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NDA/NA(II) Exam 2018 General Ability Test Previous Year Paper

NDA/NA(II) Exam 2018 General Ability Test

Questions: 1 – 5

Each item in this section has a sentence with three words in quotation marks labelled (a),(b),(c). Read each sentence to find out whether there is any error in any part in the quotation and indicate error, your response should be indicated as (d)

Q. 1 ‘He appears'(a)/ ‘to be'(b)/ ‘a honest man'(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 2 ‘One of the members'(a)/ ‘expressed doubt if'(b)/ ‘the Minister was an atheist'(c). /’No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 3 ‘This view has been taken'(a)/ ‘by one of the ablest persons'(b)/ ‘who has written on this subject(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 4 ‘Slow and steady'(a)/ ‘owns the race,'(b)/ ‘as the wise would say,'(c). ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 5 ‘We often hear people say'(a)/ ‘that most human beings have not evolved'(b)/ ‘or grow up enough to stick to truth or non-violence'(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Questions: 6 – 10

Each item in this section consists of a sentence with the word in the quotation followed by four words or groups of words. Select the word or group of words that is nearest in meaning to the words in the quotation and mark your response accordingly

Q. 6 The industrial revolution saw a ‘massive’ rise in the population of Europe

A. enormous

B. erroneous

C. hazardous

D. perilous

Q. 7 I bet some deepest ‘conviction’ reflected in my work

A. ideas and opinions

B. firm beliefs

C. prejudices

D. biases

Q. 8 This boy is very ‘timid’

A. courageous

B. shy

C. clever

D. dull

Q. 9 My friend is as ‘stubborn’ as a mule

A. observant

B. obnoxious

C. obstinate

D. corpulent

Q. 10 His behaviour was deliberately ‘provocative’

A. exciting desire

B. infuriating

C. pitiable

D. creating frustration

Questions: 11 – 15

Each item in this section consists of a sentence with an word in quotation followed by four words or groups of words. Select the word or group of words that is opposite in meaning to the word in the quotation and mark your response accordingly

Q. 11 Two many cooks ‘spoil’ the broth

A. tarnish

B. wreck

C. embellish

D. upset

Q. 12 He is ‘biased’ against the students from cities

A. open

B. prejudiced

C. liked

D. impartial

Q. 13 It is easy to be an ‘orthodox’

A. idolatrous

B. intelligent

C. malignant

D. heterodox

Q. 14 ‘Permit’ me to present you with a book

A. allow

B. enclose

C. prohibit

D. persuade

Q. 15 None but the ‘brave’ deserves the fair

A. ugly person

B. coward

C. jealous person

D. weak person

Questions: 16 – 20

In this section, your have two short passages. After each passage. you will find some items based on the package. First, read a passage and answer the items based on it and mark your response on the answer sheet accordingly. You are required to select your answers based on the contents of the passage and opinion of the author only “Now, ladies and gentlemen,” said the conjurer, “having shown you that the cloth is absolutely empty, I will pretend to take from it a bowl of goldfish. Presto!” All around the hall people were saying, “Oh, how wonderful! How does he do it?” But the Quick Man on the front seat said in a big whisper to the people near him, “He-had-it-up-his-sleeve.” “My next trick,” said the conjurer, “is the famous Hindostanee rings. You will notice that the rings are apparently separate; at a blow they all join(clang,clang,clang)—Presto!” There was a general buzz of stupefaction till the Quick Man was heard to whisper,

“He-must-have-had-another-lot-up-his-sleeve,”

Again everybody nodded and whispered, “The-rings-were-up-his-sleeve.”

The brow of the conjurer was clouded with a gathering frown.

“I will now,” he continued,”show you a most amusing trick by which I am enabled to take any number of eggs from a hat. Will some gentleman kindly lend me his hat? Ah, thank you—Presto!”

He extracted seventeen eggs, and for thirty-five seconds the audience began to think that he was wonderful. Then the Quick Man whispered along the front bench, “He-has-a-hen-up-his-sleeve,” and all the people whispered it on. “He-has a- hen-up-his-sleeve.”

The egg trick was ruined. It went on like that all through. It transpired from the whispers of the Quick Man that the conjurer must have concealed up his sleeve, in addition to the rings, hens, and fish, several packs of cars, a loaf of bread, a doll’s cradle, a live guinea pig, a fifty-cent piece, and a rocking chair.

Q. 16 “The brow of the conjurer was clouded with a gathering frown,” The sentence means that the conjurer.

A. was very pleased

B. was very sad

C. was very angry

D. was very afraid

Q. 17 “The egg trick was ruined.” This means that

A. eggs were all broken

B. people were unconvinced

C. conjurer was disappointed

D. the trick could not be performed

Q. 18 According to the Quick Man, the conjurer

A. had everything bought for production

B. produced things with the magic he knew

C. had things in the large sleeves of his coat

D. created an illusion of things with his magic

Q. 19 The author believed that the Quick Man was really

A. foolish

B. clever

C. wrong

D. right

Q. 20 The conjurer extracted seventeen eggs from the hat of

A. the Quick Man

B. his own

C. one gentleman from the audience

D. none of the above

Questions: 21 – 25

Magda: Good Morning, Mrs. Smiles. It’s wet, isn’t it?

Mrs. Smiles: Yes, it is, isn’t it? How are you today? All right? You haven’t been studying too hard, have you? You look a bit pale.

Magda: I don’t, do I? Well. I haven’t been out much lately. I don’t like this weather a bit. Why, we haven’t had a dry day for weeks, have we?

Mrs. Smiles: No, I don’t think we have. Let’s see, you’ll be going back home next month, won’t you?

Magda: Oh no, I’m not going back yet. My sister’s coming over first.

Mrs. Smiles: Oh, is she? You’re looking forward to that. How long is it since you saw her?

Magda: Nearly a year now. Yes, I am looking forward to it very much.

Mrs. Smiles: She’s coming over here to study?

Magda: Yes, that’s right. I shan’t go back home until she’s settled down. I don’t think I ought to, ought I?

Mrs. Smiles: Well, no, she’s younger than you are, is she?

Magda: Yes, she’s only eighteen.

Q. 21 Magda had not been out much lately because

A. she had not been keeping well

B. she was busy with her studies

C. the weather had been unpleasant

D. her sister had come over to stay

Q. 22 Magda was not going back home yet because

A. it had been raining heavily

B. her sister was coming over

C. her studies were not completed

D. she was not feeling well

Q. 23 Mrs. Smiles says, “You’re looking forward to that.” This means, Magda was________ her sister’s arrival.

A. expecting with pleasure

B. preparing hard for

C. thanking greatly about

D. watching with joy

Q. 24 Magda’s sister was coming to

A. visit her sister

B. help Mrs. Smiles

C. settle down in England

D. pursue her studies

Q. 25 Mrs. Smiles and Magda are

A. classmates

B. school friends

C. neighbours

D. sister-in-law

Questions: 26 – 35

Each of the following sentences in this section has a blank space and four words groups of words given after the sentence. Select whichever word or group of words you consider most appropriate for the blank space and indicate your response accordingly

Q. 26 We fail to understand your reasons for _____________ the college without completing the degree

A. attending

B. joining

C. leaving

D. refusing

Q. 27 She ___________ her energy and started shouting only when she heard the noise of bulldozers and cranes

A. checked

B. conserved

C. maintained

D. controlled

Q. 28 The British ____________ all over Africa and Asia collapsed in the first half of the twentieth century.

A. hegemony

B. domicile

C. residence

D. inheritance

Q. 29 The football match has to be _____________ because of the weather

A. called off

B. continued

C. put off

D. turned off

Q. 30 If I were rich, ______________ a lot

A. I’ll travel

B. I can travel

C. I would travel

D. I travelled

Q. 31 They apologized _______________ me for what happened

A. to

B. at

C. for

D. with

Q. 32 If you are tired of swimming, just _______________ for a while

A. struggle

B. stroke

C. float

D. streak

Q. 33 He had _______________ spoken for two minutes when there was a commotion in the crowd

A. even

B. hardly

C. often

D. little

Q. 34 I would not commit myself _______________ that course of action

A. of

B. to

C. by

D. with

Q. 35 The soldiers waiting to go into battle for the first time were full of _____________

A. apprehension

B. consideration

C. anticipation

D. frivolity

Questions: 36 – 40

Given below are some idioms/phrases followed by four alternative meanings to each. Choose the response (a),(b),(c) or (d) which is the most appropriate meaning and mark your response accordingly

Q. 36 ‘A red-letter day’

A. a trivial day

B. a very important or significant day

C. a day of bloodshed and violence

D. a mourning day

Q. 37 ‘ The gift of the gab’

A. ability to speak easily and confidently

B. ability to spoil something

C. ability to sell things

D. gift from a sacred institution

Q. 38 ‘Walk to a tightrope’

A. to be forced to leave your job

B. to be ready to fall

C. to act very carefully

D. to invite danger

Q. 39 ‘To be in a fix’

A. to receive strong criticism

B. to support oneself

C. to fix problems

D. to be in a difficult situation

Q. 40 ‘To fish in troubled waters’

A. to borrow money

B. to steal belongings of

C. to get benefit in bad situation

D. to extend a helping hand

Questions: 41 – 45

Each of the following items in this section consists of a sentence of the parts of which have been jumbled. These parts have been labelled P,Q,R and S. Given below each sentence are four sequences namely (a),(b),(c) and (d). Your are required to rearrange the jumbled parts of the sentence and mark your response accordingly

Q. 41 Domestic fired in Indian villages

P: as the heat is dispersed

Q: an unhealthy smoke accumulates in unventilated houses

R: are wasteful

S: lit in Chulhas

The correct sequence should be

A. PQSR

B. PQRS

C. SPQR

D. SRPQ

Q. 42 Bold rocks neat at hand

P: makes a fine forest for the imagination

Q: than distant Alpa

R: are more inspiring

S: and the thick fern upon a heath

The correct sequence should be

A. QRSP

B. RSQP

C. RQSP

D. SRQP

Q. 43 Newton discovered that

P: due to the gravitational pull

Q: of the earth

R: the apple falls

S: on the ground

The correct sequence should be

A. QPRS

B. RSPQ

C. QSPR

D. SQRP

Q. 44 The knocking

P: were still in the house

Q: for some time

R: although the echoes of it

S: ceased

The correct sequence should be

A. SRPQ

B. SQRP

C. PQSR

D. RSPQ

Q. 45 The history of mankind is

P: and steady progress

Q: continuous change

R: the history of

S: from barbarian to refinement

The correct sequence should be

A. PQRS

B. RQPS

C. QSPR

D. SQRP

Questions: 46 – 50

In the following passage, there are some blank spaces with four words or group of words given. Select whichever word or given words you consider most appropriate for the blank space and indicate your response on the answer sheet accordingly.

The honeybee is a very unusual kind of insect, (46) other insects which live alone, the honeybee lives as a/an (47) of community, these bees live together in what is known as a bee (48) house. The head of the bees is called the queen bee. She is (49) than the rest of the bees. Her main task is to (50) eggs

Q. 46 Choose the most appropriate option

A. unlike

B. similar to

C. with

D. like

Q. 47 Choose the most appropriate option

A. group

B. individual

C. member

D. troop

Q. 48 Choose the most appropriate option

A. house

B. home

C. army

D. colony

Q. 49 Choose the most appropriate option

A. heaviest

B. heavier

C. largest

D. larger

Q. 50 Choose the most appropriate option

A. lay

B. hatch

C. make

D. bear

Questions: 51 – 56

The following six(6) items consist of two statements. Statement I and Statement II. Examine these two statements carefully and select the correct answer using the code given below

Code:

(a) Both the statements are individually the true and Statement II is the correct

explanation of Statement I

(b) Both the statements are individually true but Statements II is not the correct

explanation of Statement I

(d) Statement I is false but Statement II is true

Q. 51 Statement I: The pitch of the sound wave depends upon its frequency

Statement II: The loudness of the sound wave depends upon its amplitude

A. (a)

B. (b)

C. (c)

D. (d)

Q. 52 Statement I: Sound wave cannot propagate in vacuum

Statement II: Sound waves are elastic waves and require a medium to propagate

A. (a)

B. (b)

C. (c)

D. (d)

Q. 53 Statement I: The government of India Act, 1935 introduced Dyarchy at the centre

Statement II: The provincial autonomy was granted to the Provinces

A. (a)

B. (b)

C. (c)

D. (d)

Q. 54 Statement I: Mughal Painting reached its climax during the reign of Jahangir

Statement II: Aurangzeb’s Court was adorned by some of the best known artists of the

Mughal School of Painting

A. (a)

B. (b)

C. (c)

D. (d)

Q. 55 Statement I: Phytoplankton produce most of the organic carbon in the ocean

Statement II: Algae are produced in the cold water biome

A. (a)

B. (b)

C. (c)

D. (d)

Q. 56 Statement I: Geostrophic wind blows above a height of 600 metres, parallel to the isobars

Statement II: Geostrophic wind is the horizontal wind velocity, in which the Coriolis force balances the horizontal pressure force

A. (a)

B. (b)

C. (c)

D. (d)

Q. 57 Which one of the following groups of cellular organelles contains DNA?

A. Mitochondria, nucleus, chloroplast

B. Mitochondria, golgi bodies, nucleus

C. Mitochondria, plasma, membrane, nucleus

D. chloroplast, nucleus , ribosomes

Q. 58 One of the additional functions of smooth endoplasmic reticulum(SER) is

A. protein synthesis

B. lipid synthesis

C. storage of biomolecules

D. detoxification of toxic substances

Q. 59 Damage to the apical meristem of a growing plant will affect the

A. length of the plant

B. colour of the flower

C. colour of the leaves

D. taste of the fruits

Q. 60 Which of the following kingdoms has/have only unicellular organisms

A. monera only

B. protista only

C. monera and protista both

D. protista and fungi both

Q. 61 Which one of the following is a waterborne disease?

A. jaundice

B. tuberculosis

C. rabies

D. arthritis

Q. 62 The atomic number of an element is 8. How many electrons will it gain to form a compound with sodium?

A. one

B. two

C. three

D. four

Q. 63 A sample of oxygen contains two isotopes of oxygen with masses 16 u and 18 u

respectively. The proportion of these isotopes in the sample 3:1. What will be the average atomic mass of oxygen in this sample?

A. 17.5 u

B. 17 u

C. 16 u

D. 16.5 u

Q. 64 Which one of the following is a heterogeneous mixture?

A. hydrochloric acid

B. vinegar

C. milk

D. soda water

Q. 65 What is the formula mass of anhydrous sodium carbonate?(Given that the atomic masses of sodium, carbon and oxygen are 23 u, 12 u and 16 u respectively)

A. 286 u

B. 106 u

C. 83 u

D. 53 u

Q. 66 Which one of the following is called ‘syngas’?

A. C(s)+H₂O(g)

B. CO(g)+H₂O(g)

C. CO(g)+H₂(g)

D. NO₂(g)+H₂(g)

Q. 67 The frequency of ultrasound waves is

A. less than 20 Hz

B. between 20 Hz and 2 kHz

C. between 2 kHz and 20 kHz

D. greater than 20 kHz

Q. 68 The magnetic field strength of a current-carrying wire at a particular distance from the axis of the wire

A. depends upon the current in the wire

B. depends upon the radius of the wire

C. depends upon the temperature of the surroundings

D. none of the above

Q. 69 A stainless steel chamber contains Ar gas at a temperature T and Pressure P. The total number Ar atoms in the chamber is n. Now Ar gas in the chamber is replaced by CO₂ gas and the total number of CO₂ molecules in the chamber is n/2 at the same temperature T. The pressure in the chamber now is P′. Which one of the following relations holds true?

(Both the gases behave as ideal gases)

A. P′=P

B. P′=2P

C. P′=P/2

D. P′=P/4

Q. 70 Which one of the following is the correct relation between A and nm?

A. 1 nm=10⁻¹ A

B. 1 nm=10 A

C. 1 nm=1 A

D. 1 nm=10⁻² A

Q. 71 The full form of LED is

A. light emitting diode

B. light emitting device

C. light enhancing device

D. light enhancing diode

Q. 72 If a free electron moves through a potential difference of 1kV, then the energy gained by the electron is given by

A. 1.6X10⁻¹⁹ J

B. 1.6X10⁻¹⁶ J

C. 1X10⁻¹⁹ J

D. 1X10⁻¹⁶ J

Q. 73 Consider the following places of India:

1. Itanagar

2. Imphal

3. Agartala

4. Aizawl

Which one of the following is the correct chronological order of the above places in terms of sunrise time?

A. 3-2-1-4

B. 2-1-4-3

C. 1-4-3-2

D. 4-3-2-1

Q. 74 Which one of the following is known as uplands of delta region?

A. Bef

B. Bils

C. Peh

D. Chars

Q. 75 Consider the following wildlife sanctuaries of india:

1. shikari devi

2: bhadra

3: simlipal

4. pachmarhi

which one of the following is the correct order of the above wildlife sanctuaries in terms of their location from south to north?

A. 1-2-3-4

B. 2-4-3-1

C. 2-3-4-1

D. 3-1-2-4

Q. 76 Which one of the following statements about temperature is correct?

A. temperature decreases with height in the stratosphere

B. temperature is constant at different heights in the atmosphere

C. temperature increases with height in the troposphere at an average rate of 6-5⁰ C per kilometre

D. temperature decreases with height in the troposphere at an average rate of 6-4⁰ C

per kilometre

Q. 77 Which one of the following is known as a zone of sharp salinity change in the vertical section of ocean?

A. thermocline

B. halocline

C. photic zone

D. pycnocline

Q. 78 Permanent hardness of water cannot be removed by which one of the following methods?

A. treatment with washing soda

B. calgon’s method

C. boiling

D. ion exchange method

Q. 79 Which one of the following reactions will given NO(nitric oxide) gas as one of the products?

A. 3Cu+8HNO₃(dilute)->

B. Cu+4HNO₃(conc.)->

C. 4Zn+10HNO₃(dilute)->

D. Zn+4HNO₃(conc.)->

Q. 80 Which one of the following is a tribasic acid?

A. hydrochloric acid

B. nitric acid

C. sulphuric acid

D. phosphoric acid

Q. 81 Which one of the following statements is not correct?

A. all carbons in diamond are linked by carbon-carbon single bond

B. graphite is layered structure of which layers are held together by weak van der waals forces

C. graphite layers are formed by hexagonal rings of carbon atoms

D. graphite layers are held together by carbon-carbon single bond

Q. 82 Which one of the following is called dry ice?

A. solid carbon dioxide

B. liquid carbon dioxide

C. liquid nitrogen

D. liquid ammonia

Q. 83 The acidic semi digested food coming out of the stomach is neutralized by

A. pancreatic acid

B. duodenal secretion

C. large intestine secretion

D. bile juice

Q. 84 The oxygenated blood from the lungs is received by the

A. left auricle

B. left ventricle

C. right auricle

D. right ventricle

Q. 85 The oxygen evolved during photosynthesis comes from splitting of

A. water

B. carbon dioxide

C. oxygen

D. light

Q. 86 Which one of the following depicts the correct circuit of a reflex arc?

A. effector-sensory neuron-spinal cord-motor neuron-receptor

B. receptor-sensory neuron-spinal cord-motor neuron-effector

C. receptor-sensory neuron-brain-motor neuron-effector

D. sensory neuron-receptor-brain-effector-motor neuron

Q. 87 If one set of chromosomes for a given plant is represented as N; in case of double fertilization, the zygote and the endosperm nucleus of a diploid plant would have how many sets of chromosomes respectively?

A. N and 2N

B. 2N and 2N

C. N and 3N

D. 2N and 3N

Q. 88 Consider the figure. Which one of the following is the value of the resistance between points A and B in the circuit given above?

A. 2/5 R

B. 3/5 R

C. 3/2 R

D. 4R

Q. 89 The absolute zero temperature is 0 Kelvin. In ⁰C unit, which one of the following is the absolute zero temperature?

A. 0⁰C

B. -100⁰C

C. -273.15⁰C

D. -173.15⁰C

Q. 90 Consider the following statements about visible light, UV and X-rays:

1. The wavelight of the visible light is more than that of X-rays

2. The energy of X-ray photons is higher than that of UV light photons

3. The energy of UV light photons is less than that of visible light photons

which of the statements given above is/are correct?

A. 1,2,3

B. 1,2

C. 2,3

D. 1

Q. 91 The time period of oscillation of a simple pendulum having length L and mass of the bob m is given a T. If the length of the pendulum is increased to 4L and the mass of the bob is increased to 2m, then which one of the following is the new time period of oscillation?

A. T

B. 2T

C. 4T

D. T/2

Q. 92 The connecting cable of electrical appliance like electric iron, water heater or room heater contains three insulated copper wires of three different colors-red, green and black. Which one of the following is the correct colour code?

A. red-live wire, green-neutral wire, black-live wire

B. red-neutral wire, green-ground wire, black-live wire

C. red-live wire, green-ground wire, black- neutral wire

D. red-ground wire, green-live wire, black-neutral wire

Q. 93 The graphs between current (I) and voltage (V) for three linear resistors 1,2,3 are given in the figure and match it with the answer figures

A. (a)

B. (b)

C. (c)

D. (d)

Q. 94 Consider the following statements about a microscope and a telescope:

1. Both the eyepiece and the objective of a microscope are convex lenses

2. The focal length of the objective of a telescope is larger than the focal length of its

eyepiece

3. The magnification of a telescope increases with the increase in focal length of its

objective

4. The magnification of a microscope increases with the increase in focal length of its

objective

which of the statements given above are correct?

A. 1,3

B. 1,4

C. 2,3,4

D. 1,2,3

Q. 95 A planet has a mass M₁ and radius R₁. The value of acceleration due to gravity on its surface is g₁. There is another planet 2, whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet 2?

