UPSC Exam - Page 5 of 9 - Vidhyarthi Darpan

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

NDA/NA(I) Exam 2018 General Ability Test

Questions: 1 – 10

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

Q. 1 I do not want you to lead a life of ‘sychophancy’ as you did during the foreign rule

A. admiration

B. love

C. appreciation

D. flattery

Q. 2 In India, it has become easy to ‘attack’ cultural artefacts these days

A. beckon

B. assault

C. belch

D. appreciate

Q. 3 A local court ‘granted’ bail to the criminal on thursday

A. confessed

B. donated

C. allowed

D. yielded

Q. 4 The judge told that he would analyze

A. liberate

B. surrender

C. transfer

D. pronounce

Q. 5 The growth and development of the peasant movement was ‘indissolubly’ linked with the national struggle for freedom

A. firmly

B. vaguely

C. individually

D. steadily

Q. 6 Weather conditions have been ‘improving’ over the past few weeks

A. mending

B. amending

C. becoming better

D. advancing

Q. 7 The confusion on the ‘interocutor’s’ face was gratifying

A. government officer

B. party worker

C. dialogist

D. revolutionary

Q. 8 He spends his money ‘lavishly’

A. hesitatingly

B. generously

C. foolishly

D. carefully

Q. 9 The government’s new policies will come into force from the next ‘fiscal’ year

A. calendar

B. academic

C. financial

D. leap

Q. 10 ‘Abundant’ food was available for the soldiers in the mess

A. little

B. plentiful

C. delicious

D. wholesome

Questions: 11 – 20

Each item in this section consists of a sentence with quotation marks followed by four words. Select the option that is opposite in meaning to the word in the quotation marks and mark your response in your answer sheet accordingly

Q. 11 The country’s economy must be ‘geared to’ wartime requirements

A. subordinated to

B. related to

C. adjusted to

D. unlinked to

Q. 12 Why does fire ‘attract’ insects?

A. discharge

B. destroy

C. repel

D. remove

Q. 13 The party was excellent, and I would like to thank all the people ‘concerned’

A. cared

B. attentive

C. dependable

D. uninvolved

Q. 14 He is very ‘serious’ by temperament

A. grave

B. trivial

C. sober

D. stupid

Q. 15 There are a few ‘miscellaneous’ items to discuss in this meeting

A. pure

B. mixed

C. homogenous

D. discordant

Q. 16 Due to the postal strike, the ‘outgoing’ mail got delayed

A. urgent

B. incoming

C. ordinary

D. speedy

Q. 17 He has a ‘fine’ ear for music

A. small

B. close

C. coarse

D. smooth

Q. 18 There is no ‘likeness’ between him and his brother

A. unlikeliness

B. unlikelihood

C. dissimilarity

D. disaffinity

Q. 19 Cultural ‘diversity’ in the working place is good for business

A. uniformity

B. conformity

C. identity

D. similarity

Q. 20 The company was ‘liquidated’ within five years

A. bankrupt

B. closed down

C. flourishing

D. privatised

Questions: 21 – 25

Each item in this section has a sentence with three words in quotation labelled (a),(b) and (c). Read each sentence to find out whether there is any error in any part under the quotations and indicate your response in the answer sheet against the corresponding letter i.e., (a),(b) or (c). If you find no error, your response should be indicated as (d)

Q. 21 ‘The political lost face in his constituency'(a)/ ‘when he broke the pre-election promises'(b)/ ‘he made to his people'(c)./ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 22 At the ‘request of the defence attorney,'(a)/ ‘the jury were called'(b)/ ‘and their individual verdicts were recorded'(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 23 Frank Lloyd Wright ‘has been acclaimed'(a)/ ‘by colleagues'(b)/ ‘as greater of all modern architects'(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 24 ‘In my younger days'(a)/ ‘I could run four miles'(b)/ ‘at a stretch'(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 25 ‘The owner'(a)/ ‘as well as his servants'(b)/ ‘ is honest'(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Questions: 26 – 30

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 expression

Q. 26 ‘Cry over spilt milk’

A. complaining about a loss in the past

B. too much inquisitive about something

C. when something is done badly to save money

D. dealing with a problem only in an emergency situation

Q. 27 ‘Cut the mustars’

A. prepare spices out of mustard seeds

B. to come up to expectations

C. making absurd expectations

D. very enthusiastic

Q. 28 ‘Devil’s advocate

A. a dangerous person

B. to present a counter argument

C. very argumentative person

D. creating an unpleasant situation

Q. 29 ‘Don’t count your chicken before the eggs have hatched’

A. if you are not good at something, better to avoid that

B. don’t make plans for something that might not happen

C. not to come up to expectations

D. don’t put all your resources in one possibility

Q. 30 ‘Give the benefit of doubt’

A. to be partial to someone

B. to be judgmental

C. regard someone as innocent until proven otherwise

D. say something exactly right

Questions: 31 – 35

In this section each item consists of six sentences of a passage. The first and sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled P,Q,R and S. Your are required to find the proper sequence of the four sentences and mark your response accordingly on the answer sheet

