 

Q. 30 Liquids u and v form ideal solution over the entire range of composition. At temperature T, equimolar binary solution of liquids u and v has vapour pressure 45 Torr. At the same temperature, a new solution of u and v having mole fractions xᵤ and xᵥ, respectively, has vapour pressure of 22.5 Torr. The value of xᵤ/xᵥ in the new solution is (given that the vapour pressure of pure liquid u is 20 Torr at temperature T)

 

Q. 31 The solubility of a salt of weak acid (AB) at pH 3 is Y×10⁻³ mol/L. The value of Y is .(Given that the value of solubility product of AB (Ksp) = 2×10⁻¹⁰ and the value of ionization constant of HB (Kₐ) = 1×10⁻⁸)

 

Q. 32 The plot given below shows P − T curves (where P is the pressure and T is the temperature) for two solvents X and Y and isomolar solutions of NaCl in these solvents. NaCl completely dissociates in both the solvents. On addition of equal number of moles of a non-volatile solute S in equal amount (in kg) of these solvents, the elevation of boiling point of solvent X is three times that of solvent Y. Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in solvent Y, the degree of dimerization in solvent X is .

Questions: 33 – 34

Treatment of benzene with CO/HCl in the presence of anhydrous AlCl₃/CuCl followed by reaction with Ac₂O/NaOAc gives compound X as the major product. Compound X upon reaction with Br₂/Na₂CO₃, followed by heating at 473 K with moist KOH furnishes Y as the major product. Reaction of X with H₂/Pd-C, followed by H₃PO₄ treatment gives Z as the major product. (There are two questions based on PARAGRAPH “X”, the question given below is one of them)

Q. 33 The compound Y is

A. A

B. B

C. C

D. D

 

Q. 34 The compound Z is

A. A

B. B

C. C

D. D

 

Questions: 35 – 36

An organic acid P (C₁₁H₁₂O₂) can easily be oxidized to a dibasic acid which reacts with ethylene glycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic ketone as one of the products. P undergoes the following reaction sequences to furnish R via Q. The compound P also undergoes another set of reactions to produce S.(There are two questions based on PARAGRAPH “A”, the question given below is one of them)

Q. 35 The compound R is

A. A

B. B

C. C

D. D

 

Q. 36 The compound S is

A. A

B. B

C. C

D. D

 

Q. 37 For a non-zero complex number z, let arg(z) denote the principal argument with − n < arg(z) ≤ n. Then, which of the following statement(s) is (are) FALSE?

A. arg(−1 − i) =n/4, where i = √−1

B. The function ƒ: ℝ → (−n, n], defined by ƒ(t) = arg(−1 + it) for all t ∈ ℝ, is continuous at all points of ℝ, where i = √−1

C. For any two non-zero complex numbers z₁ and z₂, arg (z₁/z₂) − arg( z₁) + arg( z₂) is an integer multiple of 2n

D. For any three given distinct complex numbers z₁, z₂ and z₃, the locus of the point z

satisfying the condition arg ((z−z₁) (z₂−z₃)/(z−z₃) (z₂−z₁)) = n,lies on a straight line

 

Q. 38 In a triangle PQR, let ∠PQR = 30° and the sides PQ and QR have lengths 10√3 and 10, respectively. Then, which of the following statement(s) is (are) TRUE?

A. ∠QPR = 45°

B. The area of the triangle PQR is 25√3 and ∠QRP = 120°

C. The radius of the incircle of the triangle  PQR is 10√3 − 15

D. The area of the circumcircle of the triangle PQR is 100

 

Q. 39 Let P₁: 2x + y − z = 3 and P₂: x + 2y + z = 2 be two planes. Then, which of the following statement(s) is (are) TRUE?

 

A. The line of intersection of P₁ and P₂ has direction ratios 1, 2, −1

B. The line (3x − 4)/9=(1 − 3y)/9= z/3 is perpendicular to the line of intersection of P₁ and P₂

C. The acute angle between P₁ and P₂ is 60°

D. If P₃ is the plane passing through the point (4, 2, −2) and perpendicular to the line of intersection of P₁ and P₂, then the distance of the point (2, 1, 1) from the plane P₃ is 2/√3

 

Q. 40 For every twice differentiable function ƒ: ℝ → [−2, 2] with (ƒ(0))² + (ƒ′(0))² = 85, which of the following statement(s) is (are) TRUE?

A. There exist r, s ∈ ℝ, where r < s, such that ƒ is one-one on the open interval (r, s)

B. There exists x0 ∈ (−4, 0) such that |ƒ′(x₀)| ≤ 1 

C. limx→∞ ƒ(x) = 1

D. There exists α ∈ (−4, 4) such that ƒ(α) + ƒ′′(α) = 0 and ƒ′(α) ≠ 0

 

Q. 41 Let ƒ: ℝ → ℝ and g: ℝ → ℝ be two non-constant differentiable functions. If ƒ′(x) = (e(ƒ(x) −g(x)))g′(x) for all x ∈ ℝ, and ƒ(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE? 