A. g₁

B. 2g₁

C. g₁/2

D. g₁/4

Q. 96 Match List-I with List-II and select the correct answer from the solution figure using the code given

A. (a)

B. (b)

C. (c)

D. (d)

Q. 97 Match List-I and List-II and select the correct answer using the code given in figure and match it with the solution figure

A. (a)

B. (b)

C. (c)

D. (d)

Q. 98 ‘Majuli’, the river island, is located in which one of the following rivers?

A. jamuna

B. padma

C. ganga

D. brahmaputra

Q. 99 Which one of the following Indian states has recorded negative growth of population as per census 2011?

A. manipur

B. mizoram

C. tripura

D. nagaland

Q. 100 Which one of the following types of cloud is characterized by continuous precipitation?

A. cirrocumbulus

B. cumulus

C. nimbostratus

D. cumulonimbus

Q. 101 Match List-I and List-II and select the correct answer using the code given in figure and match it with the solution figure

A. (a)

B. (b)

C. (c)

D. (d)

Q. 102 Which one of the following is not an agent of metamorphism?

A. heat

B. compression

C. decomposition

D. solution

Q. 103 The solution of which one of the following will have pH less than 7?

A. NaOH

B. KCl

C. FeCl₃

D. NaCl

Q. 104 Which one of the following is an oxidation-reduction reaction?

A. NaOH+HCl->NaCl+H₂O

B. CaO+H₂O->Ca(OH)₂

C. 2Mg+O₂->2MgO

D. Na₂SO₄+BaCl₂->BaSO₄+2NaCl

Q. 105 Which one of the following is not used as fertilizer?

A. ammonium nitrate

B. ammonium sulphide

C. ammonium phosphate

D. ammonium sulphate

Q. 106 Which one of the following is the chemical formula of gypsum?

A. CaSO₄.2H₂O

B. Ca₂SiO₄

C. 2CaSO₄.H₂O

D. CaSO₄

Q. 107 Which one of the following statements about the law of conservation of mass is correct?

A. a given compound always contains exactly same proportion of elements

B. when gases combine in a reaction, they do so in a simple ratio by volume, provided all gases are at room temperature

C. Matter can neither be created nor destroyed

D. equal volumes of all gases at same temperature and pressure contain equal number

of molecules

Q. 108 The wavelength of X-rays is of the order of

A. 1 A

B. 1 μm

C. 1 mm

D. 1 cm

Q. 109 Consider the velocity and time graph in the figure:

Which one of the following is the value of average acceleration from 8 s to 12 s?

A. 8 m/s²

B. 12 m/s²

C. 2 m/s²

D. -1 m/s²

Q. 110 If the focal length of a convex lens is 50 cm, which one of the following is its power?

A. +2 dioptre

B. +0.02 dioptre

C. -0.5 dioptre

D. +0.5 dioptre

Q. 111 A ball is released from rest and rolls down an inclined plane, as shown in the following figure, requiring 4 s to cover a distance of 100 cm along the plane as shown in the figure. Which one of the option is correct value from the solution figure of angle θ that the plane makes with the horizontal?(g=1000 cm/s²)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 112 The coefficient of areal expansion of a material is 1.6*10⁻⁵K⁻¹. Which one of the following gives the value of coefficient of volume expansion of this material?

A. 0.8*10⁻⁵K⁻¹

B. 2.4*10⁻⁵K⁻¹

C. 3.2*10⁻⁵K⁻¹

D. 4.8*10⁻⁵K⁻¹

Q. 113 The refractive indices of two media are denoted by n₁ and n₂, and the velocities of light v₁ and v₂. If n₁/n₂ is 1.5, which one of the following statements is correct?

A. v₁ is 1.5 times v₂

B. v₂ is 1.5 times v₁

C. v₁ is equal to v₂

D. v₁ is 3 times v₂

Q. 114 Which one of the following greenhouse gases is in largest concentration in the atmosphere

A. chlorofluorocarbon

B. nitrous oxide

C. carbon dioxide

D. methane

Q. 115 Match List-I and List-II and select the correct answer using the code given in figure and match it with the solution figure

A. (a)

B. (b)

C. (c)

D. (d)

Q. 116 Match List-I and List-II and select the correct answer using the code given in figure and match it with the solution figure

A. (a)

B. (b)

C. (c)

D. (d)

Q. 117 Which one of the following is the correct descending order of Indian states in terms of sex ratio as per census 2011?

A. mizoram-manipur-tripura-meghalaya

B. tripura-manipur-meghalaya-mizoram

C. meghalaya-manipur-mizoram-tripura

D. manipur-meghalaya-tripura-mizoram

Q. 118 Steppe(temperature continental) climate is not experienced in which one of the following places?

A. pretoria

B. saskatchewan

C. perth

D. buenos aires

Q. 119 Which one of the following is not a process of chemical weathering?

A. solution

B. carbonation

C. oxidation

D. exfoliation

Q. 120 Which one of the following statements is correct for a plane mirror?

A. its focal length is zero

B. the size of the image of an object placed in front of the mirror is slightly less than that of the object

C. the image is virtual, erect and laterally inverted

D. the focal length is 200 cm

Q. 121 An object is placed in front of a convex mirror. Which one of the following statements is correct?

A. it will never form an inverted image

B. the image moves towards the focus when the object moves towards the mirror

C. depending on the position of the object with respect to the mirror, the image can be

inverted and real

D. the size of the image becomes larger than that of the object when the object is placed at a distance equal to half of the focal length

Q. 122 A circular coil of radius R having N number of turns carries a steady current I. The magnetic induction at the centre of the coil is 0.1 tesla. If the number of turns is doubled and the radius is halved, which one of the following will be the correct value for the magnetic induction at the centre of the coil?

A. 0.05 tesla

B. 0.2 tesla

C. 0.4 tesla

D. 0.8 tesla

Q. 123 Which one among the following is not a fundamental right under the constitution of india?

A. right to equality

B. right to freedom

C. right to citizenship

D. right against exploitation

Q. 124 Which one of the following crops was introduced by the portuguese in india?

A. opium

B. coffee

C. betel leaf

D. chili

Q. 125 Consider the following statements about merchant guilds of south india:

1. Ayyavole merchant guild was originally established in Aihole

2. Manigraman merchant guild was subordinated to the Anjuvannam merchant guild in the 13th century

Which of the statements given above is/are correct?

A. 1 only

B. 2 only

C. both 1,2

D. neither 1 nor 2

Q. 126 Which one of the following pairs is correctly matched and mark is with the solution figure?

A. (a)

B. (b)

C. (c)

D. (d)

Q. 127 When did the stamp act congress consisting of delegates from 9 of the 13 colonies of america meet in new york city?

A. 1763

B. 1764

C. 1765

D. 1766

Q. 128 Who among the following travellers was from italy and visited vijayanagar kingdom in the fifteenth century?

A. nikitin

B. fa-hien

C. bernier

D. nicolo conti

Q. 129 Where did the french east india company first establish its factory in india?

A. calicut

B. surat

C. pondicherry

D. masulipatnam

Q. 130 The central vigilance commission was established on the recommendation of which one of the following committees?

A. santhanam committee

B. dinesh goswami committee

C. tarkunde committee

D. narasimham committee

Q. 131 Which one of the following pairs is correctly matched and mark it with the solution figure

A. (a)

B. (b)

C. (c)

D. (d)

Q. 132 Which one of the following is the official mascot of the FIFA world cup, 2018?

A. fuleco

B. zakumi

C. pille

D. zabivaka

Q. 133 The headquarters of the proposed national sports university (as per the national sports university ordinance, 2018) will be set up in

A. chattisgarh

B. manipur

C. kerala

D. west bengal

Q. 134 Sentosa island, which was in news recently, is located in

A. singapore

B. china

C. australia

D. sri lanka

Q. 135 India, in june 2018,asserted that any mega connectivity project must respect sovereignty and territorial integrity of the countries. The project referred to above is

A. north-south corridor project

B. belt and road initiative

C. chabahar fort

D. panama canal expansion

Q. 136 Who among the following is not a member of G7?

A. france

B. germany

C. russia

D. japan

Q. 137 Who among the following leaders started the indian home rule league?

A. gopal krishna gokhale

B. mahatma gandhi

C. bal gangadhar tilak

D. J.B.Kripalani

Q. 138 Every judge of the supreme court of india is appointed by

A. the supreme court collegium

B. the cabinet

C. the president of india

D. the lok sabha

Q. 139 The nehru-mahalanobis strategy of development was implemented for the first time by which one of the following five-year plans?

A. first five-year plan

B. second five-year plan

C. third five-year plan

D. seventh five-year plan

Q. 140 Which one of the following is not a part of the directive principles of state policy as enshrined in the constitution on india?

A. equal justice and free legal aid

B. protection of monuments and places and objects of national importance

C. protection of personal law

D. separation of judiciary from executive

Q. 141 The word ‘socialist’ was inserted into the preamble to the constitution of india through which one of the following amendment acts?

A. 41st amendment act

B. 42nd amendment act

C. 43rd amendment act

D. 44th amendment act

Q. 142 The place of english east india company settlement in madras was known as

A. fort william

B. for St. George

C. elphinstone circle

D. marble palace

Q. 143 Which one of the following indian states(other than himalayan or NE states) ranked first in the composite water management index as per the report issued by the NITI Aayog in june 2018?

A. madhya pradesh

B. karnataka

C. gujarat

D. maharashtra

Q. 144 Who among the following is the ex office chairman of the north eastern council ?

A. the president of india

B. the prime minister of india

C. the union home minister

D. the union minister of state(independent charge), ministry of development of north

eastern region

Q. 145 Which one of the following is the theme of the world blood donor day, 2018?

A. blood connects us all

B. be there for someone else. Give blood. Share life

C. Give blood. GIve now. GIve often

D. Thank you for saving my life

Q. 146 ‘Serve Bhoj Yojana’, a scheme of the Government of India that seeks to reimburse Central share of CGST and IGST on food/ prasad/ langar/ bhandara offered by religious institutions, is introduced recently by which one of the following mnistrics?

A. the ministry of culture

B. the ministry of home affairs

C. the ministry of consumer affairs, food and public distribution

D. the ministry of social justice and empowerment

Q. 147 Dr. Bindeshwar Pathak, who was awarded Nikkei Asia Prize, 2018 for Culture and Community, is the founder of

A. Bachpan Bachao Andolan

B. PRS Legislative Research

C. Sulabh Sanitation and Social Reform Movement

D. Smile Foundation

Q. 148 Article 352 of the constitution of india contains provisions related to

A. financial emergency

B. failure of constitutional machinery in states

C. suspension of the enforcement of rights conferred in part III of the constitution

D. general emergency

Q. 149 The Theosophical Society was led by

A. A.O.Hume

B. Arthur Griffith

C. Annie Besant

D. Lord Dufferin

Q. 150 Which one of the following statements about Bipin Chandra Pal is correct?

A. He was a member of the moderate group of Congress

B. He was a member of the extremist group of Congress

C. He was the member of Defence in the first Government of Independent of India

D. He was the chief Minister of west bengal

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

NDA/NA(II) Exam 2016 General Ability Test Previous Year Paper

NDA/NA(II) Exam 2016 General Ability Test

Questions: 1 – 10

Read each sentence to find out whether there is any error in any part of the sentence

Q. 1 My friend was(a)/ habitual to drive a car(b)/ at very high speed(c). No error(d)

A. a

B. b

C. c

D. d

Q. 2 Being a day of national mourning(a)/ the offices were closed (b)/and the national flag flew half mast(c)/. No error(d)

A. a

B. b

C. c

D. d

Q. 3 If you are wanting to watch(a)/ the birds nesting(b)/ you must not let them see you(c). No error(d)

A. a

B. b

C. c

D. d

Q. 4 He does not listen to(a)/ what I say,(b)/ although I am advising him for a long time(c) No error(d).

A. a

B. b

C. c

D. d

Q. 5 It is most essential for us(a)/ to reach the station before noon(b)/ lest we should miss the train(c). No error(d)

A. a

B. b

C. c

D. d

Q. 6 I asked him(a)/ what had brought(b)/ him there.(c)/ No error(d).

A. a

B. b

C. c

D. d

Q. 7 The guards(a)/ dare not(b)/ to harm him(c)/. No error(d)

A. a

B. b

C. c

D. d

Q. 8 The Principal looks very worried(a)/because students are on strike for the Iast fifteen days as a protest against(b)/his disciplinary action against some miscreants.(c) No error. (d)

A. a

B. b

C. c

D. d

Q. 9 The king was embarrassed(a)/ to find evidences(b)/ against his own queen.(c)/No error(d)

A. a

B. b

C. c

D. d

Q. 10 As I prefer coffee than tea(a)/ my friends always take the trouble (b)/to get me a cup of coffee whenever I visit them(c) No error. (d)

A. a

B. b

C. c

D. d

Questions: 11 – 15

Select the word or groups of words that is most similar in meaning to that word which is in brackets

Q. 11 {Hospitality} is a virtue for which the natives of the East in general are highly admired.

A. duty of a doctor

B. generosity shown to guests

C. cleanliness in hospitals

D. kindness

Q. 12 House rent in cities like Murnbai or Delhi has risen to {astronomical} figures beyond the reach of even high-salaried people.

A. erorbitant

B. commercial

C. planetary

D. illogical

Q. 13 {Appropriate} technology holds the key to a nation’s development

A. modern

B. suitable

C. effective

D. growing

Q. 14 He was {enamoured} of his own golden voice.

A. very fond of

B. concerned with

C. obsessed with

D. imbued with

Q. 15 Some journalists are guilty of indulging in {yellow journalism}.

A. misrepresentation

B. vulgarization

C. sensational reporting

D. loud gestures

Questions: 16 – 20

Select the word or groups of words that is most opposite in meaning to that word which is in braces

Q. 16 The culprit was {sentenced} by the Court.

A. acquitted

B. punished

C. relieved

D. pardoned

Q. 17 {Thrifty} as he is, he can well afford to live within his means,

A. careless

B. instinctive

C. sentimental

D. extravagant

Q. 18 Do not give him a responsible job, he is {immature}.

A. thoughtful

B. cautious

C. calculating

D. seasoned

Q. 19 I was prepared {to show my hand} provided he agreed to do the same.

A. to yield

B. to shake hands

C. to conceal my plan

D. to lose my ground

Q. 20 Akbar the great was a {sagacious} ruler

A. haughty

B. cunning

C. rude

D. unwise

Questions: 21 – 30

Each of the following sentences has a blank space and four words giver after the sentence. Select whichever word you consider most appropriate for the blank space.

Q. 21 She has been lying in bed for the last fortnight, I hope she will ________

A. come out

B. pull out

C. pull through

D. go out

Q. 22 The path of progress is beset______ difficulties.

A. with

B. by

C. through

D. along

Q. 23 I feel______for those who are cruel to their children

A. sympathy

B. contempt

C. admiration

D. craving

Q. 24 Both the parties were keen to have an _____ settlement of the dispute.

A. enviable

B. inimical

C. worthy

D. amicable

Q. 25 I have come to know that the two brothers have __________.

A. fallen through

B. fallen out

C. fallen for

D. fallen short

Q. 26 Everybody finds his own work _______ whereas he feels that others have delightful jobs.

A. tedious

B. fabulous

C. unprofitable

D. indecent

Q. 27 The accident took place because of the criminal _______ of the driver.

A. performance

B. disregard

C. negligence

D. slackness

Q. 28 The belief in the _________ of vaccination is gaining ground.

A. immunity

B. prevalence

C. efficacy

D. workablity

Q. 29 Our new leader is a _______ young man and will take us forward

A. haughty

B. intoxicated

C. fanciful

D. dynamic

Q. 30 They found a world of ______ between what he said and what he did.

A. chaos

B. bitterness

C. difference

D. hope

Questions: 31 – 37

Each of the following items in this section consists of a sentence the parts of which have been jumbled. These parts have been labelled P, Q, R and S. Given below each sentence are four sequences namely (a), (b),. (c) and (d), You are required to rearrange the jumbled parts of the sentence and mark your response accordingly.

Q. 31 The statement {therefore you must listen carefully}(P)/ {what the speaker has said}(Q)/{in order to understand}(R)/ {will be made just once}(S). The proper sequence should be

A. SPRQ

B. SRQP

C. RSPQ

D. SPQR

Q. 32 The small boy who {broke his leg}(P)/{fell down}(Q)/{ and}(R)/{ climbed the wall}(S). The proper sequence should be

A. PSRQ

B. SQRP

C. QSRP

D. SPRQ

Q. 33 According to an engineer {might hit the market next year}(P)/{a newly developed air -cooler system}(Q)/ {that employed in conventional room coolers}(R)/{which is based on a principle radically different from}(S).The proper sequence should be

A. SQRP

B. RSQP

C. QSRP

D. PQRS

Q. 34 The clerk {on the desk}(P)/ {Ieft the money}(Q)/ {in the safe}(R)/ {which he should have locked up}(S). The proper sequence should be

A. SRQP

B. QRSP

C. PQRS

D. QPSR

Q. 35 Hardly had my brother descended from the plane {when the people}(P)/ {waved and cheered }(Q)/ {who had come to receive him}(R)/{ from the lounge}(S). The proper sequence should be

A. PQRS

B. RSPQ

C. RPQS

D. PRSQ

Q. 36 The essay {like that of the human face}(P)/ {because its variety is finite}(Q)/ {is a literary form}(R)/ {which is not easy to define}(S). The proper sequence should be

A. PQRS

B. PQSR

C. RSQP

D. RSPQ

Q. 37 The exhibition committee {attractive and useful}(P)/ {to make exhibition}(Q)/ {making efforts }(R)/ {has been}(S). The proper sequence should be

A. QSRP

B. SRQP

C. QPSR

D. SPQR

Questions: 38 – 50

Fill the part that is in brackets if any improvement is needed. Otherwise, select no improvement

Q. 38 My old teacher gave many poor students money {in spite of} he was poor.

A. even though

B. as if

C. however

D. no improvement

Q. 39 You {should to} read the newspapers regularly if you want to be well informed

A. ought

B. have to

C. should be

D. no improvement

Q. 40 If he had {listening to me} he would not have got lost

A. listened me

B. listened to me

C. listen me

D. no improvement

Q. 41 He asked for a bank loan {also} he didn’t have sufficient resources

A. because

B. even if

C. requiring

D. no improvement

Q. 42 I went to the shop to buy some {stationeries}

A. stationery

B. stationary

C. stationeries

D. no improvement

Q. 43 I have been waiting here {for} the last two hours.

A. from

B. since

C. by

D. no improvement

Q. 44 The table needs to be {painted}.

A. paint

B. painting

C. having paint

D. no improvement

Q. 45 It began to rain heavily just when I {prepare} to go out

A. prepared

B. was preparing

C. have prepared

D. no improvement

Q. 46 The couple seemed to love {one another} very much.

A. every other

B. each

C. each other

D. no improvement

Q. 47 It is high time that we {did} something

A. had done

B. would do

C. have done

D. no improvement

Q. 48 If l were a millionaire, l {would have helped} the poor.

A. am capable of helping

B. could have helped

C. would help

D. no improvement

Q. 49 The training programme was extended {for} a month.

A. from

B. until

C. since

D. no improvement

Q. 50 The painting {which} they were looking at was done by my sister

A. what

B. that

C. whom

D. not improvement

Questions: 51 – 56

The following 6 (Sit) items consist of two statements, Statement I and Statement II. Examine these two statements carefully and select the correct answer using the code given below :

Code

(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

(d) Statement I is false but Statement II is true

Q. 51 Statement I: Variability of annual rainfall is very high in western part of Rajasthan.

Statement II: Average annual rainfall is extremely low in western Rajasthan.

A. a

B. b

C. c

D. d

Q. 52 Statement I: Ozone is a tri-atomic molecule of oxygen.

Statement II : Ozone is concentrated mainly in the stratosphere.

A. a

B. b

C. c

D. d

Q. 53 Statement I: The laterite soils develop in areas with high temperature and high rainfall.

Statement II: Laterite soils are the result of intense leaching process.

A. a

B. b

C. c

D. d

Q. 54 Statement I: Too much salt content in diet could be one of the reason for kidney failure.

Statement II: High salt may cause high blood pressure.

A. a

B. b

C. c

D. d

Q. 55 Statement I : The city of Rome revived in n spectacular way in the 15th century.

Statement II :From the 15th century onwards, artists were known individually by name., not as member of a group or a guild, in Roman society.

A. a

B. b

C. c

D. d

Q. 56 Statement I: Chartism was the political reform campaign for democratic rights which swept over Britain between 1838 and 1848.

Statement II: The trade union movement declined by the 1830s as it failed to fulfil the aspirations of the working class.

A. a

B. b

C. c

D. d

Q. 57 ‘Sahel’ region of Sahara desert was associated with

A. core area of Sahara desert

B. southern moving edge of Sahara desert

C. northern fringe or Sahara desert bordering Mediterranean sea

D. another name of Sahara desert

Q. 58 Which one of the following pairs of a river and its tributary is not correctly matched ?

A. Godavari : Wainganga

B. Cauvery : Bhavani

C. Narmada : Amaravati

D. Krishna : Bhima

Q. 59 In which of the following countries, the Mediterranean type of Biome is found?

A. Chile

B. Kenya

C. Argentina

D. Bolivia

Q. 60 Arrange the following states in the order of their decreasing population size as per the census 2011 :

1.West Bengal

2.Bihar

3.Maharashtra

4.Andhra Pradesh

Select the correct order.

A. 2, 3, 1, 4

B. 3, 2, 1, 4

C. 1, 4, 3, 2

D. 3, 1, 4, 2

Q. 61 Match List I with List II and select the correct answer using the code given below the Lists :

Select correct answer from code:

A. a

B. b

C. c

D. d

Q. 62 Match List I with List II and select the correct answer using the code given below the Lists :

Select correct answer from code:

A. a

B. b

C. c

D. d

Q. 63 Identify the element having zero valency

A. Sulphur

B. Phosphorous

C. Lead

D. Radon

Q. 64 There are six electrons, six protons and six neutrons in an atom or an element. What is the atomic number of the element?