Q. 31 S1: The subsidiary Alliance system was extremely advantageous to the British

S6: They controlled the defence and the foreign relations of the protected ally

P: They could now maintain a large army at the cost of Indian states

Q: If any war occured in the territories

R: either of the British ally or of the Britishers

S: This enabled them to fight wars far away from their own territories

The proper sequence should be

A. P Q R S

B. P S Q R

C. Q R P S

D. S R P Q

Q. 32 S1: In reality, by signing a Subsidiary Alliance, an Indian state virtually signed away its independence

S6: In fact, the Indian ruler lost all vertiges of sovereignty in external matters

P: of maintaining diplomatic relations

Q: it lost the right of self defence

R: with its neighbors

S: and of selling its disputes

The proper sequence should be

A. P Q R S

B. R S P Q

C. Q P S R

D. Q S R P

Q. 33 S1: A mighty popular Revolt broke out in Northern and Central India in 1857

S6: Millions of peasants, artisans and soldiers fought heroically and wrote a glorious

chapter

P: Sepoys, or the Indian soldiers of the company’s army

Q: but soon engulfed wide regions and involved masses

R: and nearly swept awaay the British rule

S: it began with a mutiny of the

the proper sequence should be

A. R S P Q

B. P Q R S

C. S R P Q

D. Q R P S

Q. 34 S1: The Indian Civil Service gradually developed into one of the most efficient and powerful civil services in the world

S6: though these qualities obviously served British, and not Indian interests

P: and often participated in the making of policy

Q: independence, integrity and hard work

R: they developed certain traditions of

S: its members exercised vast power

The proper sequence should be

A. P Q R S

B. Q R S P

C. R S Q P

D. S P R Q

Q. 35 S1: The ruin of Indian handicrafts was reflected in the ruin of the towns and cities which were famous for their manufacturers

S6: centres were developed and laid waste

P: Dacca, Surat, Murshidabad and many other risinf industrial

Q: ravages of war and plunder, failed to

R: survive British conquest

S: Cities which had with stood the

The proper sequence should be

A. P Q R S

B. S Q R P

C. S R P Q

D. Q R S P

Questions: 36 – 40

In this section you have few short passages. After each passage, you will find some items based on the passage. First, read a passage and answer the items based on it. You are required to select your answers based on the contents of the passage and opinion of the author only.

Passage:

The rule of the road means that in order that the liberties of all may be preserved, the liberties of everybody must be curtailed. When the policeman, say, at a roadcrossing steps into the middle of the road and puts our his hand, he is the symbol not of tyranny but of liberty. You have submitted to a curtailment of private liberty in order that you may enjoy a social order which makes your liberty a reality. We have both liberties to preserve-our individual liberty and our social liberty. That is, we must have a judicious mixture of both. I shall not permit any authority to say that my child must go to this school or that, shall specialize in science and arts. These things are personal. But if I say that my child shall have no education at all, then society will firmly tell me that my child must have education whether I like it or not

Q. 36 According to the author, the “rule of the road” implies

A. the rule regulating the traffic on the road

B. the principle on which a road is constructed to ensure safe traffic

C. unrestricted freedom for all to lead a happy life

D. restricted individual freedom to ensure freedom for all

Q. 37 The author thinks that when a policeman signals you to stop on a road-crossing he is

A. behaving in a whimsical manner

B. interfering with your freedom to the road

C. protecting the liberty of all to use the road

D. mischievously creating hurdles in your way from some personal motive

Q. 38 The author is of view that we should

A. have absolute individual liberty without any restrictions imposed by the society

B. have everything controlled by the society without any kind of individual liberty

C. try to strike a sensible balance between our individual liberty and our social liberty

D. have more of social liberty than individual liberty

Q. 39 The author holds that

A. educating or not educating his child is a matter of personal liberty

B. educating or not educating his child is also a matter of social liberty

C. choosing the school for his child is a matter of social liberty

D. choosing the subject of study for his child is a matter of social liberty

Q. 40 The most suitable title of the passage would be

A. the policeman at a road crossing

B. the laws of the road

C. importance of liberty

D. education of children

Questions: 41 – 45

My most interesting visitor comes at night, when the lights are still burning—a tiny bat who prefers to fly in through the open door, and will use the window only if there is no alternative. His object in entering the house is to snap up the moths that cluster around the lamps. All the bats I have seen fly fairly high, keeping near the ceiling; but this particular bat flies in low, like a dive-bomber, zooming in and out of chair legs and under tables. Once, he passed straight between my legs. Has hits radar wrong, I wondered, or is her just plain crazy?