A. A

B. B

C. C

D. D

 

Q. 42 Let ƒ:[0, ∞) → ℝ be a continuous function such that x0 for all x ∈ [0, ∞). Then, which of the following statement(s) is (are) TRUE?

A. The curve y = ƒ(x) passes through the point (1, 2)

B. The curve y = ƒ(x) passes through the point (2, −1)

C. The area of the region {(x, y) ∈ [0, 1] × ℝ ∶ ƒ(x) ≤ y ≤ √1 − x₂} is (n−2)/4

D. The area of the region {(x, y) ∈ [0,1] × ℝ ∶ ƒ(x) ≤ y ≤ √1 − x₂} is (n−1)/4

 

Q. 43 The value of the given equation is ______ .

 

Q. 44 The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is _____ .

 

Q. 45 Let X be the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, … , and Y be the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23, … . Then, the number of elements in the set X ∪ Y is  

 

Q. 46 The number of real solutions of the equation lying in  the interval (-1/2,1/2).(Here, the inverse trigonometric functions sin−1x and cos−1x assume values in [−n/2,n/2] and [0, n], respectively.)

 

Q. 47 For each positive integer n, let For x ∈ ℝ, let [x] be the greatest integer less than or equal to x. If the limit is given then the value of [L] is ________.

 

Q. 48 Let a and b be two unit vectors such thata ⋅ b = 0. For some x, y ∈ ℝ, let c = x a + y b + (a × b ) . If |c   = 2 and the vector c⃗ is inclined at the same angle α to both a and b , then the value

of 8 cos² α is  

 

Q. 49 Let  a, b, c be three non-zero  real numbers such that the equation √3 a cos x + 2 b sin x = c, x ∈ [−n/2,n/2], has two distinct real roots α and þ with α + þ = n/3. Then, the value of ba is_____ .

 

Q. 50 4 A farmer F₁ has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1) and R(2, 0). From this land, a neighbouring farmer F₂ takes away the region which lies between the side PQ and a curve of the form y = xⁿ (n > 1). If the area of the region taken away by the farmer F₂ is exactly 30% of the area of ∆PQR, then the value of n is .

 

Questions: 51 – 52

Let S be the circle in the xy-plane defined by the equation x Let S be the circle in the xy-plane defined by the equation x² + y² = 4. (There are two questions based on PARAGRAPH “X”, the question given below is one of them)

Q. 51 Let E₁E₂ and F₁F₂ be the chords of S passing through the point P₀ (1, 1) and parallel to the x-axis and the y-axis, respectively. Let G₁G₂ be the chord of S passing through P₀ and having slope −1. Let the tangents to S at  E₁ and E₂ meet at E₃, the tangents to S at F₁ and F₂ meet at F₃, and the tangents to S at G₀ and G₂ meet at G₃. Then, the points E₃, F₂, and G₃ lie on the curve

(A) (B)

A. x + y = 4

B. (x − 4)² + (y − 4)²= 16 (C) (D)

C. (x − 4)(y − 4) = 4

D. xy = 4

 

Q. 52 Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve

A. (x + y)² = 3xy

B. x^2/3 + y^2/3 = 2^4/3

C. x² + y² = 2xy

D. x² + y² = x² y²

 

Questions: 53 – 54

There are five students S₁, S₂, S₃, S₄ and S₅ in a music class and for them there are five seats R₁, R₂, R₃, R₄ and R₅ arranged in a row, where initially the seat Rᵢ is allotted to the student Sᵢ, i = 1, 2, 3, 4, 5. But, on the examination day, the five students are randomly allotted the five seats.

(There are two questions based on PARAGRAPH “A”, the question given below is one of them)

Q. 53 The probability that, on the examination day, the student S₁ gets the previously allotted seat Rᵢ, and NONE of the remaining students gets the seat previously allotted to him/her is 

A. 3/40

B. 1/8

C. 7/40

D. 1/5

 

Q. 54 For i = 1, 2, 3, 4, let Tᵢ denote the event that the students Sᵢ and Sᵢ₊₁ do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event T₁ ∩ T₂ ∩ T₃ ∩ T₄ is 

A. 1/15

B. 1/10

C. 7/60

D. 1

Answer Sheet 
Question 1 2 3 4 5 6 7 8 9 10
Answer ABD BCD CD ABD ABD BCD 2.00 5.00 2.00 2.09
Question 11 12 13 14 15 16 17 18 19 20
Answer 1.50 2.00 130.00 4.00 C D B C BC BC
Question 21 22 23 24 25 26 27 28 29 30
Answer ABC B ABD BC1 1 2992 3 10 2.22 19
Question 31 32 33 34 35 36 37 38 39 40
Answer 4.47 0.05 C A A B ABD BCD CD ABD
Question 41 42 43 44 45 46 47 48 49 50
Answer BC BC 8 625 3748 2 1 3 0.5 4
Question 51 52 53 54
Answer A D A C  
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