A. 6

B. 12

C. 18

D. 24

Q. 65 Which one of the following has a different number of molecules? (All are kept at normal temperature and pressure)

A. 3 gram of Hydrogen

B. 48 gram of Oxygen

C. 42 gram of Nitrogen

D. 2 gram of Carbon

Q. 66 Combination of one volume of nitrogen with three volumes of hydrogen produces

A. one volume of ammonia

B. two volume of ammonia

C. three volume of ammonia

D. one and a half volumes of ammonia

Q. 67 Consider the following statements about cactus:

1. The leaves are reduced to spines.

2. The stem does the photosynthesis. Which of the statements is/are true?

A. 1 only

B. 2 only

C. 1 and 2

D. neither 1 nor 2

Q. 68 In which of one or the following, methanogens, i.e., methane-producing bacteria are not present?

A. Rumen of cattle

B. Aerobic environment

C. Anaerobic sludge

D. Excreta of cattle

Q. 69 Malarial parasite is a

A. bacteria

B. protozoa

C. virus

D. fungus

Q. 70 With reference to biodiversity, which of the following statements is/are correct?

1.Species richness and high degree of endemism arc important criteria for identifying

biodiversity hot spots

2. Species diversity is highest in the tropics and decreases down the poles

3. Biodiversity conversation may be in situ as well as ex situ. Select the correct answer

A. 1 only

B. 2 and 3 only

C. 1,2 and 3 only

D. 1 and 3 only

Q. 71 It is difficult to kill viruses because they

A. consist of tough protein coat

B. are very small in size

C. lack cellular structure

D. spend a lot or time inside the host’s cells

Q. 72 When a ray of light enters a glass slab, then

A. only the frequency changes

B. frequency and velocity changes

C. frequency does not changes

D. frequency and wavelength changes

Q. 73 A ball is thrown vertically upward from the ground with a speed of 25.2 m/s. The ball will reach the highest point in its journey in

A. 5.14 s

B. 3.57 s

C. 2.57 s

D. 1.29 s

Q. 74 1 kilowatt hour is equal to

A. 36 x 10³ joule

B. 36 x 10⁵ joule

C. 10³ joule

D. 10⁵ joule

Q. 75 When sound waves are propagated through a medium, the physical quantity/quantities transmitted is/are

A. matter only

B. energy only

C. energy and matter only

D. energy, momentum and matter

Q. 76 Pressure is a scalar quantity because

A. it is the ration of force to area and both area and force are vectors

B. it is ration of magnitude of force to area

C. it is ration of component (normal to area0of force to area

D. none of above

Q. 77 A person is unable to read a newspaper without his glasses. He is most probably suffering from

A. myopia

B. presbyopia

C. astigmatisrn

D. hypermetropia

Q. 78 The free fall acceleration g increases as one proceeds, at sea level, from the equator toward either pole. The reason is

A. Earth is a sphere with same density everywhere

B. Earth is a sphere with different density at the polar regions than in the equatorial

regions

C. Earth is approximately an ellipsoid having its equatorial radius greater than its polar radius by 21 km

D. Earth is approximately an ellipsoid having its equatorial radius smaller than its polar radius by 21 km

Q. 79 Which one of the following statements is correct?

A. The measurement of mass taken by a spring weighing balance is incorrect at all places

B. The measurement of mass taken by a spring weighing balance is correct at all places

C. The measurement of mass taken by a spring weighing balance is correct at the places where the acceleration due to gravity is same with the place where the spring balance is calibrated for

D. A spring balance cannot be used to measure mass at any place

Q. 80 Which one of the following is not a correct force?

A. push force

B. gravitational force

C. frictional force

D. strain force

Q. 81 When a force of 1 newton acts on a mass of 1 kg which is able to move freely, the object moves in the direction of force with a/an

A. speed of 1 km/s

B. acceleration of 1 m/s²

C. speed of 1 m/s

D. acceleration of 1 km/s²

Q. 82 Which of the following items is used in the household wirings to prevent accidental fire in case of short circuit?

A. insulated wire

B. plastic switches

C. Non-metallic coatings on conducting wires

D. electric fuse

Q. 83 Which of the following are the features of the ideology of utilitarianism?

1.utilitarians believe that all value derives from land

2.The most celebrated spokesmen of utilitarianism were Jeremy Bentham and John Stuart Mill

3.Utilitarians were advocates of the idea that India could be ruled through indigenous laws and custom

4.Utilitarians were advocates of the idea of the `greatest good for the greatest number of people’.

Select correct answer from code:

A. 1 and 4 only

B. 2 and 4 only

C. 1, 2 and 4 only

D. 2 and 3

Q. 84 Who among the following invented the power loom that revolutionized the cotton textile industry?

A. Edmund Cartwright

B. Samuel Crompton

C. Richard Arkwright

D. James Hargreaves

Q. 85 Subsidiary Alliance was a system devised by

A. Lord Wellesley

B. Lord Dalhousie

C. Lord Canning

D. Lord Ripon

Q. 86 Consider- the following statements :

1. Periplus is a Greek word meaning sailing around

2. Erythraean was the Greek name for the Meditemmean sea.

Which of the statements given above is/are correct?

A. 1 only

B. 2 only

C. 1 and 2

D. neither 1 nor 2

Q. 87 Who among the following was defeated by Saina Nehwal to win the women’s title of the Australian Open. Super Series Badminton Tournament, 2016?

A. Sun Yu

B. Carolina Marin

C. Wang Yihan

D. Sung Ji Hyun

Q. 88 Consider the following statements:

He was an Indian journalist, editor and author. He was associated with the Statesman, the Guardian. the Times of India etc. He received the Ramnath Goenka Lifetime Achievement Award in 2013. He died in June 2016. The person referred to above is

A. B K Karanjia

B. K M Mathew

C. Inder Malhotra

D. Nanasaheb parulekar

Q. 89 Achyta Lahkar, who died recently, was a

A. sports administrator

B. wildlife photographer

C. mobile theatre personality

D. bureaucrat

Q. 90 Recently Microsoft announced its 26.2 billion dollar acquisition of which one of the following professional networking sites?

A. PartnerUp

B. PerfectBusiness

C. StartupNation

D. Linkedln

Q. 91 Which of the following statements concerning Mediterranean climatic region are correct?

1.It is found in the latitude range 30° to 45° northern arid southern hemisphere

2. Mediterranean climate experiences extreme temperature conditions

3. In Mediterranean climate, rainfall occurs mainly during summer season.

4. In Mediterranean climate, rainfall occurs mainly due to Westerlies.Select correct answer

A. 1, 2 and 4

B. 1 and 4 only

C. 1, 2 and 3

D. 3 and 4

Q. 92 Arrange the following states in decreasing order of their total area under forest cover :

1.Jharkhand

2. Chattisgarh

3. Arunachal Pradesh

4. Madhya Pradesh

A. 4 3 2 1

B. 4 2 3 1

C. 3 4 1 2

D. 2 1 3 4

Q. 93 Which of the following statements concerned Scheduled Castes (SC) population in India are correct?

1. The highest % of SC population out of total population of the state is found in Punjab

2. Bihar is the second largest state in respect of total SC population in India

3. Uttar Pradesh has the highest number of SC population in India

4. Among the Indian states, the lowest % of SC population out of the total population of the state is found in Goa

A. 1,2 and 3

B. 1 and 3

C. 2 and 4

D. 1,2 and 4

Q. 94 Match List I with Lisa II and select the correct answer using the code given below the lists :

Select the correct answer from code

A. a

B. b

C. c

D. d

Q. 95 Which one of the following species is not capable of showing disproportionation reaction?

A. ClO⁻

B. ClO2⁻

C. ClO3⁻

D. ClO4⁻

Q. 96 Which one of the following statements is correct

A. Covalent bonds are directional

B. Ionic bonds are directional

C. Both Covalent and ionic bonds are directional

D. Both Covalent and ionic bonds are non-directional

Q. 97 When one strikes a safety match, the first step is

A. burning of sulhur

B. decomposition of potassium chlorate into potassium chloride and oxygen

C. conversion of small amount of red phosphorous into white phosphorous

D. burning of glue and starch

Q. 98 The LPG cooking gas contains propane and butane as the constituents. A sulfur containing compound is added to the LPG, because

A. It lower the cost of production

B. it enhances the efficiency of LP

C. it facilitates easy detection of leakage of the gas

D. it assists in liquefying hydrocarbons

Q. 99 The genetic material of bacteria is found in

A. nucleus

B. cytoplasm

C. cell membrane

D. ribosome

Q. 100 A horse and a donkey can breed to produce mule which is an infertile animal.The infertility is because horse and donkey belong to different

A. class

B. order

C. species

D. genus

Q. 101 A plant having yellow leaves with dead spots has the deficiency of

A. potassium

B. magnesium

C. nitrate

D. phosphate

Q. 102 Flouride toothpaste is sometimes recommended because flouride

A. prevents plaque formation

B. hardens the enamel of the tooth

C. kills pathogenic bacteria

D. prevents tooth ache

Q. 103 Along a streamline flow of fluid

A. the velocity of all fluid particles at a given instant is constant

B. the speed of a fluid particle remains constant

C. the velocity of all fluid particles crossing a given position is constant

D. velocity of fluid particle remains constant

Q. 104 How is the kinetic energy of a moving object affected if the net work done on it is positive

A. decreases

B. increases

C. remains constant

D. becomes zero

Q. 105 A particle is executing simple harmonic motion_ Which one of the following statements about the acceleration of the oscillating particle is true?

A. It is always in the opposite direction to velocity

B. It is proportional to the frequency of oscillation

C. It is minimum when the speed is maximum

D. It decreases as the potential energy increases

Q. 106 Which one of the following four particles, whose displaement x and acceleration ax are related as follows, is executing simple harmonic motion?

A. aₓ = +3x

B. aₓ = +3x²

C. aₓ = -3x²

D. aₓ = -3x

Q. 107 If we plot a graph between volume V and inverse of pressure P for an ideal gas at constant temperature T, the curve so obtained is

A. straight line

B. circle

C. parabola

D. hyperbola

Q. 108 Which one of the following statements is correct?

A. The speed of sound waves in a medium depends upon the elastic property of the

medium but not on inertia property

B. The speed of sound waves in a medium depends upon the inertia property of the

medium but not on elastic property

C. The speed of sound waves in a medium depends neither on its elastic property nor

on its inertia property

D. The speed of sound waves in a medium depends both on elastic and inertia

properties of the medium

Q. 109 Which one of the following statements not correct?

A. Pitch of a sound is its characteristic by which we can generally differentiate between a male voice and a female voice

B. The loudness of sound is related to its frequency

C. A musical sound has certain well defined frequencies which are generally harmonics of a fundamental frequency

D. The timbre of a particular musical sound is related to the waveform of the sound

wave

Q. 110 A particle executes linear simple harmonic motion with amplitude of 2cm. When the particle is at 1cm from mean position, the magnitudes of the velocity and the acceleration are equal. Then its time period(in seconds) is

A. 2Π/√3

B. √3/2Π

C. √3/Π

D. 1/2Π√3

Q. 111 Which one of the following statements is not correct?

A. The longest wavelength of light visible to human eye is about 700 mm

B. The shortest wavelength of light visible to human eye is about 400 mm

C. The wavelength of gamma rays is longer than that of X-rays

D. The ability of a telescope to form separable images of close objects is called its

resolving power.

Q. 112 If the image of an object, formed by a concave mirror is virtual, erect and magnified, then the object is placed

A. at the principal focus

B. at the centre or curvature

C. beyond the centre or curvature

D. between the pole of the mirror and the principal focus

Q. 113 When three resistors, each having resistance r, are connected in parallel, their resultant resistance is x. If these three resistances are connected in series, then the total resistance will be

A. 3x

B. 3rx

C. 9x

D. 3/x

Q. 114 Which of the following was/were the feature(s) of Lenin’s New Economic Policy (NEP) for the Soviet Union?

1.Private retail trading was strictly forbidden

2.Private enterprise trading was strictly forbidden

3.Peasants were not allowed to sell their surplus

4.To secure liquid capital, concessions were allowed to foreign capitalists, but the State retained the option or purchasing the products of such concerns

A. 1 only

B. 2 and 3

C. 1,2 and 4

D. 4 only

Q. 115 which of the following was/were the reasons for the defeat of British during the American War of Independence?

1.The remoteness of the American Continent and the lack of good roads

2.The British authorities failed to rally the loyalist Americans

3.The Americans benefited from the extraordinary military leadership of George

Washington

4. The Americans had access to superior arms and ammunition

A. 1,2 and 4

B. 3 only

C. 2 and 3 only

D. 1,2 and 3

Q. 116 The industrial revolution in England had a profound impact on the lives of people. Which of the following statements are correct about that?

1.Women were the main workers in the silk, lace-making and knitting industries

2.Factory managers were well aware of the health risks of industrial work on children

3.Children Were often employed in textile factories

4.The novel ‘Hard Times’ by Charles Dickens was a severe critique of the horrors of

industrialization

A. 1,3

B. 1,2

C. 1,3,4

D. 3,4

Q. 117 Consider the following statements

1. British colonialism continued to grow steadily in the 18th and 19th centuries

2.Raw cotton for the textile industry in Britain during the industrial revolution needed to be imported

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. 118 Who among the following was the author of Neel Darpan, published in 1860?

A. Reverend James Long

B. Michael Madhusudan Dutta

C. Raja Ram Mohan Roy

D. Dinabandhu Mitra

Q. 119 Which one of the following organizations was started by Jyotirao Phule in 1873 ?

A. Prarthana Samaj

B. Bahujan Samaj

C. Justice party

D. Satyashodhak Samaj

Q. 120 Although used earlier by French and German writers, the term Industrial Revolution’ in English was first popularized by

A. Adam Smith

B. Arnold Toynbee

C. James Mill

D. Bertrand Russell

Q. 121 In the 19th century, the majority of the workers in Japan’s modern industries were mainly

A. Japanese men and children

B. Japanese women and Chinese men

C. Women

D. Japanese and Chinese men

Q. 122 Which of Ilse following statements regarding recent developments in international affairs is/are correct?

1.NATO’s defence ministers agree to boost support for Ukraine. with a comprehensive package of assistance whit will help it strengthen defence and to modernize its armed forces.

2.Israel announces plans for construction of dwelling units for Jewish settlers in a

Palestinian neighbour¬hood of East Jerusalem

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 123 As per the RBI guidelines, which one of the following is the minimum tenure of Masala Bonds that an Indian company can issue offshore?

A. 5 years

B. 4 years

C. 3 years

D. 2 years

Q. 124 Which of the following, statements about Krishi Kalyan Cess (KKC) is/are correct?

1.KKC is calculated in the same way as Service Tax is calculated

2.The current rate of KKC is 0-50%.

3. KKC is similar to the KKS (Krishi Kalyan Surcharge).

A. 1,2,3

B. 1,2

C. 2,3

D. 1 only

Q. 125 Which country won the Thomas Cup Badminton Championship, 2016?

A. Indonesia

B. Denmark

C. China

D. Malaysia

Q. 126 Match List I with List II and select the correct answer using the code given below the lists

A. a

B. b

C. c

D. d

Q. 127 The world’s largest biomass cookstove system for cooking in community kitchen has been installed at

A. Tirupati

B. Amritsar

C. Shirdi

D. Udipi

Q. 128 Which one of the following sectors is the largest contributor to carbon dioxide emissions from fuel consumption in India?

A. Electricity and heat production

B. Transport

C. Manufacturing industries and constructions

D. Others

Q. 129 As per census 2011, which one of the following states has the highest number of inhabited villages?

A. Uttar Pradesh

B. Odisha

C. Rajasthan

D. Maharashtra

Q. 130 The properly of electric current which is applicable in the fuse wire is

A. chemical effect of current

B. magnetic effect of current

C. heating effect of current

D. Optical property of current

Q. 131 Which one of the following statements is not correct?

A. The Si unit of charge is ampere-second

B. Debye is the unit of dipole moment

C. Resistivity of a wire of length l and area of cross-section a depends upon both I and a

D. The kinetic energy of an electron of mass m kg and charge e coulomb, when accelerated through a potential difference of V volt, is eV joule

Q. 132 Two balls, A and B, are thrown simultaneously, A vertically upward with a speed of 20 m/s from the ground and B vertically downward from a height of 40 m with the same speed and along the same line of motion. At what points do the two balls collide by taking acceleration due to gravity as 9.8m/s²

A. The balls will collide after 3s at a height of 30.2 m from the ground

B. The balls will collide after 2s at a height of 20.1 m from the ground

C. The balls will collide after 1s at a height of 15.1 m from the ground

D. The balls will collide after 5s at a height of 20 m from the ground

Q. 133 The setting time of cement is lowered by adding

A. oxides of aluminium

B. gypsum

C. oxides of magnesium

D. silica

Q. 134 Emulsion is known as a

A. colloidal solution of substances having different physical states

B. true solution

C. distillation mixture for making alcohols

D. colloidal solution of two liquids

Q. 135 If one mixes up ashes with animal fat, the substance received in the crude form is called

A. Pheromone

B. Soap

C. Cement

D. Concrete

Q. 136 Which of the following statements with regard to coverage rate of Aadhar cards during 2015 is/are correct?

1.The coverage rate Aadhar cards in western India is quite high and it is above 90 per cent in Gujarat

2.The coverage rate of Aadhar cards is the highest in southern India and it is almost 100 per cent in the states of Telangana and Andhra Pradesh

3.The penetration of Aadhar cards has been very low in north-eastern part of India and it is the lowest in Assam and Meghalaya

A. 2 only

B. 1,3

C. 2,3

D. 1,2,3

Q. 137 Which one of the following is the correct descending order of countries in terms of per capita availability of arable land?

A. India — China — Brazil

B. China — Brazil — India

C. Brazil — China — India

D. Brazil — India — China

Q. 138 Match List I with List II and select the correct answer using the code given below the lists :

A. a

B. b

C. c

D. d

Q. 139 Which of the following statements concerning temperature is/are correct?

1.In winter season isotherms Northern Hemisphere are more or

less circular on continents

2.Isotherms are parallel to latitude in Southern Hemisphere in oceans

3.Minimun temperature during winter is recorded in Northern Canada

A. 1,2

B. 1,3

C. 1,2,3

D. 2 only

Q. 140 Which of the following statement(s) concerning natural regions of the world is/are correct?

1.Equatorial climatic regions have less urbanization

2. Mediterranean climatic regions have high level of urbanization

3.Equatorial climatic regions have high concentration human population

4.Mediterranean climatic regions practice platation farming

A. 1,2

B. 1,2,3

C. 2,4

D. 1 only

Q. 141 Which one of the following gases gives acidic solution on dissolving in water

A. Hydrogen

B. Carbondioxide

C. Nitrogen

D. Oxygen

Q. 142 How many moles of hydrogen atom are present in one mole of Aluminium hydroxide?

A. 1 mole

B. 2 moles

C. 3 moles

D. 4 moles

Q. 143 The United Nations proclaimed 21 June as

A. International Mother Language Day

B. International Widows’ Day

C. International Day of Yoga

D. International Day against Drug Abuse and Illicit Trafficking

Q. 144 Who are Bhawana Kanth, Avani Chaturvedi and Mohana Singh?

A. Sprinters

B. Rock climbers

C. Fighter pilots

D. Mountaineers

Q. 145 Corpsider the following statements but the Constitution of India:

1.A Member of Parliament enjoys freedom of speech in the Parliament as a Parliamentary Privilege protected by the Constitution of India

2.The Constitution has vested the power to amend the Constitution in the Parliament

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 146 Which one of the following statements about the Union Executive in India is correct?