Q. 41 Consider the following statements:

1. The tiny bat flew in low like a dive-bomber

2. The tiny bat like all bats keeps near the ceiling

3. It has lost direction because its radar has gone wrong

4. It wants to entertain the author with its skill in flying

Which of the above statements may be assumed to be true from the information given in the passage?

A. 1 only

B. 1 and 3

C. 2 and 4

D. 3 and 4

Q. 42 The bat entered the room

A. because there was no alternative

B. to eat the moths round the lamps

C. as it had gone mad

D. as it preferred to fly in through the open door

Q. 43 After comparing the habits of the tiny bast with those of other bats, the author was

A. sure that this bat had lost its direction

B. not sure to find that it was an expert flier

C. surprised to find that it was an expert flier

D. unable to give the correct explanation for its behaviour

Q. 44 The author calls the tiny bat an “interesting visitor”. This means

A. the bat visits him at night

B. the bat is interested in the moths

C. this bat has peculiar qualities

D. this bat surprises him by zooming in and out like a dive-zoomer

Q. 45 What, according to you, can be the most suitable title for the passage?

A. someone visits me

B. night of mysteries

C. my nocturnal visitor

D. a funny visitor

Questions: 46 – 50

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

Q. 46 The tired traveller ________________ on in the hope of finding some resting place

A. strolled

B. scurried

C. paraded

D. ploded

Q. 47 The car was damaged beyond repair in the ___________________ accident

A. outrageous

B. ghastly

C. nasty

D. heinous

Q. 48 They gave a _________ dinner to celebrate the occasion, which impressed every guest

A. austere

B. public

C. sumptuous

D. summary

Q. 49 Once the ________________ manuscript is received by the publishers, it is typed in double space

A. total

B. full

C. complete

D. filled

Q. 50 I am used to ___________________ in queues

A. stand

B. standing

C. stand up

D. standing still

Q. 51 Which of the following statements is correct?

A. any energy transfer that does not involve temperature difference in some way is not heat

B. any energy transfer always requires a temperature differences

C. On heating the length and volume of the object remain exactly the same

D. whenever there is a temperature difference, heat it the only way of energy transfer

Q. 52 If T is the time period of an oscillating pendulum, which one of the following statements is NOT correct?

A. the motion repeats after time T only once

B. T is the least time after which motion repeats itself

C. the motion repeats itself after nT, where n is a positive integer

D. T remains the same only for small angular displacement

Q. 53 If an object moves with constant velocity then which one of the following statements is NOT correct?

A. its motion is along a straight line

B. its speed changes with time

C. its acceleration is zero

D. its displacement increases linearly with time

Q. 54 An object is moving with uniform acceleration a. Its initial velocity is u and after time t its velocity is v. The equation of its motion is v=u+at. The velocity(along y-axis) time(along xaxis) graph shall be a straight line

A. passing through origin

B. with x-intercept u

C. with y-intercept u

D. with slope u

Q. 55 What is the net force experienced by a bar magnet placed in a uniform magnetic field?

A. zero

B. depends upon length of the magnet

C. never zero

D. depends upon temperature

Q. 56 Which one of the following has maximum inertia?

A. an atom

B. a molecule

C. a one-rupee coin

D. a cricket ball

Q. 57 Which one of the following is the value of 1 kWh of energy converted into joules?

A. 1.8*10⁶J

B. 3.6*10⁶J

C. 6.0*10⁶J

D. 7.2*10⁶J

Q. 58 Which one of the following statements about gravitational force is NOT correct?

A. it is experienced by all bodies in the universe

B. it is a document force between celestial bodies

C. it is a negligible force for atoms

D. it is same for all pairs of bodies in our universe

Q. 59 Whether an object will float or sink in a liquid, depends on

A. mass of the object only

B. mass of the object and density of liquid only

C. differences in the densities of the object and liquid

D. mass and shape of the object only

Q. 60 Which one of the following devices is non-ohmic?

A. conducting copper coil

B. electric heating coil

C. semi conductor diode

D. rheostat

Q. 61 Which one of the following is the natural phenomenon based on which a simple periscope works?

A. reflection of light

B. refraction of light

C. dispersion of light

D. total internal reflection of light

Q. 62 Which one of the following frequency ranges is sensitive to human ear?

A. 0-200 Hz

B. 20-20,000 Hz

C. 200-20,000 Hz only

D. 2,000-20,000 Hz only

Q. 63 The accidental touch of Nettle leaves creates a burning sensation, which is due to inject of

A. hydrochloric acid

B. methanoic acid

C. citric acid

D. sulphuric acid

Q. 64 Which of the following properties is true for a tooth paste?

A. it is acidic

B. it is neutral

C. it is basic

D. it is made up of calcium phosphate, the material of tooth enamel

Q. 65 Which one of the following given the highest amount of hydrogen ions(H⁺)?

A. sodium hydroxide solution

B. milk of magnesia

C. lemon juice

D. gastric juice

Q. 66 Brine is an aqueous solution of

A. NaCl

B. NaOH

C. NaHCO₃

D. Na₂CO₃

Q. 67 Which one of the following is the chemical formula of washing soda?

A. NaHCO₃

B. Na₂CO₃.10H₂O

C. Na₂CO₃.5H₂O

D. NaOH

Q. 68 Which one of the following is NOT true for bleaching powder?

A. it is used as a reducing agent in chemical industries

B. it is used for bleaching wood pulp in paper factories

C. it is used for disinfecting drinking water

D. it is used for bleaching linen in textile industry

Q. 69 AIDS is caused by virus whose genetic material is

A. single stranded circular DNA

B. double stranded DNA

C. single stranded RNA

D. double stranded RNA

Q. 70 Which one of the following is an organelle that is NOT found in pro-karyotic cells?

A. cell wall

B. mitochondria

C. plasma membrane

D. ribosome

Q. 71 Which one of the following parts of body does NOT take part in the process of breathing?

A. Bronchi

B. Bowman’s capsule

C. Diaphragm

D. Trachea

Q. 72 Which one of the following statements about classification of plants is correct?

A. Thallophytes have well differentiated body design

B. Funaria is a fungus

C. All Pteridophytes are Phanerogams

D. Vascular system is not found among Bryophytes

Q. 73 Which one of the following is the correct sequence of hierarchy of classification of organisms from higher to lower?

A. Phylum-Class-Order-Family-Genus

B. Phylum-Class-Family-Order-Genus

C. Family-Order-Class-Species-Genus

D. Class-Family-Order-Species-Genus

Q. 74 Which one of the following statements about meristematic tissues in plants is correct?

A. these are dead tissues and form wood

B. they provide flexibillity to plant due to their thickened walls

C. these are present in the bark of a tree only

D. growth occurs in plants due to division of cells of these tissues

Q. 75 Which one of the following Union Territories has the highest female literacy rate?

A. Chandigarh

B. Lakshadweep

C. Andaman and Nicobar Islands

D. Puducherry

Q. 76 Consider the following statements about Roaring Forties:

1. They are strong Westerly winds found in the oceans of Southern Hemisphere

2. The strong east to west air currents are caused by the combination of air being displaced from the Equator towards the south pole and the earth’s rotation and abundance of landmasses to serve as wind breaks.

Which of the statement given above 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. The doldrums is a low pressure area around Equator where the prevailing winds are calm

2. Chinook is a hot and dry wind that blows in winter and therefore raises the temperature in a short time

which of the statements given above is/are correct?

A. 1

B. 2

C. both 1,2

D. neither i nor 2

Q. 78 Which one of the following is the driest desert of the world?

A. atacama

B. gobi

C. sahara

D. kalahari

Q. 79 Which of the following statements about latent heat heat for a given substance is/are correct?

1. It is fixed upon the temperature

2. It depends upon the temperature and volume

3. It is independent of temperature and volume

4. It depends on the temperature but independent of volume

select the correct answer using the code given below:

A. 2

B. 1,3

C. 4

D. 1,4

Q. 80 Which one of the following statements about the mass of a body is correct?

A. it changes from one place to another

B. it is same everywhere

C. it depends on its shape

D. it does not depend on its temperature

Q. 81 A ball balanced on a vertical rod is an example of

A. stable equilibrium

B. unstable equilibrium

C. neutral equilibrium

D. perfect equilibrium

Q. 82 Which of the following statements about a fluid at rest in a cup is/are correct

1. Pressure is same at all the points in the fluid

2. Pressure is exerted on the walls

3. Pressure exists everywhere in the fluid

select the correct answer using the code given below:

A. 1,2 only

B. 2,3 only

C. 1 only

D. 1,2,3

Q. 83 Which one of the following devices is used to measure atmospheric pressure?

A. ammeter

B. barometer

C. potentiometer

D. lactometer

Q. 84 Which one of the following is the number of water molecules that share with two formula unit CaSO₄ in plaster of Paris?