A. According to the Constitution of India, the total number of members of the Council of Ministers cannot exceed 20% of the total number of Members of the House of the People

B. The rank or the different Ministers is determined by the President

C. The Ministers are appointed by the President on the advice of the Prime Minister

D. Only a member of either House of Parliament can he appointed as a Minister

Q. 147 Which one of the following statements about Money Bill is correct?

A. A Bill shall be deemed to be a Money BiIl only if it provides for the imposition of fines or penalties

B. A Money Bill shall be introduced in the Rajya Sabha

C. The Rajya Sabha can reject the Money Bill

D. The Speaker of the Lak Sabha finally decides if it is a Money Bill, should any dispute about it arise

Q. 148 Which one of the following powers of the Prime Minister of India is codified in the Constitution of India itself?

A. The power of advising the President as regards the appoinLtment of other Ministers

B. The power to allocate business amongst the Ministers

C. The power to summon the meeting of the Cabinet

D. The power to transfer a Minister from one Department to another

Q. 149 The cylindrical stone seals were used in which civilization?

A. Harappan

B. Egyptian

C. Roman

D. Mesopotamiam

Q. 150 Which of the following statements with regards to the Civil Disobedience movement is/are correct?

1.The movement received a massive response from business groups and peasantry

2.The movement was marked by the mass participation of lawyers and students

A. 1 only

B. 1, 2

C. 2, 3

D. 1, 2, 3

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

NDA/NA(I) Exam 2016 General Ability Test Previous Year Paper

NDA/NA(I) Exam 2016 General Ability Test

Q. 1 When the bus was at full speed its breaks failed and an accident was __________

A. inevitable

B. undeniable

C. fatal

D. miserable

Q. 2 To explain his design to his visitors, the architect a simple plan on the blackboard.

A. built

B. finalised

C. sketched

D. arranged

Q. 3 Though Bonsai, a well-known art form, originated in China, it was by __________by the Japanese

A. cultivated

B. finished

C. perfected

D. enlarged

Q. 4 He is greatly admired for his_______________ behaviour.

A. decrepit

B. decadent

C. decorative

D. decorous

Q. 5 Would you mind ___________ to the Principal how the trouble started ?

A. remarking

B. saying

C. explaining

D. talking

Q. 6 Vaccination will make people immune __________________ certain diseases for a given period.

A. against

B. to

C. with

D. for

Q. 7 The two boys looked so alike that it was impossible to ______________ between them.

A. discriminate

B. discern

C. distinguish

D. identify

Q. 8 The campers ____________ their tents at the base of the mountain.

A. installed

B. dug

C. pitched

D. established

Q. 9 The enemy had captured him and his life was at stake, still he refused to __ the state secrets.

A. divulge

B. divert

C. indulge

D. invert

Questions: 10 – 20

Each item in this section consists of an word in quotation in given sentences. Each sentence is followed by four words. Select the word which is most nearly opposite in meaning to the underlined word

Q. 10 He handled the machine with “deft” fingers. (opposite of the word in ” “)

A. delicate

B. sturdy

C. quick

D. clumsy

Q. 11 I was deeply affected by his “urbane” behaviour.(opposite of the word in ” “)

A. rural

B. rude

C. irrational

D. indifferent

Q. 12 His “timidity” proved costly.(opposite of the word in ” “)

A. arrogance

B. boldness

C. skillfulness

D. cunning

Q. 13 Arrangements were made to handle the “mammoth” gathering tactfully.(opposite of the word in ” “)

A. significant

B. small

C. unruly

D. noisy

Q. 14 He was “engrossed” in his work when I walked in(opposite of the word in ” “)

A. occupied

B. inattentive

C. engaged

D. absent

Q. 15 These are the main. points of the “preceding” paragraph.(opposite of the word in ” “)

A. following

B. previous

C. first

D. last

Q. 16 He made a “shrewd” guess.(opposite of the word in ” “)

A. clever

B. wild

C. incorrect

D. discriminating

Q. 17 He is suffering from a “severe” cough,(opposite of the word in ” “)

A. violent

B. mild

C. bad

D. continuous

Q. 18 “Cumulatively”, the effect of these drugs is quite bad.(opposite of the word in ” “)

A. Individually

B. Obviously

C. Clearly

D. Collectively

Q. 19 He was “conspicuous” because of his colourful shirt.(opposite of the word in ” “)

A. charming

B. ugly

C. small

D. unnoticeable

Q. 20 He hates these “continual” arguments with his friend.(opposite of the word in ” “)

A. repeated

B. irrational

C. occasional

D. regular

Questions: 21 – 30

Each question in this section has a sentence with three labelled part (a), (b), (c).

Read each sentence to find out whether there is any error in any quotation part and indicate your response. If you not find any error, response should be indicated as (d).

Q. 21 She said that ‘she was understanding’ (a)/ ‘his point of view ‘(b)/’ very well’ (c)/. No Error(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 22 All the houses ‘having been washed away'(a)/ ‘by the floods’ (b)/ ‘the villagers sought shelter’ in the panchayat office. (c)/ No error(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 23 It is necessary for us ‘to familiarize with'(a)/ and ‘get used to'(b)/ the ways of the people ‘among whom we live'(c)/. ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 24 ‘The mother asked the child'(a)/ ‘why did she cry out'(b)/ ‘in her sleep'(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 25 ‘I asked him that'(a)/ ‘why her was angry'(b)/ ‘but he did not answer'(c)/’No error’

A. (a)

B. (b)

C. (c)

D. (d)

Q. 26 ‘Had I not taken ill'(a)/ I would ‘have sent you'(b)/ my research paper ‘much earlier'(c)/’No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 27 The barn owl helps the farmer ‘by destroying'(a)/ rats which could, ‘if left unchecked'(b)/ do a lot of ‘damage to the crops'(c)/. ‘No error’

A. (a)

B. (b)

C. (c)

D. (d)

Q. 28 He ‘had gone'(a)/ home three weeks ago and ‘was expected'(b)/ yesterday, but he ‘has not come'(c)/ yet. ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 29 We ‘must sympathize'(a)/ ‘for other'(b) ‘in their troubles'(c). ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 30 ‘The scientists in America ‘(a)/ ‘are trying for long'(b)/ ‘to discover the genes responsible for ageing'(c)/ ‘No errors’

A. (a)

B. (b)

C. (c)

D. (d)

Questions: 31 – 40

In this section, look at the word in quotation of each sentence. Below each sentence are given three possible substitutions for the underlined part. If one of them (a),(b) or (c) is better than the underlined part, indicate your response on the Answer sheet against the corresponding letter (a), (b) or (c). If none of the substitutions improves the sentence, indicate (d) as your response on the Answer Sheet. Thus a “No improvement” response will be signified by the letter (d)

Q. 31 When he heard the rhetorical speech of the leader, he was ‘carried along’ by his

enthusiasm

A. carried aloft

B. carried down

C. carried away

D. No improvement

Q. 32 After the heavy rains last week, the water in the lake ‘raised another two feet’

A. rose another two feet

B. arisen another two feet

C. would raise another two feet

D. no improvement

Q. 33 One can live and work in a town without being aware of the daily march of the sun acrossthe sky without ‘never’ seeing the moon and stars

A. seldom

B. hardly

C. ever

D. no improvement

Q. 34 Applications of those ‘who are not graduates’ will be considered

A. whom are graduates

B. whose are graduates

C. whom are only graduates

D. no improvement

Q. 35 It ‘is raining ‘ heavily all through this week

A. has rained

B. rains

C. rained

D. no improvement

Q. 36 The sparrow took no ‘notice about’ the bread

A. notice of

B. notice from

C. notice to

D. no improvement

Q. 37 As he spoke about his achievements, his ‘high’ claims amused us

A. big

B. tall

C. long

D. no improvement

Q. 38 We ought to ‘stand’ for what is right

A. stand at

B. stand on

C. stand up

D. no improvement

Q. 39 He enjoys ‘to tell stories’ to children

A. how to tell stories

B. telling stories

C. to narrate stories

D. no improvement

Q. 40 In a few minutes’ time, when the clock strikes six, I ‘would be waiting’ here for an hour

A. shall be waiting on

B. shall have been waiting

C. shall wait

D. no improvement

Questions: 41 – 50

Each item in this section consists of word in quotation in given sentences. Each sentence is followed by four words. Select the word which is most similar in meaning to the underlined word and mark your response in the answer sheet accordingly

Q. 41 Suddenly there was a bright flash, followed by a ‘deafening’ explosion

A. dangerous

B. terrifying

C. mild

D. very loud

Q. 42 He showed ‘exemplary’ courage during the crisis

A. usual

B. durable

C. commendable

D. some

Q. 43 When the new teacher entered the classroom, he found the pupils ‘restive’

A. at rest

B. idle

C. quiet

D. impatient

Q. 44 There is no ‘dearth’ of talent in this country

A. scarcity

B. availability

C. plenty

D. absence

Q. 45 The servants ‘retired’ to their quarters

A. entered

B. went away

C. ran away

D. mobilised

Q. 46 The navy gave ‘tactical’ support to the marines

A. sensitive

B. strategic

C. immediate

D. expert

Q. 47 A genius tends to ‘deviate’ from the routine way of thinking

A. dispute

B. disagree

C. distinguish

D. differ

Q. 48 He was greatly ‘debilitated’ by an attack of influenza

A. depressed

B. weakened

C. worried

D. defeated

Q. 49 His effort at helping the poor are ‘laudable’

A. welcome

B. sincere

C. good

D. praiseworthy

Q. 50 His conduct brought him ‘reproach’ from all quarters

A. rebuke

B. sympathy

C. indifference

D. remorse

Questions: 51 – 55

The following five items consist of two statements. Statement I and Statement II. Examine these two statements carefully and select the answers to these items using the code given below:

Code:

(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.

(d) Statement I is false but Statement II is true.

Q. 51 Statement I: Petroleum is a mixture of many different hydrocarbons of different densities

Statement II: The grade of petroleum depends mainly on the relative proportion of the

different hydrocarbons

A. (a)

B. (b)

C. (c)

D. (d)

Q. 52 Statement I: There is high salinity in Red Sea.

Statement II: Rate of evaporation is high in Red Sea

A. (a)

B. (b)

C. (c)

D. (d)

Q. 53 Statement I: Volcanic eruption is accompanied by earthquakes.

Statement II: Volcanoes erupt water vapours and dust particles in the atmosphere

A. (a)

B. (b)

C. (c)

D. (d)

Q. 54 Statement I: Plantation farming has mostly been practiced in humid tropics

Statement II: The soil of humid tropics is highly fertile

A. (a)

B. (b)

C. (c)

D. (d)

Q. 55 Statement I: India has wide variation in population density

Statement II: Factors like agricultural productivity and history of settlements have greatly influenced the population density pattern in India

A. (a)

B. (b)

C. (c)

D. (d)

Q. 56 A container is first filled with water and then the entire water is replaced by mercury. Mercury has a density of 13.6 * 10³ kg/m³. If X is the weight of the water and Y is the weight if mercury, then

A. X=Y

B. X=13.6Y

C. Y=13.6X

D. None of the above

Q. 57 Density of water is

A. maximum of 0⁰ C

B. minimum of 0⁰ C

C. maximum of 4⁰ C

D. minimum of -4⁰ C

Q. 58 The phosphorous used in the manufacture of safety matches is

A. red phosphorous

B. black phosphorous

C. white phosphorous

D. scarlet phosphorous

Q. 59 Which of the following is not a chemical change?

A. ripening of fruits

B. curdling of milk

C. freezing of water

D. digestion of food

Q. 60 One of the main causes of air pollution in cities is emissions from vehicles like cars and trucks. Cars emit various pollutants which are bad for human health when inhaled, like

1. Nitrogen oxide(NOₓ)

2. carbon monoxide(CO)

3. carbon dioxide(CO₂)

4. benzene

Which of the above pollutants are not tolerated by human beings even at very low levels?

A. 1 and 4 only

B. 1 and 2 only

C. 1,2 and 3 only

D. 1,2 and 4 only

Q. 61 Arrange the following centres of AIIMS from east to west:

1. Rishikesh

2. New delhi

3. Patna

4. Bhubaneswar

Select the correct answer using the code given below:

A. 4-3-1-2

B. 4-1-3-2

C. 3-4-2-1

D. 3-2-1-4

Q. 62 Suppose the force of gravitation between two bodies of equal masses is F. If each mass is doubled keeping the distance of separation between them unchanged, the force would become

A. F

B. 2F

C. 4F

D. F/4

Q. 63 A body has a free fall from a height of 20 m. After falling through a distance of 5 m, then body would

A. lose one-fourth of its total energy

B. lose one-fourth of its potential energy

C. gain one-fourth of its potential energy

D. gain three-fourth of its total energy

Q. 64 Soap is sodium or potassium salt of

A. Stearic acid

B. Oleic acid

C. Palmitic acid

D. All of the above

Q. 65 Mass of a particular amount of substance

1. is the amount of matter present in it

2. does not vary from place to place

3. changes with change in gravitational force

Select the correct answer using the code given below:

A. 1,2,3

B. 1,2 only

C. 2,3 only

D. 1 only

Q. 66 Which of the following substances are harmful for health if present in food items?

1. Pesticide residues

2. lead

3. metanil yellow

4. mercury

Select the correct answer using the code given below:

A. 1,2 only

B. 1,2,4 only

C. 3,4 only

D. 1,2,3,4 only

Q. 67 In India, glacial terraces known as ‘Karewas’ are found in

A. Sapt Kosi Valley

B. Jhelum Valley

C. Alakananda Valley

D. Teesta Valley

Q. 68 Structurally, the Meghalaya region is a part of

A. Shiwalik Range

B. deccan plateau

C. greater himalaya

D. aravalli range

Q. 69 Two bodies A and B are moving with equal velocities. The mass of B is double that of A. In this context, which one of the following statements is correct?

A. momentum of B will be double that of A

B. momentum of A will be double that of B

C. momentum of B will be four times that of A

D. momentum of both A and B will be equal

Q. 70 During solar eclipse

A. the earth comes in between the sun and the moon

B. the moon comes in between the sun and the earth

C. the moon comes exactly halfway between the earth and the sun

D. the sun comes in between the earth and the moon

Q. 71 The S.I unit of acceleration is

A. ms⁻¹

B. ms⁻²

C. cms⁻²

D. kms⁻²

Q. 72 An atom of carbon has 6 protons. Its mass number is 12. How many neutrons are present in an atom of carbon?

A. 12

B. 6

C. 10

D. 14

Q. 73 Which one of the following is a reduction reaction?

A. 2Mg(s)+O₂(g)->2MgO(s)

B. S(s)+O₂->SO₂(g)

C. 2HgO(s)->2Hg(l)+O₂(g)

D. Mg(s)+S(s)->Mg(s)

Q. 74 Which of the commonly used household item(s) release Bisphenol A(BPA) which is an endocrine disruptor and bad for human health?

1. steel utensils

2. Plastic coffee mugs

3. Aluminium utensils

4. Plastic water storage bottles

Select the correct answer using the code given below:

A. 1 only

B. 1,2 only

C. 2,4 only

D. 1,2,3 only

Q. 75 The Nagarjuna Sagar Project is located on which one of the following rivers?

A. godavari

B. krishna

C. kavery

D. mahanadi

Q. 76 Consider the following statements:

1. Rajmahal highlands consist of lava flow deposits

2. Bundelkhand geneiss belong to the oldest Achaean rocks of India

Which of the statements given below is/are correct?

A. 1 only

B. 2 only

C. both 1,2

D. neither 1 nor 2

Q. 77 An object is placed at the centre of curvature of a concave mirror of focal length 16 cm. If the object is shifted by 8 cm towards the focus, the nature of the image would be

A. real and magnified

B. virtual and magnified

C. real and reduced

D. virtual and reduced

Q. 78 A pencil is placed upright at a distance of 10 cm from a convex lens of focal length 15 cm. The nature of the image of the pencil will be

A. real,inverted and magnified

B. real, erect and magnified

C. virtual, inverted and reduced

D. virtual, erect and magnified

Q. 79 Which one of the following is a conventional energy source?

A. tidal energy

B. geothermal energy

C. solar energy

D. biomass energy

Q. 80 Which one of the following oxides of nitrogen is known as ‘anhydride’ of nitric acid?

A. N₂O

B. N₂O₃

C. NO₂

D. N₂O₅

Q. 81 Which of the following is the chemical name for baking soda?

A. sodium bicarbonate(sodium hydrogen carbonate)

B. sodium carbonate

C. potassium bicarbonate(potassium hydrogen carbonate)

D. potassium carbonate

Q. 82 Which of the following statements about DNA is/are correct?

1. DNA is the hereditary material of all living organisms

2. All segments of DNA code for synthesis of proteins

3. Nuclear DNA is double helical with two nucleotide chains which run anti-parallel

4. DNA is also found in mitochondria

select the correct answer using the code given below:

A. 1,2,3 only

B. 3,4 only

C. 1,3,4 only

D. 4 only

Q. 83 Which organisation prepares the topographical maps of India?

A. geographical survey of India

B. archaeological survey of India

C. survey of India

D. National atlas and thematic mapping organisation

Q. 84 Which one of the following is not an international boundary line?

A. dresden line

B. durand line

C. maginot line

D. 38th parallel

Q. 85 A lady is standing in front of a plane mirror at a distance of 1 m from it. She walks 60 cm towards the mirror. The distance of her image now from herself(ignoring the thickness of the mirror) is

A. 40 cm

B. 60 cm

C. 80 cm

D. 120 cm

Q. 86 The brightness of a tar depends on its

A. size and temperature only

B. size and distance from the earth

C. size, temperature and mass

D. size, temperature and distance from the earth

Q. 87 When a solid is heated, it turns directly into a gas. This process is called

A. condensation

B. evaporation

C. sublimation

D. diffusion

Q. 88 Which one of the following is water gas?

A. mixture of carbon monoxide and hydrogen

B. mixture of carbon monoxide and nitrogen

C. mixture of carbon dioxide and water vapour

D. mixture of carbon monoxide and water vapour

Q. 89 Which of the following statements are correct?

In honey bees

1. Males are haploid

2. workers are sterile and diploid

3. queen develops from diploid larvae that fed on royal jelly

4. honey is collected/made by males

select the correct answer using the code given below:

A. 1,2,3,4

B. 2,3 only

C. 1,2,3 only

D. 1,4 only

Q. 90 The Amarkantak Hills is the source of which of the following rivers?

1. narmada

2. Mahanadi

3. Tapti

4. Son

select the correct answer using the code given below:

A. 1,2 only

B. 2 only

C. 1,3,4 only

D. 1,2,4 only

Q. 91 Which of the following statements in the context of northern hemisphere is/are correct?

1. vernal equinox occurs on march 21

2. summer solstice occurs on december 22

3. autumnal equinox occurs on september 23

winter solstice occurs on june 21

A. 1 only

B. 1.3 only

C. 2,4 only

D. 1,2,3 only

Q. 92 A glass vessel is filled with water to the rim and a lid is fixed to it tightly. Then it is left inside a freezer for hours. What is expected to happen?

A. the water freezes to ice and the level of ice comes down

B. the water in the glass vessel simply freezes to ice

C. the glass vessel breaks due to expansion as water freezes to ice

D. the water does not freeze at all

Q. 93 A simple circuit contains 12 V battery and a bulb having 24 ohm resistance. When you turn on the switch, the ammeter connected in the circuit would read

A. 0.5 A

B. 2 A

C. 4 A

D. 5 A

Q. 94 Three resistors with magnitudes 2, 4 and 8ohm are connected in. parallel. The equivalent resistance of the would be

A. less than 2 ohm

B. more than 2 ohm but less than 4 ohm

C. 4 ohm

D. 14 ohm

Q. 95 Suppose you have four test tubes labelled as ‘A’, ‘B’, ‘C’ and ‘D’. ‘A’ contains plain water, ‘B’ contains solution of an alkali, ‘C’ contains solution of an acid, and ‘D’ contains solution of sodium chloride. Which one of these solutions will turn phenolphthalein solution pink ?

A. Solution ‘A’

B. Solution ‘B’

C. Solution ‘C’

D. Solution ‘D’

Q. 96 Which one of the following oxides dissolves in water?

A. CuO

B. Al₂O₃

C. Fe₂O₃

D. Na₂O

Q. 97 To prevent heart problems, blood of a normal healthy persqn should have © 1. Low choleserol level.

2. high HDL level.

3. high VLDL level.

4, high LDL level.

Select the correct answer using the code piven below :

(a) Land2only –

(b) 1,2 and 4 only

(c)

(d)

A. 1,2 only

B. 1,2,4 only

C. 3 and 4 only

D. 1, 2 and 8 only

Q. 98 Spruce and Cedar are tree varieties of

A. Equatorial forest

B. Temperate, coniferous forest

C. Monsoon forest

D. Temperate deciduous forest

Q. 99 ‘Sal’ tree is a

A. Tropical evergreen tree

B. Tropical semi-evergreen tree

C. Dry deciduous tree

D. Moist deciduous tree

Q. 100 Matter around us can exist in three different states, namely, solid, liquid and gas. The correct order of their compressibility is

A. Liquid < Gas < Solid

B. Solid < Liquid < Gas

C. Gas < Liquid < Solid

D. Solid < Gas < Liquid

Q. 101 The temperature at which a solid melts to become a liquid at the atmospheric pressure is called its melting point. The melting point of a solid is an indication of

A. strength of the intermolecular forces of attraction

B. strength of the intermolecular forces of repulsion

C. molecular mass

D. molecular size

Q. 102 Consider the circuit in the diagram:

The equivalent resistance of the circuit will be

A. 12 Ω

B. 8(11/2) Ω

C. 9(1/11) Ω

D. 24/25 Ω

Q. 103 Which one of the following elements will not react, with dilute HCl to produce H₂?

A. Hg

B. Al

C. Mg

D. Fe

Q. 104 Which of the following pairs in the figure of vector and disease is/are correctly matched ? Select the correct answer using the code given below :

A. 1,3,4 only

B. 3,4 only

C. 2 and 4 only

D. 2 only

Q. 105 Consider the following statements :

1. All Echinoderms are not marine.

2. Sponges are exclusively marine.

3. Insects are found in all kinds of habitats.

4. Many primates are arboreal.

Which of the statements given above is/are correct ?

A. 1,3,4 only

B. 3,4 only

C. 2,4 only

D. 3 only

Q. 106 Areas which are engines for economic growth

supported by quality infrastructure and complemented by an attractive fiscal package

are known as

A. Export Processing Zones

B. Duty Free Tariff Zones

C. Special Economic Zones

D. Technology Parks

Q. 107 Deserts, fertile plains and moderately forested mountains are the characteristic features of which one of the following regions of India?

A. South-Western border along Arabian Sea

B. Coromandel Coast

C. North-Eastern Frontier

D. North-Western India

Q. 108 A racing car accelerates on a straight road. from rest to a speed of 50 m/s in 25s. Assuming uniform acceleration of the car throughout, the distance covered in this time will be

A. 625 m

B. 1250 m

C. 2500 m

D. 50 m

Q. 109 A man’weighing 70 kg is coming down in a lift. If the cable.of the lift breaks suddenly, the weight of the man would become

A. 70 kg

B. 35 kg

C. 140 kg

D. zero

Q. 110 A given’ conductor carrying a current of 1 A produces an amount of heat equal to 2000 J. If the current through the conductor is doubled, the amount of heat produced will be

A. 2000 J

B. 4000 J

C. 8000 J

D. 1000 J

Q. 111 Which one of the following carbon compounds will not give a sooty flame ?

A. Benzene

B. Hexane

C. Naphthalene

D. Anthracene

Q. 112 Match List I with List II and select the correct answer using the code given in the figure and match with the solution figure

A. (a)

B. (b)

C. (c)

D. (d)

Q. 113 In Thar region, the shifting sand dunes are locally known as

A. Dhrian

B. Daurs

C. Dhoros

D. Dhaya

Q. 114 The impulse on a particle due to a force acting on it during a given time interval is equal to the change in its

A. force

B. momentum

C. work done

D. energy

Q. 115 Which one of the following statements with regard to expansion of materials due to heating is not correct?

A. As ice melts, it expands uniformly up to 4⁰ C

B. mercury thermometer works using the principle of expansion due to heating

C. small gap is kept between two rails to allow for expansion due to heating

D. the length of metallic wire increases when its temperature is increased

Q. 116 Which of the following pairs is/are correctly matched?

select the correct answer using the code given below:

A. 1,2,3 only

B. 1,2 only

C. 1,4 only

D. 2 only

Q. 117 Which one of the following is not a form of stored energy?

A. nuclear energy

B. potential energy

C. electrical energy

D. chemical energy

Q. 118 The motion of a car along a straight path is shown by the following figure:

The car starts from O and reaches at A, B and C at different instants of time. During its motion from O to C and back to B, the distance covered and the magnitude of the displacement are, respectively

A. 25 km and 60 km

B. 95 km and 35 km

C. 60 km and 25 km

D. 85 km and 35 km

Q. 119 Jelep La pass is located in

A. punjab himalayas

B. sikkim himalayas

C. kumaon himalayas

D. kashmir himalayas

Q. 120 What is the number of mole(s) of H₂(g) required to saturate one mole benzene?

A. 1

B. 2

C. 3

D. 4

Q. 121 Which one of the following pairs of the schedule in the constitution of India and its content is not correctly matched?