A. 1

B. 2

C. 5

D. 10

Q. 85 How is carbon black obtained?

A. by heating wood at high temperature in absence of air

B. by heating coal at high temperature in absence of air

C. by burning hydrocarbons in a limited supply of air

D. by heating coal at a high temperature in presence of air

Q. 86 Which of the following properties is NOT true for graphite?

A. hybridisation of each carbon atom is sp³

B. hybridisation of each carbon atom is sp²

C. electrons are delocalized over the whole sheet of atoms

D. each layer is composed of hexagonal rings

Q. 87 Which one of the following is the purest form of carbon?

A. charcoal

B. coke

C. fullerene

D. carbon black

Q. 88 The poisonous nature of carbon monoxide(CO) is due to

A. insolubility of water

B. ability to form a complex with haemoglobin

C. ability to reduce some metal oxides

D. property of having one sigma bond

Q. 89 Which one of the following elements is needed in the human body to transfer electrical signals by nerve cells?

A. lithium

B. sodium

C. rubidium

D. caesium

Q. 90 Who among the following first discovered cell?

A. robert brown

B. robert hooke

C. leeuwen hoek

D. rudolf virchow

Q. 91 Which one of the following group of organisms forms a food chain?

A. grass, human and fish

B. grass, goat and human

C. tree, tree cutter and tiger

D. goat,cow and human

Q. 92 Which one of the following types of tissues will have contractile proteins?

A. nervous tissue

B. muscle tissue

C. bone tissue

D. blood tissue

Q. 93 If by an unknown accident the acid secreting cells of the stomach wall of an individual are damaged, digestion of which one of the following biomolecule will be affected to a greater extent?

A. protein only

B. lipid

C. carbohydrate only

D. protein and carbohydrate

Q. 94 In which one of the following places, headquarters of a railway zone is located?

A. kanpur

B. lucknow

C. hajipur

D. new jalpaiguri

Q. 95 Which of the following statements about Indian academy of highway engineers is/are correct?

1. It is a registered society

2. It is a collaborative body of both central government and state governments

select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1,2

D. neither 1 nor 2

Q. 96 Which one of the following is NOT a tributary of Indus river?

A. beas

B. ravi

C. chenah

D. tawi

Q. 97 Which one among the following is the largest tiger reserve of India in terms of area of the core/critical tiger habitat?

A. manas

B. pakke

C. nagarjunasagar srisailam

D. periyar

Q. 98 Which of the following is NOT a coastal depositional featute?

A. tombolo

B. sand bar

C. stack

D. spit

Q. 99 Which of the following is/are coastal erosional feature(s)

1. Notch

2. Sea Arch

3. Cliff

4. Hook

select the correct answer using the code given below:

A. 1,2,3

B. 2,3,4

C. 2,3

D. 1

Q. 100 Chemical weathering of rocks is much greater in a place with

A. cold and dry climate

B. hot and humid climate

C. hot and dry climate

D. cold and humid climate

Q. 101 Which of the following statements about specific heat of a body is/are correct?

1. It depends upon mass and shape of the body

2. It is independent of mass and shape of the body

3. It depends only upon the temperature of the body

select the correct answer using the code given below:

A. 1

B. 2,3

C. 1,3

D. 2

Q. 102 Which one of the following is an example of the force of gravity of the earth acting on a vibrating pendulum bob?

A. applied force

B. frictional force

C. restoring force

D. virtual force

Q. 103 Which one of the following statements about the refractive index of a material medium with respect to air is correct?

A. it can be either positive or negative

B. it can have only zero value

C. it is unity for all materials

D. it is always greater than one

Q. 104 Which one of the following statements about magnetic field lines is NOT correct?

A. they can emanate from a point

B. they do not cross each other

C. field lines between two poles cannot be precisely straight lines at the ends

D. there are no field lines within a bar magnet

Q. 105 Two convex lenses with power 2 dipotre are kept in contact with each other. The focal length of the combined lens system is

A. 0.10 m

B. 2 m

C. 4 m

D. 0.25 m

Q. 106 Which one of the following alkali metals has lowest melting point?

A. sodium

B. potassium

C. rubidium

D. caesium

Q. 107 Which one of the following metals is alloyed with sodium to transfer heat in a nuclear reactor?

A. potassium

B. calcium

C. magnesium

D. strontium

Q. 108 Which one of the following metals is used in the filament of photo-electric cells that convert light energy into electric energy?

A. tungsten

B. copper

C. rubidium

D. aluminium

Q. 109 Which of the following statements about Ring of Fire is/are correct?

1. It is a zone of convergence plate boundaries

2. It is an active seismic and volcanic zone

3. It is associated with deep trench

Select the correct answer using the code given below:

A. 1,2

B. 2,3

C. 1

D. 1,2,3

Q. 110 Which one of the following Himalayan vegetation species is found between the altitudes of 1800 to 2600 metres?

A. saal

B. chir

C. spruce

D. deodar

Q. 111 Which one of the following rivers is NOT a tributary of river Cauvery?

A. Hemavati

B. Arkavati

C. Indravati

D. Amravati

Q. 112 Which of the following conditions is/are essential for tea cultivation?

1. Tropical and sub-tropical climate

2. Heavy rainfall ranging from 150 cm to 250 cm

3. Soil should contain good amount of lime

select the correct answer using the code given below:

A. 1,2,3

B. 1,2

C. 2,3

D. 1

Q. 113 Bharatmala Project is related to

A. improving road connectivity

B. interlinking ports and railways

C. interlinking of rivers

D. interlinking major cities with gas pipelines

Q. 114 Which one of the following is a local wind that blows out from Siberia?

A. bora

B. purga

C. mistral

D. blizzard

Q. 115 Which one of the following centres is NOT known for iron and steel industry?

A. bhadravati

B. salem

C. vishakhapatnam

D. renukoot

Q. 116 Which one of the following are essential pre-requisites for establishment of a thermal power station?

1. availability of fossil fuels

2. proximity to a river, lake or sea

3. good transport network

4. proximity to an urban centre

select the correct answer using the code given below:

A. 1,2,3

B. 2,4

C. 2,3

D. 1,3

Q. 117 Which of the following statements about ‘Aadi Mahotsav’ held recently in New Delhi is/are correct?

1. The theme of the festival was ‘A celebration of the spirit of tribal culture, cuisine and commerce’

2. The festival was organized by the ministry of tourism, government of India

select the correct answer using the code given below:

A. 1

B. 2

C. both 1,2

D. neither 1 nor 2

Q. 118 Light year is a unit for measurement of

A. age of universe

B. very small time intervals

C. very high temperature

D. very large distance

Q. 119 Which of the following statements about electromagnetic waves, sound waves and water waves is/are correct?

1. they exhibit reflection

2. they carry energy

3. they exert pressure

4. they can travel in vacuum

select the correct answer using the code given below:

A. 1,2,3

B. 2,4

C. 1,3

D. 1

Q. 120 Thermal capacity of a body depends on the

A. mass of the body only

B. mass and shape of the body only

C. density of the body

D. mass, shape and temperature of the body

Q. 121 Who among the following first used the term ‘industrial revolution’ in english to describe the changes that occured in british industrial development between 1760 and 1820?

A. karl marx

B. georges michelet

C. arnold toynbee

D. friedrich engels

Q. 122 Which one of the following statements about the Olympe de Gouges(1748-1793) is correct?

A. she declared that although citizens should have equal rights, they are not entitled to the same honours by the state

B. she was supporter of the Jacobin government

C. she was jailed for treason by the National Assembly

D. she declared that the nation is the union of woman and man

Q. 123 Who among the following built a model steam engine in 1698 called “Miner’s Friend” to drain mines?

A. thomas savery

B. thomas newcomen

C. james watt

D. richard arkwright

Q. 124 Which one of the following statements about Renaissance Humanist culture is NOT true?

A. it slackened the control of religion over human life

B. it believed that human nature was many-sided

C. it was concerned with good manners

D. it criticized material wealth, power and glory

Q. 125 Who gifted the ‘Badshah Nama’ to King George in 1799?

A. abul fazl

B. abdul hamid lahori

C. nawab of awadh

D. william jones

Q. 126 What is the name of the award given to meritorious men in the Mughal Court in the form of a robe of honour that was once worn by the Emperor?

A. sarapa

B. patka

C. padma murassa

D. khilat

Q. 127 Who among the following social reformer started a society for the encouragement of a widow remarriage in 1866 in maharashtra?

A. bal gangadhar tilak

B. jyotirao phule

C. vishnushastri pandit

D. pandita ramabai

Q. 128 Name the first major voluntary association representing primarily Indian landlords interests that was set up in Calcutta in 1851?