A. (a)

B. (b)

C. (c)

D. (d)

Q. 122 Consider the following statements :

1. The Constitution of India empowers the Parliament to form new States and to alter the areas, boundaries or names of existing States by passing a resolution in simple majority.

2. Jammu and Kashmir has been given special status under Article 370 of the Constitution 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. 123 The Speaker of the Lok Sabha may resign his office by writing, addressed to the

A. President of India

B. Prime Minister of India

C. Vice President of India

D. Deputy Speaker of the Lok Sabha

Q. 124 Who among the following is the founder of the ‘Bachpan Bachao Andolan’ ?

A. Shantha Sinha

B. Kuilaah Satyarent

C. Aruna Roy

D. Anil Agarwal

Q. 125 Which of the following are the features of Pradhan Mentri Jan Dhan Yojana?

1. Ensuring financial inclusion of the poor

2. Enhancing financial literacy

3. Provision for accidental insurance to account holders

4. Allowing bank accounts with zero balance

Select the correct answer using the code given” below:

A. 1 and 4 only

B. 1,2 and 3 only

C. 2 and 4 only

D. 1,2,3 and 4

Q. 126 The Election Commission recognizes a political party as a national party if

1. it secures at least six percent of the total valid -votes polled in four or more States in a general election to the Lok Sabha or to ‘the State Legislative Assemblies.

2. it wins at least four seats in a general election to the Lok Sabha from any State or States. , Select the correct answer using the code given

below :

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 127 Which one of the following is not a feature of the Nehru Mahalanobis model of

Development strategy ?

A. Development of capital goods industries

B. Major involvement of the State in the economy

C. Industrial deregulation and disinvestment in the public sector

D. Enhancing the scope and importance of the public sector

Q. 128 Which of the following best explains the stated broad vision and aspirations of the Twelfth Five Year Plan(2012-2017)?

A. faster, sustainable and more inclusive growth

B. modernisation of industries and strengthiening infrastructure

C. enhancing agricultural and rural incomes

D. checking inflation and strengthening non-economic variables like nutritional

requirements, health and family planning

Q. 129 Nabhah sparsam diptam is the motto of

A. central industrial security force

B. indian air force

C. ISRO

D. indian navy

Q. 130 Consider the following statements:

1. The amendment procedure has been provided in Article 368 of the constitution of India

2. The consent of the states is mandatory for all Amendments to the constitution of India Which of the statements given above is/are correct?

A. 1 only

B. 2 only

C. both 1,2

D. neither 1 nor 2

Q. 131 Which of the following statements relating to the Comptroller and Auditor General(CAG) of India is/are correct?

1. The CAG can attend the sittings of the Committee on Public Accounts

2. The CAG can attend the sittings of Lok Sabha and Rajya Sabha

3. The jurisdiction of CAG is co-extensive with powers of the Union Government

Select the correct answer using the code given below:

A. 1 only

B. 2,3 only

C. 1,2 only

D. 1,2,3 only

Q. 132 Which of the following statements relating to election as the President of India is/are correct?

1. A person above the age of thirty-five years is eligible for election as the President of India

2. The President of India is eligible for re-election for more than one term

3. A person is not eligible for election as the President of India if the person holds an office of profit

Select the correct answer using the code given below:

A. 1,2 only

B. 2 only

C. 1,2,3

D. 3 only

Q. 133 Which one of the following nations adopted its first democratic Constitution in September 2015?

A. bhutan

B. myanmar

C. nepal

D. singapore

Q. 134 Who among the following was defeated by Novak Djokovic in the final of the US Open Tennis Tournament Men’s Singles event (2015)?

A. Tommy Robredo

B. Fabio Fognini

C. Roger Federer

D. Pablo Cuevas

Q. 135 The citizens of India do not have which of the following Fundamental Rights?

A. right to reside and settle in any part of India

B. right to acquire, hold and disperse of property

C. right to practice any profession

D. right to form co-operative societies

Q. 136 Which one among the following Acts for the first time allowed Indians, at least theoretically, entry to higher posts in British Indian administration?

A. character act, 1813

B. character act, 1833

C. charles wood’s education despatch, 1854

D. indian councils act, 1861

Q. 137 Consider the Consider the following statements about Rashtrakuta kings :

1. They were ardent patrons of Shaivism and did not support other forms of religion.

2. They promoted only Sanskrit scholars and gave them large grants.

Which of the statements given above is/are correct ?

A. 1 only

B. 2 only

C. Both l and 2

D. Neither 1 nor 2

Q. 138 After a ban on unscientific coal mining and transportation of coal in this region by the National Green Tribunal, many of those engaged in the activity have been switching to turmeric farming for their livelihood. The region referred above is

A. Jaintia Hills, Meghalaya

B. Koriya, Chhattisgarh

C. Angul, Odisha

D. Bardhaman, West Bengal

Q. 139 Which of the following statements about the first act of the Revolt of 1857 is/are true ?

(1) It occurred in Meerut when two sepoys stole a superior officer’s rifle.

(2) It began when the Rani of Jhansi declared war on the British.

(3) It began when Mangal Pandey fired at a European officer in Meerut.

(4) It began when Mangal Pandey fired at a European officer in Barrackpore.

Select the correct answer using the code given below :

A. 2 only

B. 1, 2 and 3 only

C. 4 only

D. 1 and 4 only

Q. 140 Which of the following statements about Gandhiji’s Hind Swaraj writtén in 1909 is/are true?

1. Hind Swaraj offers a civilizational concept of the Indian nation.

2. Hind Swaraj states that Parliamentary democracy was necessary for the amelioration of the sufferings of Indians.

3. Hind Sweraj argues that Industrial capitalism was responsible for the immorality of

society.

Select the correct answer using the code given below:

A. 3 only

B. 1,2 and 3

C. 1 and 3 only

D. 1 only

Q. 141 Division of labour often involves

1. specialized economic activity.

2. highly distinct productive roles.

3. involving everyone in many of the same activities.

4. individuals engage in only a single activity and are dependent on others to meet their various needs.

Select the correct answer using below:

A. 1, 3 and 4 only

B. 1, 2 and 4 only

C. 3 only

D. 2 and 4 only

Q. 142 Who among the following is/was associated with Maharashtra Andhashraddha Nirmoolan Samiti?

A. Chandi Prasad Bhatt

B. Narendra Dabholkar

C. G.D. Agrawal

D. Kailash Satyarthi

Q. 143 Consider the following statements :

1. Warren Hastings set up the. Calcutta Madrassa for the study and teaching of Muslim law related subjects.

2. Jonathan Duncan started a Sanskrit | College at Varanasi for the study of Hindu law and philosophy.

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. 144 Consider the following statements about Sufism in India

1. Pilgrimage called ziyarat to tombs of Sufi saints is an important feature.

2. The most influential group of Sufis in India were the Chishtis.

Which of the statements above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 145 Which of the following thinkers and movements influenced the development of Gandhiji’s political ideas?

1. Henry David Thoreau

2. John Ruskin

3. John Milton

4. Jainism

Select the correct answer using the a given below :

A. 1 only

B. 1,2 and 3 only

C. 1, 2 and 4 only

D. 2 and 4 only

Q. 146 Consider the following statements:

1. The Arthashastra is the first Indian text to define a State.

2. The main concerns of the Arthashastra are theoretical issues like the origins of the state.

Which of the statements Shown above is/are correct ?

A. 1 only

B. 2 only

C. both 1,2

D. neither 1 nor 2

Q. 147 Which of the following is/are not FDi policy change(s) after 2010?

1. Permission of 100 percent FDI in automotive sector

2. Permitting of foreign airlines to make FDI up to 49 percent

3. Permission of up to 51 percent FDI under the government approval route in multi-brand retailing, subject to specified conditions

4. Amendment of policy on FDi in single-brand product retail trading for aligning with global practices.

Select the correct answer using the code given below:

A. 1 only

B. 2,4 only

C. 1,2 only

D. 1,2,3 only

Q. 148 Which of the following is/are the component/components of the Integrated Power Development Scheme launched by the Government of India recently?

1. Strengthening of sub-transmission and distribution networks in the urban areas

2. Metering of distribution transformers/feeders/consumers in the rural areas

Select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 149 Which of the following statements about Brahmo Samaj is/are correct?

1. The brahmo marriage act of 1872 allowed inter-caste and widow re-marriage only if the contracting parties declared themselves to be non-Hindus

2. Keshub Chandra Sen arranged the marriage of his minor daughter with the Maharaja or Burdwan

3. Keshub Chandra Sen’s followers broke away to form the Naba Brahmo Samaj

4. The Brahmo Samaj gre from a small elite group to a mass movement in the 19th century.

Select the correct answer using the code given below:

A. 1 only

B. 1,2 only

C. 2,3 only

D. 1,2,3,4

Q. 150 Which of the following statements about the aims of the United Nations is/are correct?

1. To foster a mutual appreciation of each other’ culture and literature among nations

2. To achieve international co-operation in solving problems of an economic, social,cultural or humanitarian character

3. To foster relations between scholars and academics in different countries

4. To organize international conferences

select the correct answer using the code given below:

A. 1 only

B. 1,2,4 only

C. 2 only

D. 1,2,3 only

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

NDA/NA(II) Exam 2016 Mathematics Previous Year Paper

NDA/NA(II) Exam 2016 Mathematics

Q. 1 Let S be a set of all distinct numbers of the form P/Q , where p, q ∈ { 1, 2, 3, 4, 5, 6 }. What is the cardinality of the set S?

A. 21

B. 23

C. 32

D. 36

Q. 2 If c > 0 and 4a + c < 2b, then ax² – bx + c = 0 has a root in which one of the following intervals?

A. (0, 2)

B. (2, 3)

C. (3, 4)

D. (–2, 0)

Q. 3 If A = {x ∈ R : x² + 6x – 7 < 0} and B = {x ∈R : x² +9x +14 > 0} , then which of the following is/are correct?

1. A ∩ B {X∈ R : –2 < x < 1}

2. A \ B = {x ∈R : –7 < x < –2}

Select the correct answer using the code given below:

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 4 If A is a square matrix of order 3 and det A= 5, then what is det[(2A)⁻¹] equal to?

A. 1/10

B. 2/5

C. 8/5

D. 1/40

Q. 5 What is ω¹⁰⁰ + ω²⁰⁰ + ω³⁰⁰ equal to, where w is the cube root of unity?

A. 1

B. 3ω

C. 3ω²

D. 0

Q. 6 If Re((z-1)/(z+1))= 0 where 2 = x + iy is a complex number, then which one of the following is correct?

A. z = 1+ i

B. |z| = 2

C. z = 1 – i

D. | z| = 1

Q. 7 Is equal to?

A. a

B. b

C. c

D. d

Q. 8 Out of 15 points in a plane, n points are in the same straight line. 445 triangles can be formed by joining these points. What is the value of n?

A. 3

B. 4

C. 5

D. 6

Q. 9 what is the imaginary part of z equal to?

A. 0

B. 1/2

C. √3/2

D. 1

Q. 10 If both of the roots of the equation x² – 2kx + k² – 4 = 0 lies between -3 and 5 then which of the following is correct?

A. -2 < k < 2

B. -5 < k < 3

C. -3 < k < 5

D. -1 < k < 3

Q. 11 What is the number of distinct solutions of the equation z²+ IzI = 0 (where z is a complex number)

A. 1

B. 2

C. 3

D. 5

Q. 12 How many geometric progressions is/are possible containing 27, 8 and 12 are three of its/ their terms?

A. 1

B. 2

C. 4

D. infinitely many

Q. 13 Let R be a relation from A= {1,2,3,4} to B={1,3,5} such that R={(a,b): a < b, where aεA and b ε B }. What is RoR⁻¹ equal to ?

A. {(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)}

B. {(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)}

C. {(3,3),(3,5),(5,3),(5,5)}

D. {(3,3)(3,4)(4,5)}

Q. 14 A five digit number divisible by 3 is to be formed using the digits 0,1,2,3 and 4 without repetition of digits. what is the number of ways this can be done?

A. 96

B. 48

C. 32

D. no number can be formed

Q. 15 Equation(in figure) is equal to?

A. ⁵²C₄

B. ⁵¹C₅

C. ⁵³C₄

D. ⁵²C₅

Questions: 16 – 18

Consider the following for the next three items that follow:

Let a,x,y,z,b in AP, where x+y+z=15. let a,p,q,r,b `be in HP , where p⁻¹+q⁻¹+r⁻¹ = 5/3

Q. 16 what is the value of ab?

A. 10

B. 9

C. 8

D. 6

Q. 17 what is the value of xyz?

A. 120

B. 105

C. 90

D. cannot be determined

Q. 18 what is the value of pqr?

A. 35/243

B. 81/35

C. 243/35

D. cannot be determined

Questions: 19 – 20

Consider the following for the next two items that follow:

The sixth term of an AP is 2 and its common difference is greater than 1.

Q. 19 What is the common difference of the AP so that the product of the first, fourth and fifth terms is greatest?

A. 8/5

B. 9/5

C. 2

D. 11/5

Q. 20 What is the first term of the AP so that the product of the first, fourth and fifth terms is greatest?

A. -4

B. -6

C. -8

D. -10

Questions: 21 – 22

Consider the following for the next two items that follows:

Q. 21 What is the value of c?

A. -1

B. 34

C. 35

D. 50

Q. 22 what is the value of a + b + c + d?

A. 62

B. 63

C. 65

D. 68

Questions: 23 – 24

Consider the following for the next two items that follows:

The interior angles of a polygon of n sides are in AP. The smallest angle is 120⁰ and the common difference is 5⁰

Q. 23 how many possible values can n have?

A. one

B. two

C. three

D. infinitely many

Q. 24 what is the largest interior angle of the polygon?

A. 160⁰ only

B. 195⁰ only

C. either 160⁰ or 195⁰

D. neither 160⁰ nor 195⁰

Q. 25 then, what is the value of the determinant of m cos θ – n sin θ ?

A. -1

B. 0

C. 1

D. 2

Q. 26 select the correct answer using the code given below:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Q. 27 Which of the following correct in respect of the system of equations x + y+ z =8 , x – y + 2z =6 and 3x – y + 5z =k?

1. They have no solution, if k =15

2. They have infinitely many solutions, if k = 20

3. They have unique solution, if k = 25

select the correct answer using the code given below:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Q. 28 which of the following is / are correct?

1. AB(A⁻¹B⁻¹) is a unit matrix.

2. (AB)⁻¹ = A⁻¹ ⁻B¹

Select the correct answer usin the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 29 which of the following is correct?

A. ln y is the GM of ln x, ln x, ln x and ln z

B. ln y is the AM of ln x, ln x, ln x and ln z

C. ln y is the HM of ln x, ln x, ln x and ln z

D. ln y is the AM of ln x, ln x , ln x and ln z

Q. 30 If the number 235 in decimal system is converted into binary then what is the resulting number?

A. (11110011)₂

B. (11101011)₂

C. (11110101)₂

D. (11011011)₂

Questions: 31 – 32

Consider the following for the next two items that follow :

let α and β be the roots of the equation x²-(1-2a²)x+(1-2a²)= 0

Q. 31 under what condition does the above equation have real roots?

A. a² < 1/ 2

B. a² < 1/2

C. a²≤ 1/2

D. a²≥ 1/2

Q. 32 under what conditions is 1/α² + 1/ β² < 1?

A. a² < 1/2

B. a² > 1/2

C. a² > 1

D. a² ε (1/3, 1/2 ) only

Q. 33 What is √[(1+ω²)/(1+ω)] equal to, where ω is the cube root of unity?

A. 1

B. ω

C. ω²

D. iω, where i = √-1

Q. 34 In an examination 70% students passed in physics, 80% students passed in chemistry , 75% students passed in mathematics and 85% students passed in biology , and x% students failed in all the four subjects. what is the minimum value of x?

A. 10

B. 12

C. 15

D. none of the above

Questions: 35 – 36

consider the following for the next two items that follow

for the system of linear equations 2x+ 3y + 5z = 9, 7x + 3y -2z = 8 and 2x + 3y + λz

= μ

Q. 35 under what condition does the above system of equations have infinitely many solutions?

A. λ=5 and μ≠ 9

B. λ=5 and μ = 9

C. λ= 9 and μ = 5

D. λ=9 and μ ≠ 5

Q. 36 under what conditions does the above system of equations have unique solutions?

A. λ=5 and μ = 9

B. λ≠5 and μ = 7 only

C. λ≠9 and μ has any real value

D. λ has any real value and μ ≠ 9

Q. 37 what is the number of odd integers between 1000 and 9999 with no digit repeated?

A. 2100

B. 2120

C. 2240

D. 3331

Q. 38 What is the greatest value of the positive integer n satisfying the condition 1 + 1/2 + 1/4 + 1/8 +…+ 1/2ⁿ⁻¹ < 2- 1/1000 ?

A. 8

B. 9

C. 10

D. 11

Questions: 39 – 40

consider the following for the next two items that follow:

2x²+3x- α =0 has roots -2 and β while the equation x² – 3mx + 2m² = 0 has both

roots positive where α > 0 and β > 0

Q. 39 what is the value of α?

A. 1/2

B. 1

C. 2

D. 4

Q. 40 If β,2,2m are in GP , then what is the value of β√m ?

A. 1

B. 2

C. 4

D. 6

Q. 41 sin A + 2 sin 2A + sin 3A is equal to which of the following?

1. 4 sin 2A cos² (A/2)

2. 2 sin 2A(sin A/2 + cos A/2)²

3. 8 sin A cos A cos² (A/2)

select the correct answer using the code given below:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Q. 42 If x = sin 70⁰ . sin 50⁰ and y = cos 60⁰ . cos 80⁰, then what is xy equal to ?

A. 1/16

B. 1/8

C. 1/4

D. 1/2

Q. 43 If sin θ₁ + sin θ₂ + sin θ₃ + sin θ₄ = 4, then what is the value of cos θ₁ + cos θ₂ + cos θ₃ + cos θ₄ ?

A. 0

B. 1

C. 2

D. 4

Q. 44 What is the value of (1+ cos π /8)(1+ cos 3π /8)(1+ cos 5π/8)(1+ cos 7π /8) ?

A. 1/2

B. 1/2 + 1/2√2

C. 1/2 – 1/2√2

D. 1/8

Q. 45 if x cos θ + y sin θ = z, then what is the value of (x sin θ – y cos θ)² ?

A. x² + y² – z²

B. x ² – y² – z²

C. x² – y² + z²

D. x² + y² + z²

Q. 46 What is the value of cos (2 cos⁻¹ 0.8)?

A. 0.81

B. 0.56

C. 0.48

D. 0.28

Q. 47 The top hill when observed from the top and bottom of a building of a height h is at angles of elevation p and q respectively. What is the height of the hill?

A. (h cot q)/(cot q – cot p)

B. (h cot p)/(cot p-cot q)

C. (2h tan p)/(tan p – tan q)

D. (2h tan q)/(tan q-tan p)

Q. 48 If sin 18⁰ =(√5 -1)/4 what is the value of sin 81⁰?

A. [√(3+√5)+√(5-√5)]/4

B. [√(3+√5)+√(5+√5)]/4

C. [√(3-√5)+√(5-√5)]/4

D. [√(3+√5)-√(5-√5)]/4

Q. 49 A moving boat is observed from the top of a cliff at 150m height. The angle of depression of the boat changes from 60⁰ to 45⁰ in 2 minutes. What is the speed of the boat in meters per hour?

A. 4500/√3

B. [4500(√3-1)]/√3

C. 4500√3

D. [4500(√3+1)]/√3

Q. 50 What is (1-tan 2 ⁰ cot 62⁰) / (tan 152⁰ – cot 88⁰) equal to

A. √3

B. -√3

C. √2 – 1

D. 1-√2

Q. 51 An equilateral triangle has one vertex at (0,0) and another at (3,√3). what are the coordinates of the third vertex?