A. british indian association

B. ladholder’s society

C. madras native association

D. bombay association

Q. 129 Who among the following introduced the permanent settlement of bengal in 1793?

A. lord cornwallis

B. lord ripon

C. robert clive

D. john adam

Q. 130 Name the rebel who fought against the British in the battle of Chinhat in the course of the 1857 revolt?

A. ahmadullah shah

B. shah mal

C. mangal pandey

D. kunwar singh

Q. 131 Who among the following are the two civil servants who assisted the constituent assembly in framing the constitution of india?

A. B.N.Rau and K.M.Munshi

B. S.N.Mukherjee and Alladi Krishna swamy Aiyar

C. B.N.Rau and S.N.Mukherjee

D. K.M.Munshi and Alladi Krishna swamy Aiyar

Q. 132 Which member of the constituent assembly proposed the resolution that the national flag of india be a “horizontal tricolour of saffron,white and dark green in equal proportion”, with a wheel in navy blue at the centre?

A. jawaharlal nehru

B. B.R.Ambedkar

C. rajendra prasad

D. sardar vallabhai patel

Q. 133 Which of the following is/are NOT historical biography/biographies?

1. Dipavamsa

2. Harshacharita

3. Vikramankadevacharita

4. Prithvirajavijaya

select the correct answer from the code given below:

A. 1

B. 2,3

C. 2,3,4

D. 1,2,3,4

Q. 134 Which of the following pairs are correctly matched from the figure

A. 1,2,3

B. 2,3

C. 1,2,3,4

D. 1,4

Q. 135 Which of the following clans are included in the Agnikula Rajputs?

1. Pratiharas

2. Chaulukyas

3. Paramaras

4. Chahamanas

select the correct answer from the code given below:

A. 1,3

B. 1,3,4

C. 1,2,3,4

D. 2,4

Q. 136 Who among the following was the author of Humayun Nama?

A. roshanara begum

B. Ruquaiya Sultan Begum

C. gulbadan begum

D. gauhara begum

Q. 137 Which one of the following about the parliament of India is NOT correct?

A. parliament consists of the president, the lok sabha and the rajya sabha

B. there are no nominated members in the lok sabha

C. the rajya sabha cannot be dissolved

D. some members of the rajya sabha are nominated bu the president

Q. 138 Which one of the following statements with regard to the Comptroller and auditor general(CAG) of india is NOT correct?

A. he is appointed by the president of india

B. he can be removed from the office in the same way as the judge of the supreme court of india

C. the CAG is eligible for further office under the government of india after he has

ceased to hold his office

D. the salary of the CAG is charged upon the consolidated fund of india

Q. 139 The superintendence, direction and control of elections of india is vested in

A. the supreme court of india

B. the parliament of india

C. the election commission of india

D. the chief election commissioner

Q. 140 Which of the following provision(s) of the constitution of india became effective from 26th november 1949?

1. elections

2. citizenship

3. emergency provisions

4. appointment of the judges

select the correct answer using the code given below:

A. 1

B. 1,2

C. 1,2,3

D. 2,4

Q. 141 Which of the following statements regarding construction of rohtang tunnel is NOT correct?

A. it is located at an altitude of 5,000 feet

B. it will provide all-year connectivity to Lahaul and Spiti valley

C. the tunnel is being built by the border roads organization

D. it will reduce the length of the leh-manali highway by approximately 50 km

Q. 142 Who among the following recently became the first woman pilot in Indian Navy?

A. astha segal

B. roopa A

C. sakthi maya S

D. shubhangi swaroop

Q. 143 Who among the following indians did NOT hold the title of Miss world?

A. reita faria

B. sushmita sen

C. diana hayden

D. yukta mookhey

Q. 144 Which one of the following countries has failed to qualify for the first time in 60 years for the FIFA world cup to be held in russia in the year 2018?

A. mexico

B. iran

C. saudi arabia

D. italy

Q. 145 The defence Technology and trade initiative(DTTI) is a forum for dialogue on defence partnership between india and

A. russia

B. USA

C. israel

D. france

Q. 146 As per the policy applicable in 2017, how much foreign direct investment (FDI) is permitted in the defence sector in India?

A. 49 percent through the automatic route

B. 26 per cent through the government route

C. 26 per cent through the automatic route and beyond that up to 49 per cent through

the government route

D. 75 per cent through the automatic route

Q. 147 Which one of the following countries did NOT participate in the 21st edition of exercise malabar?

A. USA

B. japan

C. India

D. australia

Q. 148 Justice Dalveer Bhandari of India was recently re-elected to the International Court of Justice after Christopher Greenwood pulled out before 12th round of voting. Christopher Greenwood was a nominee of

A. canada

B. russia

C. britain

D. USA

Q. 149 In order to review the income tax act, 1961 and to draft a new direct tax law in consconance with economic needs of the country, the government of india in november 2017 has constituted a task force. Who among the following is made the convenor of it?