A. (0,2√3) only

B. (3,-√3) only

C. (0,2√3) or (3,-√3)

D. neither (0,2√3) nor (3,-√3)

Q. 52 what is the equation of the right bisector of the line segment joining (1,1) and (2,3) ?

A. 2x+4y-11=0

B. 2x-4y-5=0

C. 2x-4y-11=0

D. x-y+1=0

Q. 53 what is the radius of the circle passing through the point (2,4) and having centre at the intersection of the lines x-y = 4 and 2x+3y + 7 =0

A. 3 units

B. 5 units

C. 3√3 units

D. 5√2 units

Q. 54 What is the equation of the hyperbola having latus rectum and electricity 8 and 3/√5 respectively?

A. x²/25 – y²/20 = 1

B. x²/40 – y²/20 =1

C. x²/40 – y²/30 =1

D. x²/30 – y²/25 = 1

Q. 55 if the point (a,a) lies between the lines Ix+yI = 2, then which of the following is correct?

A. IaI < 2

B. IaI < √2

C. IaI < 1

D. IaI < 1/ √2

Q. 56 What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x + 4y = 10 ?

A. 4x + 3y + 2 = 0

B. 4x – y + 2 = 0

C. 4x – 3y – 2 = 0

D. 4x – 3y + 2 = 0

Q. 57 If (a, b) is at unit distance from the line 8x + 6y + 1 =0 then which of the following conditions are correct?

1. 3a – 4b – 4 = 0

2. 8a + 6b + 11= 0

3. 8a + 6b – 9 = 0

select the correct answer using the code given below:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Q. 58 If the ellipse 9x² + 16y² =144 intercepts the line 3x + 4y = 12 then what is the length of the chord so formed?

A. 5 units

B. 6 units

C. 8 units

D. 10 units

Q. 59 A straight line cuts off an intercept of 2 units on the positive direction of x-axis and passes through the point (-3, 5). what is the foot of the perpendicular drawn from the point (3,3) on this line?

A. (1,3)

B. (2,0)

C. (0,2)

D. (1,1)

Q. 60 What is the eccentricity of rectangular hyperbola?

A. √2

B. √3

C. √5

D. √6

Questions: 61 – 62

Consider the following for the next two items that follows:

let Q be the image of the point P (-2,1,-5) in the plane 3x – 2y + 1=0

Q. 61 consider the following:

1. The coordinates of Q are (4, -3, -1)

2. PQ is of length more than 8 units

3. The point (1,-1, 3) is the midpoint of the line segment PQ and lies on the given plane

which of the above statemnets are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Q. 62 Consider the following:

1. The direction ratios of the line segment PQ are <3, -2, 2>.

2. The sum of the squares of direction cosines of the line segment PQ is unity.

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: 63 – 64

consider the following for the next two items that follows:

A line L passes through the point P (5,-6,7) and in parallel to the planes x+y+z=1 and 2x-y-2z = 3

Q. 63 what are the direction ratios of the line of intersection of the given planes?

A. <1,4,3>

B. <-1,-4,3>

C. <1,-4,3>

D. <1,-4,-3>

Q. 64 What is the equation of the line L?

A. (x-5)/-1 = (y+6)/4 = z-7/-3

B. (x+5)/-1 = (y-6)/4 = (z+7)/-3

C. (x-5)/-1 = (y+6)/-4 = (z-7)/3

D. (x-5)/-1 = (y+6)/-4 = (z-7)/-3

Questions: 65 – 66

Consider the following for the next two items that follows:

Q. 65 What is equal to vector c ?

A. a

B. b

C. c

D. d

Q. 66 Which of the following equations are correct?

A. a

B. b

C. c

D. d

Questions: 67 – 68

Consider the following for the next two items for that follow:

Q. 67 which of the following is the correct option?

A. a

B. b

C. c

D. d

Q. 68 which of the following is the correct options?

A. a

B. b

C. c

D. d

Q. 69 which of the following is correct?

A. a

B. b

C. c

D. d

Q. 70 which of the following is correct?

A. a

B. b

C. c

D. d

Q. 71 What is the domain of the function f(x) = 1/√(I x I – x) ?

A. (-∞,0)

B. (0,∞)

C. 0< x < 1

D. x > 1

Q. 72 consider the following in respect of the function f(x). which of the following is correct?

A. 1 only

B. 3 only

C. 2 and 3 only

D. 1 and 3 only

Q. 73 Let f: A → ℝ where A = ℝ∖(0) is such that f(x) = x + ∣x∣ / x. On which one of the following set is f(x) continuous?

A. A

B. B = (x ∈ ℝ: x ≥0 )

C. C = (x ∈ ℝ: x ≤0 )

D. D = ℝ

Q. 74 Which one of the following statements is correct in respect of the function f(x) = x³ sin x ?

A. it has local maximum at x = 0

B. it has local maximum at x = 0

C. it has neither maximum nor minimum at x = 0

D. it has maximum value 1

Q. 75 What is the area bounded by the curves I y I = 1- x² ?

A. 4/3 square units

B. 8/3 square units

C. 4 square units

D. 16/3 square units

Questions: 76 – 77

Consider the following function for the next two items that follows

Q. 76 which of the following statements is/are correct?

1. f(x) is increasing in the interval {-1,2}

2. f(x) is decreasing in the interval (2,3}

select the correct answer using the code given below.

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 77 which of the following statements are correct?

1. f(x) is continuous at x = 2

2. f(x) attains greatest value at x = 2

3. f(x) is differentiable at x = 2

select the correct answer using code given below

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Questions: 78 – 80

consider the following for the next three items that follow:

let f(x) = {I x I – I x-1I}²

Q. 78 what if f'(x) equal to when x > 1 ?

A. 0

B. 2x-1

C. 4x-2

D. 8x-4

Q. 79 what is f'(x) equal to when 0 < x < 1 ?

A. 0

B. 2x-1

C. 4x-2

D. 8x-4

Q. 80 which of the following equations is/are correct?

1. f(-2) = f(5)

2. f”(-2) + f”(0.5) + f”(3) = 4

select the correct answer by using the code given below

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Questions: 81 – 83

consider the following for the next three items that follow:

let f(x) = [x], where [ . ] is the greatest integer function and g(x) = sin x be two real valued functions over R

Q. 81 which of the following statements is correct?

A. bot f(x) and g(x) are continuous at x = 0

B. f(x) is continuous at x = 0 , but g(x) is not continuous at x = 0

C. g(x) is continuous at x = 0 but f(x) is not continuous at x = 0

D. both f(x) and g(x) are discontinuous at x = 0

Q. 82 which one of the following statements is correct?

A. a

B. b

C. c

D. d

Q. 83 which of the following statements are correct?

1. (fof)(x) = f(x)

2. (gog)(x) = g(x) only when x = 0

3. (go(fog))(x) can take only three values.

select the correct answer using the code given below:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 nd 3

Questions: 84 – 85

Consider the following for the next two items that follow

Q. 84 which one of the following statements is correct?

A. f(x) is a strictly decreasing function in (0,x)

B. f(x) is a strictly increasing function in (0,x)

C. f(x) is neither increasing nor decreasing function in (0,x)

D. f(x) is not decreasing function in (0,x)

Q. 85 which of the following statements is/are correct?

1. f(x) is right continuous at x = 0

2. f(x) is discontinuous at x = 1

select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Questions: 86 – 87

Consider the following for the next two items that follow:

consider the parabola y = x² + 7x + 2 and the straight line y = 3x-3

Q. 86 what are the coordinates of the point on the parabola which is closet to the

straight line?

A. (0,2)

B. (-2,-8)

C. (-7,2)

D. (1,10)

Q. 87 what is the shortest distance from the above point on the parabola to the line?

A. √10/2

B. √10/5

C. 1/√10

D. √5/4

Questions: 88 – 90

Consider the following for the next three items that follow:

Q. 88 which of the following statements is/are correct?

1. g(x) is differentiable at x =0

2. g(x) is differentiable at x = 2

select the correct answer

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 89 what is the value of the differential coefficient of g(x) at x = -2 ?

A. -1

B. 0

C. 1

D. 2

Q. 90 which of the following statements are correct ?

1. g(x) is continuous at x=0

2. g(x) is continuous at x = 2

3 g(x) is continuous at x = -1

select the correct answer:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Q. 91 choose the correct option

A. 2 f(1)

B. 0

C. 2f(-1)

D. 4f(1)

Q. 92 What is ∫[(x⁴-1)/x²√(x⁴+x²+1)] dx equal to?

A. √(x⁴+x²+1)/x + c

B. √(x⁴-1/x²+1)/x + c

C. √(x⁴+1/x²+1)/x + c

D. √(x⁴-x²+1)/x + c

Q. 93 What are the degree and order respectively of the differential equation satisfying the equation

A. 1,1

B. 1,2

C. 2,1

D. 2,2

Q. 94 what is the curve which passes through the point (1,1) and whose slope is 2y/x ?

A. circle

B. parabola

C. ellipse

D. hyperbola

Q. 95 if x dy = y dx + y² dy , y>0 and y(1) = 1, then what is y(-3) equal to?

A. 3 only

B. -1 only

C. both -1 and 3

D. neither -1 nor 3

Q. 96 what is the order of the differential equation dx/dy + ∫ y dx = x³ ?

A. 1

B. 2

C. 3

D. cannot be determined

Q. 97 which one of the following differential equations represents the family of straight lines which are at unit distance from the origin?

A. (y-x dy/dx)² = 1-(dy/dx)²

B. (y+x dy/dx)² = 1+(dy/dx)²

C. (y-x dy/dx)² = 1+(dy/dx)²

D. (y+x dy/dx)² = 1-(dy/dx)²

Q. 98 Function in figure is equal to

A. ( x + sec x) eˢᶦⁿ ˣ + c

B. ( x – sec x) eˢᶦⁿ ˣ + c

C. ( x + tan x) eˢᶦⁿ ˣ + c

D. ( x – tan x) eˢᶦⁿ ˣ + c

Q. 99 If function (in figure) then what is the value of the k?

A. 1/4

B. 1/2

C. 1

D. 2

Q. 100 what is the value equal to the given equation?

A. -232/5

B. -116/5

C. 116/5

D. 232/5

Q. 101 A special dice with number 1,-1,2,-2,0 and 3 is thrown thrice. what is the probability that the sum of the numbers occurring on the upper face is zero?

A. 1/72

B. 1/8

C. 7/72

D. 25/216

Q. 102 There is a 25% chance that it rains on any particular day. What i the probability that there is at least one rainy day within a period of 7 days?

A. 1-(1/4)²

B. (1/4)⁷

C. (3/4)⁷

D. 1-(3/4)⁷

Q. 103 A salesman has a 70% chance to sell a product to any customer. the behaviour of successive customers is independent. If two customers A and B enter, what is the

probability that the salesman will sell the product to consumer A or B?

A. 0.98

B. 0.91

C. 0.70

D. 0.49

Q. 104 A student appears for tests I,II and III. The student is considered successful if he passes in tests I,II or I,III or all of the three. The probabilities of the student passing in tests I,II and III are m, n and 1/2 respectively. If the probability of the student to be successful is 1/2 then which one of the following is correct?

A. m(1+n) = 1

B. n(m+1) = 1

C. m=1

D. mn = 1

Q. 105 Three candidates solve a question. odds in favour of the correct answer 5:2, 4:3 and what is the probability that at least two of them solve the question correctly?

A. 209/343

B. 134/343

C. 149/343

D. 60/343

Q. 106 consider the following statements:

1. the mean and median are equal in symmetric distribution

2.the range is the difference between the maximum value and minimum value in the data

3. the sum of the areas of the rectangles in the histogram is equal to the total area

bounded by the frequency polygon and horizontal axis

choose the correct one from the below

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Q. 107 The scores of 15 students in an examination were recorded as 10,5,8,16,18,20,8,10,16 mean, median and mode, an error is found. one of the values is wrongly written as 16 instead of 18. which of the following measures of central tendency will change?

A. mean and median

B. median and mode

C. mode only

D. mean and mode

Q. 108 for 10 observations on price(x) and supply(y) the following data was obtaines:

Σx=130,Σy=220,Σx² = 2288, Σy² = 5506

what is the line of regression of y on x?

A. y=0.91x + 8.74

B. y=1.02x + 8.74

C. y=1.02x – 7.02

D. y=0.91x – 7.02

Q. 109 from the data choose the correct option:

A. a

B. b

C. c

D. d

Q. 110 consider the following statements in respect of class intervals of grouped frequency distribution:

1. class intervals need not be mutually exclusive

2. class intervals should be exhaustive

3. class intervals need not be of equal width

choose correct statements

A. 1 and 2 only

B. 2 and 3only

C. 1 and 3 only

D. 1,2 and 3

Q. 111 A medicine is known to be 75% effective to cure a patient. If the medicine is given to 5 parents, what is the probability that at least one patient is cured by this medicine?

A. 1/1024

B. 243/1024

C. 1023/1024

D. 781/1024

Q. 112 choose the correct one according to the given data

A. 3/7

B. 3/4

C. 1/3

D. 4/7

Q. 113 A machine has three parts A,B and C, whose chances of being defective are 0.02,0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. what is the probability that the machine will not stop working?

A. 0.06

B. 0.16

C. 0.84

D. 0.94

Q. 114 Three independent events A₁, A₂, A₃ occur with probabilities P(Aᵢ) = 1/1+ i , i = 1, 2, 3. What is the probability that at least one of three events occurs.

A. 1/4

B. 2/3

C. 3/4

D. 1/24

Q. 115 Two varieties x and y are uncorrelated and have standard deviation σₓ and σᵧ respectively. What is the correlation coefficient between x+y and x – y?

A. a

B. b

C. c

D. d

Q. 116 what is the mean age of this group of people?

A. 41.0

B. 41.5

C. 42.0

D. 42.5

Q. 117 if the covariance between x and y is 30 variance of x is 25 and variance of y is 144 then what is the correlation coefficient?

A. 0.4

B. 0.5

C. 0.6

D. 0.7

Q. 118 A coin is tossed three times. consider the following events:

A: no head appears

B: exactly one head appears

C: at least two heads appear

which one of the following is correct?

A. (A U B) ∩ (A U C) = B U C

B. (A ∩ B’) U (A ∩ C’) =B’ U C’

C. A ∩ (B’ U C’) = A U B U C

D. A ∩ (B’ U C’) = B’ ∩ C’

Q. 119 In a series of 3 one day cricket matches between teams A and B of a college, the probability of team A winning or drawing are 1/3 and 1/6 respectively. if a win, loss or draw gives 2, 0 and 1 point respectively , then what is the probability that team A will score 5 points in the series?

A. 17/18

B. 11/12

C. 1/12

D. 1/18

Q. 120 let the random variable X follow B(6,p). If 16 P(X =4) = P(X=2), then what is the value of p?

A. 1/3

B. 1/4

C. 1/5

D. 1/6

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

NDA/NA(I) Exam 2016 Mathematics Previous Year Paper

NDA/NA(I) Exam 2016 Mathematics

Q. 1 Suppose ω is a cube root of unity with ω ≠ 1. Suppose P and Q are the points on the complex plane defined by ω and ω² . If O is the origin , then what is the angle between OP and OQ?

A. 60°

B. 90°

C. 120°

D. 150°

Q. 2 Suppose there is a relation * between the positive numbers x and y given x*y if and only if x ≤ y². Then which one of the following is correct?

A. * is reflexive but not transitive and symmetric

B. * is transitive but not reflexive and symmetric

C. * is symmetric and reflexive but not transitive

D. * is symmetric but not reflexive and transitive

Q. 3 If x² – px + 4 > 0 for all real values of x, then which one of the following is correct?

A. | p | < 4

B. | p | ≤ 4

C. | p | > 4

D. | p | ≥ 4

Q. 4 If z = x + iy = ( 1/√2 – i/√2 )⁻²⁵ , where i = √-1, then what is the fundamental amplitude of (z – √2)/(z – i√2) ?

A. π

B. π/2

C. π/3

D. π/4

Q. 5 If f(x₁) – f(x₂) = f( (x₁ – x₂)/(1 – x₁.x₂) ) for x₁,x₂ ∈ (-1, 1), then what is f(x) equal to?

A. ln( (1 – x)/(1 + x) )

B. ln( (2 + x)/(1 – x) )

C. tan⁻¹(1 – x)/(1 + x) )

D. tan⁻¹(1 + x)/(1 – x) )

Q. 6 What is the range of the function y = x²/(1 + x²) where x ∈ ℝ?

A. [0, 1)

B. [0, 1]

C. (0, 1)

D. (0, 1]

Q. 7 A straight line intersects x and y axes at P and Q respectively. If (3, 5) is the middle point of PQ, then what is the area of the triangle OPQ?

A. 12 square units

B. 15 square units

C. 20 square units

D. 30 square units

Q. 8 If a circle of radius b units with centre at (0, b) touches the line y = x – √2, then what is the value of b?

A. 2 + √2

B. 2 – √2

C. 2√2

D. √2

Q. 9 Consider the function f(θ) = 4( sin² θ + cos⁴ θ ). What is the maximum value of the function f(θ) ?

A. 1

B. 2

C. 3

D. 4

Q. 10 Consider the function f(θ) = 4( sin² θ + cos⁴θ ). What is the minimum value of the function f(θ)?

A. 0

B. 1

C. 2

D. 3

Q. 11 Consider the function f(θ) = 4( sin² θ + cos⁴ θ ). Consider the following statements : 1. f(θ) = 2 has no solution. 2. f(θ) = 7/2 has a solution. 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. 12 Consider the curves f(x) = x|x| – 1 and g(x) = { 3x/2, x>0 and 2x, x≤0}. Where do the curves intersect?

A. At (2, 3) only

B. At (-1, -2) only

C. At (2, 3) and (-1, -2)

D. Neither at (2, 3) nor at (-1, -2)

Q. 13 Consider the curves f(x) = x|x| – 1 and g(x) = { 3x/2, x>0 and 2x, x≤0}. What is the area bounded by the curves?

A. 17/6 square units

B. 8/3 square units

C. 2 square units

D. 1/3 square units

Q. 14 Consider the function f(x) = 27( x²/³ – x ) / 4 . How many solutions does function f(x) = 1 have?

A. One

B. Two

C. Three

D. Four

Q. 15 Consider the function f(x) = 27( x²/³ – x ) / 4 . How many solutions does the function f(x) = -1 have?

A. One

B. Two

C. Three

D. Four

Q. 16 Consider the functions f(x) = x.g(x) and g(x) = [1/x] where [.] is the greatest integer function. what is ∫1/3→1/2( g(x) ) dx equal to?

A. 1/6

B. 1/3

C. 5/18

D. 5/36

Q. 17 Consider the functions f(x) = x.g(x) and g(x) = [1/x] where [.] is the greatest integer function. What is ∫1→1/3 f(x)dx equal to?

A. 37/72

B. 2/3

C. 17/72

D. 37/144

Q. 18 Consider the function f(x) = | x – 1 | + x² where x ∈ ℝ. Which one of the following statements is correct?

A. f(x) is continuous but not differentiable at x = 0

B. f(x) is continuous but not differentiable at x = 1

C. f(x) is differentiable at x = 1

D. f(x) is not differentiable at x = 0 and x = 1

Q. 19 Consider the function f(x) = | x – 1 | + x² where x ∈ ℝ. Which one of the following statements is correct?

A. f(x) is increasing in (-∞, 1/2) and decreasing in (1/2, ∞)

B. f(x) is decreasing in (-∞, 1/2) and increasing in (1/2, ∞)

C. f(x) is increasing in (-∞, 1) and decreasing in (1, ∞)

D. f(x) is decreasing in (-∞, 1) and increasing in (1, ∞)

Q. 20 Consider the function f(x) = | x – 1 | + x² where x ∈ ℝ. Which one of the following statements is correct?

A. f(x) has local minima at more than one point in (-∞, ∞)

B. f(x) has local maxima at more than one point in (-∞, ∞)

C. f(x) has local minima at one point only in (-∞, ∞)

D. f(x) has neither local minima nor maxima in (-∞, ∞)

Q. 21 Consider the function f(x) = | x – 1 | + x² where x ∈ ℝ. What is the area of region bounded by x-axis, the curve y = f(x) and the two ordinates x = 1/2 and x = 1?

A. 5/12 square unit

B. 5/6 square unit

C. 7/6 square units

D. 2 square units

Q. 22 Consider the function f(x) = | x – 1 | + x² where x ∈ ℝ. What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates x = 1 and x = 3/2?

A. 5/12 square unit

B. 7/12 square unit

C. 2/3 square unit

D. 11/12 square unit

Q. 23 Consider the following statements:

1. The sequence { a₂ₙ } is in AP with common difference zero.

2. The sequence {a₂ₙ₊₁} is in AP with common difference zero. 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. 24 What is aₙ₋₁ – aₙ₋₄ equal to?

A. -1

B. 0

C. 1

D. 2

Q. 25 Consider the equation x + |y| = 2y. Which of the following statements are not correct?

1. y as a function of x is not defined for all real x.

2. y as a function of x is not continuous at x = 0

3.y as a function of x is differentiable for all x.

Select the correct answer using the code given below

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 26 Consider the equation x + |y| = 2y. Which of the following statements are not correct? What is the derivative of y as a function of x with respect to x for x < 0?

A. 2

B. 1

C. 1/2

D. 1/3

Q. 27 Consider the lines y = 3x, y = 6x and y = 9. What is the area of the triangle formed by these lines?

A. 27/4 square units

B. 27/2 square units

C. 19/4 square units

D. 19/2 square units

Q. 28 Consider the lines y = 3x, y = 6x and y = 9 The centroid of the triangle is at which one of the following points?

A. (3, 6)

B. (3/2, 6)

C. (3, 3)

D. (3/2, 9)

Q. 29 Consider the function: f(x) = (x – 1)²(x + 1)(x – 2)³ . What is the number of points of local minima of the function f( x )?

A. None

B. One

C. Two

D. Three

Q. 30 Consider the function: f(x) = (x – 1)²(x + 1)(x – 2)³ . What is the number of points of local maxima of the function f(x)?

A. none

B. One

C. Two

D. Three

Q. 31 Let f(x) and g(x) be twice differentiable functions on [0, 2] satisfying f’ ‘(x) = g’ ‘(x), f'(1) = 4, g'(1) = 6, f(2) = 3 and g(2) = 9. Then what is f(x) – g(x) at x = 4 equal to?

A. -10

B. -6

C. -4

D. 2

Q. 32 Consider the curves y =| x – 1 | and |x| = 2. What is/are the point(s) of intersection of the curves?

A. (-2, 3) only

B. (2, 1) only

C. (-2, 3) and (2, 1)

D. neither (-2, 3) nor (2, 1)

Q. 33 Consider the curves y =| x – 1 | and |x| = 2. What is the area of the region bounded by the curves and x-axis?

A. 3 square units

B. 4 square units

C. 5 square units

D. 6 square units

Q. 34 What is the value of f'(0)?

A. p³

B. 3 p³

C. 6 p³

D. -6 p³

Q. 35 What is the value of p for which f’ ‘(0) = 0?

A. -1/6 or 0

B. -1 or 0

C. -1/6 or 1

D. -1 or 1

Q. 36 Consider a triangle ABC which cos A + cos B + cos C = √3 sin π/3. What is the value of sin(A/2).sin(B/2).sin(C/2)?

A. 1/2

B. 1/4

C. 1/8

D. 1/16

Q. 37 Consider a triangle ABC which cos A + cos B + cos C = √3 sin π/3. What is the value of cos((A+B)/2).cos((B+C)/2).cos((C+A)/2)?

A. 1/4

B. 1/2

C. 1/16

D. None of the above

Q. 38 Given that tanα and tanβ are the roots of the equation x² + bx + c = 0 with b≠0. What is tan(α + β) equal to?

A. b(c – 1)

B. c(b – 1)

C. c(b – 1)^(-1)

D. b(c – 1)^(-1)

Q. 39 Given that tanα and tanβ are the roots of the equation x² + bx + c = 0 with b≠0. What is sin(α + β) secα secβ equal to?

A. b

B. -b

C. c

D. -c

Q. 40 Consider the two circles (x – 1)² + (y – 3)² = r² and x² + y² – 8x + 2y + 8 =0. What is the distance between the centres of the two circles?

A. 5 units

B. 6 units

C. 8 units

D. 10 units

Q. 41 Consider the two circles (x – 1)² + (y – 3)² = r² and x² + y² – 8x + 2y + 8 =0. If the circles intersect at two distinct points, then which one of the following is correct?

A. r = 1

B. 1 < r < 2

C. r = 2

D. 2 < r < 8

Q. 42 Consider the two lines x + y + 1 = 0 and 3x + 2y + 1 = 0. What is the equation of the line passing through the point of intersection of the given lines and parallel to x-axis?

A. y + 1 = 0

B. y – 1 = 0

C. y – 2 = 0

D. y + 2 = 0

Q. 43 Consider the two lines x + y + 1 = 0 and 3x + 2y + 1 = 0. What is the equation of the line passing through the point of intersection of the given lines and parallel to y-axis?

A. x + 1 = 0

B. x – 1 = 0

C. x – 2 = 0

D. x + 2 = 0

Q. 44 Consider the equation k sin x + cos2x = 2k – 7. If the equation possesses a solution, then what is the minimum value of k?

A. 1

B. 2

C. 4

D. 6

Q. 45 Consider the equation k sin x + cos2x = 2k – 7. If the equation possesses solution, then what is the maximum value of k?

A. 1

B. 2

C. 4

D. 6

Q. 46 Consider the function f( x ) = (a |ˣ| ⁺ ˣ – 1)/( [x] + x ) where [ . ] denotes the greatest integer function. What is lim x→ 0+ f( x ) equal to?

A. 1

B. ln a

C. 1 = a⁻¹

D. Love does not exist

Q. 47 Consider the function f( x ) = (a |ˣ| ⁺ ˣ – 1)/( [x] + x ) where [ . ] denotes the greatest integer function. What is lim x→ 0- f( x ) equal to?

A. 0

B. ln a

C. 1 – a⁻¹

D. Limit does not exist

Q. 48 Let z₁, z₂ and z₃ be the non-zero complex numbers satisfying z² = iz̅, where i = √-1. What is z₁ + z₂ + z₃ equal to?

A. i

B. -i

C. 0

D. 1

Q. 49 Let z₁, z₂ and z₃ be the non-zero complex numbers satisfying z² = iz̅, where i = √-1. Consider the following statements:

1. z₁.z₂.z₃ is purely imaginary.

2. z₁.z₂ + z₂.z₃ + z₃.z₁ is purely real.

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. 50 Given that logₓ y, log􀀁 x, logᵧ z are in GP, xyz = 64 and x³, y³, z³ are in AP. Which one of the following is correct?

x,y and z are

A. in AP only

B. in GP only

C. in both AP and GP

D. neither in AP nor in GP

Q. 51 Given that logₓ y, log􀀁 x, logᵧ z are in GP, xyz = 64 and x³, y³, z³ are in AP. Which one of the following is correct?

xy, yz and zx are

A. in AP only

B. in GP only

C. in both AP and GP

D. neither in AP nor in GP

Q. 52 Let z be a complex number satisfying | (z – 4)/(z – 8)| = 1 and | z/(z – 2)| = 3/2. What is |z| equal to?

A. 6

B. 12

C. 18

D. 36

Q. 53 Let z be a complex number satisfying | (z – 4)/(z – 8)| = 1 and | z/(z – 2)| = 3/2. What is |(z – 6)/(z + 6)| equal to?

A. 3

B. 2

C. 1

D. 0

Q. 54 A function f(x) is defined as follows: f(x) = { x + π for x∈[ -π, 0); n.cosx for x∈[ 0, π/2]; (x – π)² for x∈( π/2, π] }.

Consider the following statements:

1. The function f(x) is continuous at x = 0.

2. The function f(x) is continuous at x = 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. 55 A function f(x) is defined as follows: f(x) = { x + π for x∈[ -π, 0); n.cosx for x∈[ 0, π/2]; (x – π)² for x∈( π/2, π] }.

Consider the following statements:

1. The function f(x) is differentiable at x = 0.

2. The function f(x) is differentiable at x = 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. 56 Let α and β ( α < β ) be the roots of the equation s² + bx + c = 0, where b > 0 and c > 0. Consider the following :

1. β < -α

2. β < |α|.

Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 57 Let α and β ( α < β ) be the roots of the equation s² + bx + c = 0, where b > 0 and c > 0. Consider the following :

1. α + β + βα > 0

2. α²β + β²α > 0.

Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 58 Consider a parallelogram whose vertices are A(1,2), B(4,y), C(x,6) and D(3,5) taken in order. What is the value of AC² – BD²?

A. 25

B. 30

C. 36

D. 40

Q. 59 Consider a parallelogram whose vertices are A(1,2), B(4,y), C(x,6) and D(3,5) taken in order. What is the point of intersection of the diagonals?

A. (7/2, 4)

B. (3, 4)

C. (7/2, 5)

D. (3, 5)

Q. 60 Consider a parallelogram whose vertices are A(1,2), B(4,y), C(x,6) and D(3,5) taken in order. What is the area of parallelogram?

A. 7/2 square units

B. 4 square units

C. 11/2 square units

D. 7 square units

Q. 61 Let f: ℝ->ℝ be a function such that f(x) = x³ + x²f'(1) + xf”(2) + f”'(3) for x∈ℝ. What is f(1) equal to?

A. -2

B. -1

C. 0

D. 4

Q. 62 Let f: ℝ->ℝ be a function such that f(x) = x³ + x²f'(1) + xf”(2) + f”'(3) for x∈ℝ. What is f'(1) equal to?

A. -6

B. -5

C. 1

D. 0

Q. 63 Let f: ℝ->ℝ be a function such that f(x) = x³ + x²f'(1) + xf’ ‘(2) + f’ ‘ ‘(3) for x∈ℝ. What is f’ ‘(10) equal to?

A. 1

B. 5

C. 6

D. 8

Q. 64 Let f: ℝ->ℝ be a function such that f(x) = x³ + x²f'(1) + xf”(2) + f”'(3) for x∈ℝ.

Consider the following:

1. f(2) = f(1) – f(0)

2. f’ ‘(2) – f'(1) = 12 .

Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 65 A plane P passes through the line of intersection of the planes 2x – y + 3z = 2, x + y – z =1 and the point (1, 0, 1). What are the direction ratios of the line of intersection of the given planes?

A. <2, -5, -3>

B. <-1, -5, -3>

C. <2, 5, 3>

D. <1, 3, 5>

Q. 66 A plane P passes through the line of intersection of the planes 2x – y + 3z = 2, x + y – z =1 and the point (1, 0, 1). What is the equation of the plane P?

A. 2x + 5y – 2 = 0

B. 5x + 2y – 5 = 0

C. x + z – 2 = 0

D. 2x – y – 2z = 0

Q. 67 A plane P passes through the line of intersection of the planes 2x – y + 3z = 2, x + y – z =1 and the point (1, 0, 1). If the plane P touches the sphere x² + y² + z² = r², then what is r equal to?

A. 2 / √29

B. 4 / √29

C. 5 / √29

D. 1

Q. 68 Consider the function f(x) = | x² – 5x + 6 |. What is tf'(4) equal to?

A. -4

B. -3

C. 3

D. 2

Q. 69 Consider the function f(x) = | x² – 5x + 6 |. What is f’ ‘(2.5) equal to?

A. -3

B. -2

C. 0

D. 2

Q. 70 Let f(x) be the greatest integer functions and g(x) be the modulus function. What is (g ∘ f) (-5/3) – (f ∘ g)(-5/3) equal to?

A. -1

B. 0

C. 1

D. 2

Q. 71 Let f(x) be the greatest integer functions and g(x) be the modulus function. What is (f ∘ f) (-9/5) + (g ∘ g)(-2) equal to?

A. -1

B. 0

C. 1

D. 2

Q. 72 Consider a circle passing through the origin and the points (a, b) and (-b, -a). On which line does the centre of the circle lie?

A. x + y = 0

B. x – y = 0

C. x + y = a + b

D. x – y = a² – b²

Q. 73 Consider a circle passing through the origin and the points (a, b) and (-b, -a). What is the sum of the squares of the intercepts cut off by the circle on the axes?

A. ( a² + b²)/(a² – b²)²

B. 2( a² + b²)/(a – b)²

C. 4( a² + b²)/(a – b)²

D. None of the above

Q. 74 Let â, b̂ be two unit vectors and θ be the angle between them. What is cos(θ/2) equal to?

A. | â – b̂|/2

B. | â + b̂|/2

C. | â – b̂|/4

D. | â + b̂|/4

Q. 75 Let â, b̂ be two unit vectors and θ be the angle between them. What is sin(θ/2) equal to?

A. | â – b̂|/2

B. | â + b̂|/2

C. | â – b̂|/4

D. | â + b̂|/4

Q. 76 Consider the following statements :

1.There exists θ ∈ ( -π/2, π/2) for which tan⁻¹ ( tan θ ) ≠ θ.

2. sin⁻¹ (1/3) – sin⁻¹ (1/5) = sin⁻¹ ( 2√2( √3 – 1)/15) .

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. 77 Consider the following statements :

1. tan⁻¹ ( x ) + tan⁻¹ (1/x) = π

2. There exist x, y∈[-1, 1], where x≠y such that sin⁻¹ ( x ) + cos⁻¹ ( y ) = 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. 78 What are the order and degree respectively of the differential equation whose solution is y = cx + c² – 3c³/² + 2, where c is a parameter?

A. 1, 2

B. 2, 2

C. 1, 3

D. 1, 4

Q. 79 What is ∫ (-2→2) x dx – ∫ (-2→2) [ x ] dx equal to, where [ . ] is the greatest integer function?

A. 0

B. 1

C. 2

D. 4

Q. 80 If ∫ (-2→5) f(x)dx = 4 and ∫ (0→5) { 1 + f(x) }dx = 7 then what is ∫ (-2→0) f(x)dx equal to?

A. -3

B. 2

C. 3

D. 5

Q. 81 If lim x→0 Φ( x ) = a^2, where a ≠ 0, then what is lim x→0 Φ( x/a ) equal to?

A. a²

B. a⁻²

C. -a²

D. -a

Q. 82 What is lim x→0 e⁻¹/ˣ² equal to?

A. 0

B. 1

C. -1

D. Limit does not exist

Q. 83 If A is square matrix, then what is adj(A⁻¹) – (adj A)⁻¹ equal to?

A. 2 |A|

B. Null matrix

C. Unit matrix

D. None of the above

Q. 84 What is the binary equivalent of the decimal number 0.3125?

A. 0.0111

B. 0.1010

C. 0.0101

D. 0.1101

Q. 85 Let R be a relation on the set N of natural numbers defined by ‘nRm ⇔ n is a factor of m’. Then which one of the following is correct?

A. R is reflexive, symmetric but not transitive

B. R is transitive, symmetric but not reflexive

C. R is reflexive, transitive but not symmetric

D. R is an equivalence relation

Q. 86 What is ∫ 0→4π ( | cos x | )dx equal to?

A. 0

B. 2

C. 4

D. 8

Q. 87 What is the number of natural numbers less than or equal to 1000 which are neither divisible by 10 nor 15 nor 25?

A. 860

B. 854

C. 840

D. 824

Q. 88 (a, 2b) is the mid-point of the line segment joining the points (10, 06) and (k, 4). If a – 2b = 7, then what is the value of k?

A. 2

B. 3

C. 4

D. 5

Q. 89 Consider the following statements:

1. If ABC is an equilateral triangle then 3.tan( A + B ).tan C = 1.

2. If ABC is a triangle in which A = 78°, B = 66°, then tan(A/2 + C) < tan A.

3. If ABC is any triangle, then tan( A+B/2 ). sin(C/2) < cos(C/2).

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. 1 and 2

D. 2 and 3

Q. 90 If A = ( cos 12° – cos 36° )( sin 96° + sin 24° ) and B = (sin 60° – sin 12° )( cos 48° – cos 72° ), then what is A/B equal to?

A. -1

B. 0

C. 1

D. 2

Q. 91 What is the mean deviation from the mean of the numbers 10, 9, 21, 16, 24?

A. 5.2

B. 5.0

C. 4.5

D. 4.0

Q. 92 Three dice are thrown simultaneously. What is the probability that the sum on the three faces is at least 5?

A. 17/18

B. 53/54

C. 103/108

D. 215/216

Q. 93 Two independent events A and B have P(A) = 1/3 and P(B) = 3/4. What is the probability that exactly one of the two events A or B occurs?

A. 1/4

B. 5/6

C. 5/12

D. 7/12

Q. 94 A coin is tossed three times. What is the probability of getting head and tail alternatively?

A. 1/8

B. 1/4

C. 1/2

D. 3/4

Q. 95 if the total number of observations is 20, Σ(xi) = 1000 and Σ (xi²) = 84000, then what is the variance of the distribution?

A. 1500

B. 16000

C. 1700

D. 1800

Q. 96 A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is queen of spade?

A. 1/52

B. 1/13

C. 1/4

D. 1/8

Q. 97 If two dice are thrown, then what is the probability that the sum on the two faces is greater than or equal to 4?

A. 13/18

B. 5/6

C. 11/12

D. 35/36

Q. 98 A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired so that there is at least 80% probability that target is hit?

A. 5

B. 6

C. 7

D. None of the above

Q. 99 For two mutually exclusive events A and B, P(A) = 0.2 and P(A’∩B) 0.3. What is P(A| (A U B)) equal to?

A. 1/2

B. 2/5

C. 2/7

D. 2/3

Q. 100 What is the probability of 5 Sundays in the month of December?

A. 1/7

B. 2/7

C. 3/7

D. None of the above

Q. 101 if m is the geometric mean of (y/z)ˡᵒᵍ ⁽ʸᶻ⁾ , (z/x)ˡᵒᵍ ⁽ᶻˣ⁾ and (x/y)ˡᵒᵍ ⁽ˣʸ⁾ then what is the value of m?

A. 1

B. 3

C. 6

D. 9

Q. 102 A point is chosen at random inside a rectangle measuring 6 inches by 5 inches. What is the probability that the randomly selected point is at least one inch from the edge of the rectangle?

A. 2/3

B. 1/3

C. 1/4

D. 2/5

Q. 103 The mean of the series x₁, x₂, …, xₙ is X’. If x₂ is replaced by λᵢ then what is the new mean?

A. X’ – x₂ + λ

B. (X’ – x₂ – λ)/n

C. (X’ – x₂ + λ)/n

D. (nX’ – x₂ + λ)/n

Q. 104 For the data 3,5,1,6,5,9,2,8,6 the mean, median and mode are x, y and z respectively. Which one of the following is correct?

A. x = y ≠ z

B. x ≠ y = z

C. x ≠ y ≠ z

D. x = y = z

Q. 105 Consider the following statements in respect of a histogram :

1. The total area of the rectangles in a histogram is equal to the total area bounded by the corresponding frequency polygon and the x-axis.

2. When class intervals are unequal in a frequency distribution, the area of the rectangle is proportional to the 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. 106 A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times?

A. 1/2

B. 3/8

C. 1/4

D. 1/8

Q. 107 What is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets?

A. 60

B. 120

C. 500

D. 1000

Q. 108 If one root of the equation (l – m)x² + l.x + 1 = 0 is double the other and l is real, then what is the greatest value of m?

A. -9/8

B. 9/8

C. -8/9

D. 8/9

Q. 109 What is the number of four-digit decimal numbers (<1) in which no digit is repeated?

A. 3024

B. 4536

C. 5040

D. None of the above

Q. 110 What is a vector of unit length orthogonal to both the vectors î + ĵ + k̂ and 2 î + 3 ĵ -k̂?

A. (-4 î + 3 ĵ – k̂)/√26

B. (-4 î + 3 ĵ + k̂)/√26

C. (-3 î + 2 ĵ – k̂)/√14

D. (-3 î + 2 ĵ +k̂)/√14

Q. 111 If a̅, b̅ and c̅ are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then which one of the following is correct?

A. a̅ + b̅ + c̅ = 0̅

B. a̅ + b̅ + c̅ = unit vector

C. a̅ + b̅ = c̅

D. a̅ = b̅ + c̅

Q. 112 What is the area of the parallelogram having diagonals 3î + ĵ – 2k̂ and î – 3ĵ + 4k̂?

A. 5√5 square units

B. 4√5 square units

C. 5√3 square units

D. 15√2 square units

Q. 113 Consider the following in respect of the matrix A.

1. A² = -A

2. A³ = 4A .

Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 114 Which of the following determine have value zero? Select the correct answer using the code given below.

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 115 What is the acute angle between the lines represented by the equations y – √3 x – 5 = 0 and √3 y – x + 6 = 0?

A. 30°

B. 45°

C. 60°

D. 75°

Q. 116 The system of linear equations kx + y + z = 1, x + ky + z = 1 and x + y + kz = 1 has a unique solution under which one of the following conditions?

A. k ≠ 1 and k ≠ -2

B. k ≠ 1 and k ≠ 2

C. k ≠ -1 and k ≠ -2

D. k ≠ -1 and k ≠ -2

Q. 117 What is the number of different messages that can be represented by three 0’s and two 1’s?

A. 10

B. 9

C. 8

D. 7

Q. 118 If log(base a) (ab) = x, then what is log(base b)(ab) equal to?

A. 1/x

B. x/(x+1)

C. x/(1-x)

D. x/(x-1)

Q. 119 If y = log₁₀x + logₓ10 + logₓx + log₁₀10 then what is (dy/dx)ₓ₌₁₀ equal to?

A. 10

B. 2

C. 1

D. 0

Q. 120 Suppose ω₁ and ω₂ are two distinct cube roots of unity different from 1. Then what is (ω₁ – ω₂)² equal to?

A. 3

B. 1

C. -1

D. -3

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

NDA/NA(II) Exam 2015 Mathematics Previous Year Paper

NDA/NA(II) Exam 2015 Mathematics

Q. 1 Let X be the set of all persons living in Delhi. The persons a and b in X are said to be related if the difference in their ages is at most 5 years. The relation is

A. an equivalence relation

B. reflexive and transitive but not symmetric

C. symmetric and transitive but not reflexive

D. reflexive and symmetric but not transitive

Q. 2 The matrix A will have inverse for every real number x except for

A. x = (11±√5)/2

B. x = (9±√5)/2

C. x = (11±√3)/2

D. x = (9 ±√3)/2

Q. 3 If the value of the determinant is positive, where a≠b≠c, then value of abc

A. cannot be less than 1

B. is greater than -8

C. is less than -8

D. must be greater than 8

Q. 4 consider the following statements respect of the determinant where α,β are complementary angles

1. The value of the determinant is 1/√2 cos(α-β)/2

2. the minimum value of the determinant is 1/√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. 5 What is (1000000001)₂ – (0.0101)₂ equal to ?

A. (512.6775)₁₀

B. (512.6875)₁₀

C. (512.6975)₁₀

D. (512.0909)₁₀

Q. 6 If A is the matrix, then the matrix X for which 2X + 3A = 0 holds true is:

A. a

B. b

C. c

D. d

Q. 7 If z₁ and z₂ are complex numbers with Iz₁I = Iz₂I, then which of the following is/are correct?

1. z₁ = z₂

2. real part of z₁ = real part of z₂

3. imaginary part of z₁ = imaginary part of z₂

select the correct answer using the code given below.

A. 1 only

B. 2 only

C. 3 only

D. none

Q. 8 If A and B are two matrices given, then which of the following is/are correct?

1. A and B are commute

2. AB is a null matrix

select the correct answer using the code given below.

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 9 The number of real roots of the equation x² – 3IxI + 2 = 0 is

A. 4

B. 3

C. 2

D. 1

Q. 10 If the sum of roots of the equation ax² + bx + c=0 is equal to the sum of their squares, then

A. a²+b² = c²

B. a² + b² = a+ b

C. ab + b² = 2ac

D. ab – b² = 2ac

Q. 11 If A ={xεR: x²+6x-7<0} and B = {xεR:x²+9x+14>0}, then which of the following is/are correct?

1. )A∩B) = (-2,1)

2. (A∖B)=(-7,-2)

select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 12 A, B,C and D are four sets such that A∩B = C ∩ D =φ.consider the following:

1. A U C and B U D are always disjoint.

2.A ∩ C and B ∩ D are always disjoint.

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. 13 If A is an invertible matrix of order n and k is any positive real number, then the value of [det(KA)]⁻¹ det A

A. k⁻ⁿ

B. k⁻¹

C. kⁿ

D. nk

Q. 14 The value of the infinite product 6½ x 6½ x 6⅜ x 6¼ x… is

A. 6

B. 36

C. 216

D. ∞

Q. 15 If the roots of the equation x² – nx + m = 0 differ by 1, then

A. n²-4m-1=0

B. n²+4m-1=0

C. m²+4n+1=0

D. m²-4n-1=0

Q. 16 If different words are formed with all the letters of the ‘AGAIN’ and are arranged alphabetically among themselves as in a dictionary among themselves as in a dictionary, the word at the 50th place will be

A. NAAGI

B. NAAIG

C. IAAGN

D. IAANG

Q. 17 The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, is

A. 165

B. 364

C. 1001

D. 1365

Q. 18 In the expression of (√x + 1/3x²)¹⁰ the value of constant team (independent of x ) is

A. 5

B. 8

C. 45

D. 90

Q. 19 The value of sin² 5⁰ + sin² 10⁰ + sin² 15⁰ +sin² 20⁰ +…+sin² 90⁰ is

A. 7

B. 8

C. 9

D. 19

Q. 20 On simplifying (sin³ A + sin 3A)/sin A + (cos³ A – cos 3A)/cos A, we get

A. sin 3A

B. cos 3A

C. sin A + cos A

D. 3

Q. 21 The value of tan(2 tan⁻¹ 1/5 – π/4) is

A. -7/17

B. 5/16

C. 5/4

D. 7/17

Q. 22 Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15⁰ with the horizontal. The distance between the poles is approximately equal to

A. 36.3 m

B. 37.3 m

C. 38.3 m

D. 39.3 m

Q. 23 If g(x) = 1/f(x) and f(x) = x, x ≠ 0, then which one of the following is correct?

A. f(f(f(g(g(f(x)))))) = g(g(f((g(f(x)))))

B. f(f(g(g(g(f(x))))) = g(g(f(g(f(x)))))

C. f(g(f(g(g(g(f(x))))) = g(g(f(g(f(x)))))

D. f(f(f(g(g(f(x))))) = f(f(f(g(f(x))))

Q. 24 consider the following :

1. sin⁻¹ 4/5 + sin⁻¹ 3/5 = π/2

2. tan⁻¹ √3 + tan⁻¹ 1 = -tan⁻¹ (2+π√3)

which of the above is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 25 If A is an orthogonal matrix of order 3 and B, then which of the following is/are correct?

1.IABI = ± 47

2. AB = BA

select the correct answer using the code given below

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 26 If a,b,c are the sides of a Δ ABC, then (refer figure) where p > 1 a

A. always negative

B. always positive

C. always zero

D. positive if 1<p<2 and negative p>2

Q. 27 Id a,b,c are real number, then the value of the determinant is

A. 0

B. (a-b)(b-c)(c-a)

C. (a+b+c)²

D. (a+b+c)³

Q. 28 If the point z₁ = 1+i where i = √-1 is the reflection of a point z₂ = x+iy in the line iz̅-iz = 5, then the point z₂ is

A. 1+4i

B. 4 + i

C. 1-i

D. -1-i

Q. 29 If sin x + sin y= a and cos x + cos y = b, then tan² (x+y)/2+tan² (x-y)/2 is equal to

A. (a⁴ + b⁴+4b²)/(a²b²+b⁴)

B. (a⁴-b⁴+4b²)/(a²b²+b⁴)

C. (a⁴-b⁴+4a²)/(a²b²+a⁴)

D. none of the above

Q. 30 A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. from a point on the field , the angles of elevation of the bottom and tip of the flag staff are 30⁰ and 45⁰ respectively. Which of the following gives the best approximation to the height of the tower?

A. 3.90 m

B. 4.00 m

C. 4.10 m

D. 4.25 m

Questions: 31 – 33

For the next three items that follow:

consider the expansion of (1+x)²ⁿ⁺¹

Q. 31 If the coefficients of x^r and x^(r+1) are equal in the expansion, then r is equal to

A. n

B. (2n-1)/2

C. (2n+1)/2

D. n+1

Q. 32 The average of the coefficients of the two middle terms in the expansion is

A. A

B. B

C. C

D. D

Q. 33 The sum of the coefficients of all the terms in the expansion is

A. 2²ⁿ⁻¹

B. 4ⁿ⁻¹

C. 2 x 4ⁿ

D. none of the above

Q. 34 The nth term of A.P is (3+n)/4, then the sum of first 105 terms is

A. 270

B. 735

C. 1409

D. 1470

Q. 35 A polygon has 44 diagonals. The number of its side sides:

A. 11

B. 10

C. 8

D. 7

Q. 36 If p,q,r are in one geometric progression and a,b,c are in another geometric progression then ap, bq, cr are in

A. arithmatic progression

B. geometric progression

C. harmonic progression

D. none of the above

Questions: 37 – 38

For the next two items that follow:

consider a triangle ABC satisfying 2a sin² (C/2)+2c sin² (A/2) = 2a+2c-3b

Q. 37 The sides of the triangle are in

A. G.P

B. A.P

C. H.P

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

Q. 38 sin A, sin B, sin C are in

A. G.P

B. A.P

C. H.P

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

Q. 39 If the p=tan(-11π/6), q=tan (21π/6) and r = cot(283π/6), then which of the following is/are correct?

1. The value of p x r is 2.

2. p,q and r are in G.P.

select the correct answer using the code given below.

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 40 The number of ways in which 3 holiday tickets can be given to 20 employees of an organization if each employee is eligible for any one or more of the tickets, is

A. 1140

B. 3420

C. 6840

D. 8000

Q. 41 What is the sum of n terms of the series √2+√8+√18+√32+…?

A. [n(n-1)]/√2

B. √2n(n+1)

C. [n(n+1)]/√2

D. [n(n-1)]/2

Q. 42 The coefficient of x⁹⁹ in the expansion of (x-1)(x-2)(x-3)…(x-100) is

A. 5050

B. 5000

C. -5050

D. -5000

Q. 43 zz̅+(3-i)+(3+i)z̅+1=0 represents a circle with

A. centre (-3,-1) and radius 3

B. centre (-3,1) and radius 3

C. centre (-3,-1) and radius 4

D. centre (-3,1) and radius 4

Q. 44 The number of 3 digit even numbers that can be found from the digits 0,1,2,3.4 and 5 repetition of digits being out allowed is

A. 60

B. 56

C. 52

D. 48

Q. 45 If log₈ m + log₈ 1/6 = 2/3, then m is equal to

A. 24

B. 18

C. 12

D. 3

Q. 46 The area of the figure formed by the lines ax+by+c=0, ax-by-c=0,ax+by-c=0 and ax-by-c=0 is

A. c²/ab

B. 2c²/ab

C. c²/2ab

D. c²/4ab

Q. 47 If a line is perpendicular to the line 5x-y=0 and forms a triangle of area 5 square units with co-ordinate axes, then its equation is

A. x+5y±5√2=0

B. x-5y±5√2=0

C. 5x+y±5√2=0

D. 5x-y±5√2=0

Q. 48 Consider any point P on the ellipse x²/25 + y²/9 = 1 in the first quadrant. Let r and s represent its distances from (4,0) and (-4,0) respectively, then (r+s) is equal to

A. 10 unit

B. 9 unit

C. 8 unit

D. 6 unit

Q. 49 A straight line x=y+2 touches the circle 4(x²+y²)=r². The value of r is

A. √2

B. 2√2

C. 2

D. 1

Q. 50 The three lines 4x+4y=1,8x-3y=2,y=0 are

A. the sides of an isosceles triangle

B. concurrent

C. mutually perpendicular

D. the sides of an equilateral triangle

Q. 51 The line 3x+4y-24=0 intersects the x-axis at A and y-axis at B. Then the circumcentre of the triangle OAB where O is the origin is

A. (2,3)

B. (3,3)

C. (4,3)

D. none of the above

Q. 52 The eccentricity of the hyperbola 16x²-9y²=1 is

A. 3/5

B. 5/3

C. 4/5

D. 5/4

Q. 53 The product of the perpendiculars from the two points (±4,0) to the line 3x cos φ +5y sin φ =15 is

A. 25

B. 16

C. 9

D. 8

Q. 54 If the centre of the circle passing through the origin is (3,4), then the intercepts cut off by the circle on x-axis and y-axis respectively are

A. 3 unit and 4 unit

B. 6 unit and 4 unit

C. 3 unit and 8 unit

D. 6 unit and 8 unit

Q. 55 The lines 2x=3y=-z and 6x=-y=-4z

A. are perpendicular

B. are parallel

C. intersect at an angle 45⁰

D. intersect at an angle 60⁰

Q. 56 Two straight lines passing through the point A(3,2) cut the line 2y=x+3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ is

A. 7x+y-21=0

B. x+7y+21=0

C. 2x+y-8=0

D. x+2y+8=0

Q. 57 The radius of the sphere 3x²+3y²+3z²-8x+4y+8z-15=0 is

A. 2

B. 3

C. 4

D. 5

Q. 58 The direction ratios of the line perpendicular to the lines with direction ratios<1,-2,-2>and <0,2,1> are

A. <2,-1,2>

B. <-2,1,2>

C. <2,1,-2>

D. <-2,-1,-2>

Q. 59 What are the co-ordinates of the foot of the perpendicular drawn from the point (3,5,4) on the plane z=0

A. (0,5,4)

B. (3,5,0)

C. (3,0,4)

D. (0,0,4)

Q. 60 The lengths of the intercepts on the co-ordinate axes made by the plane 5x+2y+z-13=0 are

A. 5,2,1 unit

B. 13/5, 13/2, 13 unit

C. 5/13, 2/13, 1/13 unit

D. 1,2,5 unit

Q. 61 The area of the square, one of whose diagonals is 3î+4j is

A. 12 square unit

B. 12.5 square unit

C. 25 square unit

D. 156.25 square unit

Q. 62 ABCD is a parallelogram and P is the point of intersection of the diagonals. If the O is the origin, then

A. a

B. b

C. c

D. d

Q. 63 If b̅ and c̅ are the position vectors of the point B and C respectively, then the position vector of the point D such that

A. 4(c̅ – b̅)

B. -4(c̅ – b̅)

C. 4c̅-3 b̅

D. 4c̅ + b̅

Q. 64 If the position vector a̅ of the point (5,n) is such that I a̅I=13, then the value/values of n can be

A. ±8

B. a±12

C. 8 only

D. 12 only

Q. 65 If Ia̅I = 2 and I b̅ I = 3, them Ia̅ x b̅ I² + Ia̅.b̅I² is equal to

A. 72

B. 64

C. 48

D. 36

Q. 66 Consider the following inequilities in the respect of vectors a̅ and b̅:

1.I a̅ + b̅ I ≤ I a̅ I + I b̅ I

2. I a̅ – b̅ I ≥ a̅ I – I b̅ I

Which of the above is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 67 If the magnitude of difference of two unit vectors is √3 , then the magnitude of sum of the two vectors is

A. 1/2 unit

B. 1 unit

C. 2 unit

D. 3 unit

Q. 68 If the vectors αî + αĵ + γk̂, î + k̂, and γî + γĵ + βk̂ lie on a plane, where α, β, and γ are distinct non-negative numbers, then γ is

A. Arithmetic mean of α and β

B. geometric mean of α and β

C. Harmonic mean of α and β

D. none of the above

Q. 69 The vectors a̅, b̅, c̅ and d̅ are such that a̅ x b̅ = c̅ x d̅. Which of the following is/are correct?

1.(a̅ – d̅) x (b̅ – d̅) = 0

2. (a̅ x d̅) x (c̅ x d̅) = 0

select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 70 The value of the integral where a+b=0 is

A. 2b-a sin (b-a)

B. a+3b cos(b-a)

C. sin a – (b-a)cos b

D. 0

Q. 71 If f(x)=√(25-x)², the what is the value is equal to?

A. 1/5

B. 1/24

C. √24

D. -1/√24

Q. 72 consider the function

f(x) = { ax-2, for -2< x < -1

-1, for -1 ≤ x ≤ 1

a+2(x-1)², for 1 < x < 2

what is the value of a for which f(x) is continuous ar x = -1 and x = 1?

A. -1

B. 1

C. 0

D. 2

Q. 73 The function f(x) = (1-sin x+cos x)/(1+sin x+cos x) is not defined at x= π. The value of f(π) so that f(x) is continuous at x=π is

A. -1/2

B. 1/2

C. -1

D. 1

Q. 74 consider the following functions:

1. f(x) = { 1/x is x ≠ 0

0 if x=0

2. f(x) = { 2x+5 if x> 0

x²+2x+5 if x ≤ 0

which of the above is/are derivable at x =0?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 75 The domain of the function f(x) = 1/√(IxI-x) is

A. [0,∞]

B. (-∞,0)

C. [1,∞)

D. (-∞,0]

Q. 76 consider the following statements :

1. The function f(x)= x² + 2 cos x is increasing in the interval (0,π)

2. The function f(x) = ln (√( 1 + x² ) – x ) is decreasing in the interval (-∞,∞)

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. 77 The derivative of ln(x+sin x) with respect to (x+cos x) is

A. (1+cos x)/(x+sin x)(1-sin x)

B. (1-cos x)/(x+sin x)(1+sin x)

C. (1-cos x)/(x-sin x)(1+cos x)

D. (1+cos x)/(x-sin x)(1-cos x)

Q. 78 If y = cot⁻¹ [(√(1+sin x)+√(1-sin x))/(√(1+sin x)-√(1-sin x))] where 0 < x < π/2, then dy/dx is equal to

A. 1/2

B. 2

C. sin x+cos x

D. sin x-cos x

Q. 79 The function f(x) = x/e^x is monotonically increasing if

A. x < 0 only

B. x > 2 only

C. 0 < x < 2

D. x ∈(-∞,0) U (2,∞)

Q. 80 If x^a .y^b = (x-y)^(a+b), then the value of dy/dx – y/x is equal to

A. a/b

B. b/a

C. 1

D. 0

Q. 81 If f: R—> R, g:R—> R be two functions given by

f(x) = 2x-3 and g(x) = x³+5, then (fog)⁻¹(x) is equal to

A. [(x+7)/2]⅓

B. [(x-7)/2]⅓

C. [(x – 7/2)]⅓

D. [(x + 7/2)]⅓

Q. 82 If 0 < a < b, then the value of

A. IbI – I a I

B. I a I – I b I

C. I b I/I a I

D. 0

Q. 83 the value of the integral is equal to

A. 8/15

B. 16/15

C. 32/15

D. 0

Q. 84 If f(x) = sin(e^(x-2)-1)/ln (x-1), then

A. -2

B. -1

C. 0

D. 1

Q. 85 Consider the following statements:

1. f(x) = ln x is an increasing function on (0,∞)

2. f(x) = e^x – x (ln x) is an increasing function on (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. 86 If s = √(t² + 1), then d²s / d²t is equal to

A. 1/s

B. 1/s²

C. 1/s³

D. 1/s⁴

Q. 87 Consider the following statements:

statement 1: the function f : R—> R such that f(x) = x³ for all x R is one-one.

statement 2: f(a) = f(b) ⇒ a = b for all a,b ε R if the function f is one-one.

which of the following is correct in respect of the above statement?

A. both the statements are true and statement 2 is the correct explanation of statement 1.

B. both the statements are true and statement 2 is not the correct explanation of statement 1

C. statement 1 is true but statement 2 is false

D. statement 1 is false but statement 2 is true

Q. 88 ∫ dx/1+e^-x is equal to

where c is the constant of integration

A. 1+e^x+c

B. ln(1+e^-x)+c

C. ln(1+e^x)+c

D. 2 ln(1+e^-x)+c

Q. 89 The value of integration

A. 0

B. 2/3

C. 2

D. -2

Q. 90 The area bounded by the coordinate axes and the curve √x + √y = 1, is

A. 1 square unit

B. 1/2 square unit

C. 1/3 square unit

D. 1/6 square unit

Questions: 91 – 92

for the next two items that follow

consider the function f(x) = (1/x)^(2x^2), where x > 0

Q. 91 At what value of x does the function attain maximum value?

A. e

B. √e

C. 1/√e

D. 1/e

Q. 92 The maximum value of the function is

A. e

B. e^(2/e)

C. e^(1/e)

D. 1/e

Questions: 93 – 94

For the next two items that follow

consider f'(x) = x²/2 -kx+1 such that f(0) = 0 and f(3) = 15.

Q. 93 The value of k is

A. 5/3

B. 3/5

C. -5/3

D. -3/5

Q. 94 f”(-2/3) is equal to

A. -1

B. 1/3

C. 1/2

D. 1

Q. 95 For the next two items that follow

f(x) = -2x³ – 9x² -12x + 1

The function f(x) is an increasing function in the interval

A. (-2,-1)

B. (-∞,-2)

C. (-1,2)

D. (-1,∞)

Q. 96 For the next two items that follow

f(x) = -2x³ – 9x² -12x + 1

The function f(x) is a decreasing function in the interval

A. (-2,-1)

B. (-∞,-2) only

C. (-1,2) only

D. (-1,∞) U (-1, ∞)

Questions: 97 – 98

For the next two items that follow:

consider the integrals

Q. 97 which one of the following is correct?

A. A = 2B

B. B = 2A

C. A = B

D. A = 3B

Q. 98 What is the value of B?

A. π/4

B. π/2

C. 3π/4

D. π

Questions: 99 – 100

consider the function for the next two items that follow

f(x) = { -2 sin x if x ≤ -π/2

A sin x + B is -π/2 < x < π/2

cos x if x ≥ π/2

which is continuous everywhere.

Q. 99 The value of A is

A. 1

B. 0

C. -1

D. -2

Q. 100 The value of B is

A. 1

B. 0

C. -1

D. -2

Q. 101 The degree of the differential equation dy/dx – x = (y-x dy/dx)⁻⁴ is

A. 2

B. 3

C. 4

D. 5

Q. 102 The solution of dy/dx = √(1-x²-y² + x²y²) is

A. sin⁻¹ y = sin⁻¹ x + c

B. 2 sin⁻¹ y = √(1-x²)+ sin⁻¹ x+ c

C. 2 sin⁻¹ y = x√(1-x²)+ sin⁻¹ x + c

D. 2 sin⁻¹ y = x√(1-x²)+ cos⁻¹ x + c

Q. 103 The differential equation of the family of circles passing through the origin and having centres on the x-axis is

A. 2xy dy/dx = x²-y²

B. 2xy dy/dx = y²-x²

C. 2xy dy/dx = x²+y²

D. 2xy dy/dx+x²+y²=0

Q. 104 The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a,0) where a > 0, are respectively

A. 1,1

B. 2,1

C. 1,2

D. 2,2

Q. 105 f(xy) = f(x) + f(y) is true for all

A. polynomial functions f

B. trigonometric functions f

C. exponential functions f

D. logarithmic functions f

Q. 106 Three digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that product is odd?

A. 2/3

B. 7/48

C. 5/42

D. 5/108

Q. 107 Two events A and B are such that P(not B) = 0.8, P(A U B) = 0.5 and p(A/B)=0.4. Then P(A) is equal to

A. 0.28

B. 0.32

C. 0.38

D. none of the above

Q. 108 If mean and variance of a Binomial variate X are 2 and 1 respectively , then the probability that X takes a value greater than 1 is

A. 2/3

B. 4/5

C. 7/8

D. 11/16

Q. 109 Seven unbiased coins are tossed 128 times . In how many throws would you find at least three heads?

A. 99

B. 102

C. 103

D. 104

Q. 110 A coin is tossed five times. What is the probability that heads are observed more than three times?

A. 3/16

B. 5/16

C. 1/2

D. 3/32

Q. 111 The geometric mean of the observations x1,x2,x3……… xn is G1. The geometric mean of the observations y1,y2,y3 ….. yn is G2 . The geometric mean of observations is x1/y1 , x2/y2 , x3/y3………….. xn/yn is

A. G1G2

B. ln(G1G2)

C. G1/G2

D. ln(G1/G2)

Q. 112 the arithmetic mean of 1,8,27,64 upto n terms is given by

A. n(n+1)/2

B. n(n+1)²/2

C. n(n+1)²/4

D. n²(n+1)²/4

Q. 113 An unbiased coin is tossed until the first head appears or until four tosses are completed, whichever happens earlier. Which of the following statements is / are correct?

1. The probability that no head is observed is 1/16.

2. The probability that the experiment ends with three tosses is 1/8.

Select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 114 If x∈[ 0 , 5 ] , then what is the probability that x² – 3x + 2 ≥0 ?

A. 4/5

B. 1/5

C. 2/5

D. 3/5

Q. 115 A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black is

A. 5/24

B. 13/24

C. 1/4

D. 2/3

Q. 116 A problem in statistics is given to three students A B and C whose chances of solving it independently are 1/2 , 1/3 and 1/4 respectively . The probability that the problem will be solved is

A. 1/12

B. 11/12

C. 1/2

D. 3/4

Q. 117 An insurance company insured 2000 scooter drivers , 4000 car drivers and 5000 truck drivers. The probabilities of an accident involving a scooter driver , a car driver and a truck driver are 0.01,0.03 and 0.15 respectively. One of the insured persons meets with an accident. The probability that the person is a scooter driver is

A. 1/52

B. 3/52

C. 15/52

D. 19/52

Q. 118 A coin is tossed 5 times . The probability that tail appears an odd number of times is

A. 1/2

B. 1/3

C. 2/5

D. 1/5

Q. 119 The regression coefficients of a bivariate distribution are -0.64 and -0.36. Then the correlation coefficient of the distribution is

A. 0.48

B. -0.48

C. 0.50

D. -0.50

Q. 120 What is the probability that the sum of any two different single digit natural numbers is a prime number?

A. 5/27

B. 7/18

C. 1/3

D. none of the above

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