A. shri arvind subramanian

B. shri arbind modi

C. shri amitabh kant

D. Dr. Bibek debroy

Q. 150 The 5th global conference on cyber space(GCCS) was held in new delhi in november, 2017.

Which of the following statements about GCCS is/are correct?

1. The 4th version of GCCS was held in London

2. The main theme of GCCS 2017 is ‘Cyber4All: A secure and inclusive cyberspace for sustainable development’.

3. ‘Bindu’ is the logo of GCCS 2017

select the correct answer using the code given below:

A. 1

B. 2

C. 2,3

D. 1,2,3

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

NDA/NA(II) Exam 2018 Mathematics Previous Year Paper

NDA/NA(II) Exam 2018 Mathematics

Q. 1 What is the value of log₇ log₇ {√7[√7(√7)]} equal to?

A. 3 log₂ 7

B. 1−3 log₂ 7

C. 1−3 log₇ 2

D. 7/8

Q. 2 If an infinite GP has the first term x and the sum 5, then which one of the following is correct ?

A. x < −10

B. −10 < x < 0

C. 0 < x < 10

D. x > 10

Q. 3 Consider the following expressions:

1. x + x² – 1/x

2. √[ax² + bx + x -c + (d/x) – (e/x²)]

3. 3x² − 5x + ab

4. 2/x² − ax + b³

5. 1/x − 2/x + 5

Which of the above are rational expressions?

A. 1, 4 and 5 only

B. 1, 3, 4 and 5 only

C. 2, 4 and 5 only

D. 1 and 2 only

Q. 4 A square matrix A is called orthogonal if

Note: where A′ is the transpose of A

A. A = A²

B. A′ = A⁻¹

C. A = A⁻¹

D. A = A′

Q. 5 If A, B and C are subsets of a Universal set, then which one of the following is not correct?

Note: where A′ is the complement of A

A. A ⋃ (B ∩ C) = (A ⋃ B) ∩ (A ⋃ C)

B. A′ ⋃ (A ⋃ B) = (B′ ∩ A)′ ⋃ A

C. A′ ⋃ (B ⋃ C) = (C′ ∩ B)′ ∩ A′

D. (A ∩ B) ⋃ C = (A ⋃ C) ⋂ (B ⋃ C)

Q. 6 Let x be the number of integers lying between 2999 and 8001 which have at least two digits equal. Then x is equal to

A. 2480

B. 2481

C. 2482

D. 2483

Q. 7 The sum of the series 3 – 1 + 1/3 – 1/9 + … is equal to

A. 20/9

B. 9/20

C. 9/4

D. 4/9

Questions: 8 – 9

A survey was conducted among 300 students. It was found that 125 students like to play cricket,145 students like to play football and 90 students like to play tennis. 32 students like to play exactly two games out of the three games.

Q. 8 How many students like to play all the three games?

A. 14

B. 21

C. 28

D. 35

Q. 9 How many students like to play exactly only one game?

A. 196

B. 228

C. 254

D. 268

Q. 10 If α and β(≠0) are the roots of the quadratic equation x²+αx-β=0, then the quadratic expression -x²+αx+β where x ⋲ R has

A. Least value -1/4

B. Least value -9/4

C. Greatest value 1/4

D. Greatest value 9/4

Q. 11 What is the coefficient of the middle term in the binomial expansion of (2 + 3x)⁴?

A. 6

B. 12

C. 108

D. 216

Q. 12 For a square matrix A, which of the following properties hold?

1. (A⁻¹)⁻¹ = A

2. det(A⁻¹) = 1/detA

3. (λA)⁻¹ = λA⁻¹ where λ is a scalar

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Q. 13 Which one of the following factors does the expansion of the determinant shown in figure contain?

A. x − 3

B. x − y

C. y − 3

D. x − 3y

Q. 14 What is the adjoint of the matrix? Choose the correct option.

A. (a)

B. (b)

C. (c)

D. (d)

Q. 15 What is the value of (-1+i√3/2)³ⁿ, where i=√-1 ?

A. 3

B. 2

C. 1

D. 0

Q. 16 There are 17 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so as to include 3 bowlers?

A. C (17, 11)

B. C (12, 8)

C. C (17, 5) X C (5, 3)

D. C (5, 3) X C (12, 8)

Q. 17 What is the value of log₉ 27 + log₈ 32 ?

A. 7/2

B. 19/6

C. 4

D. 7

Q. 18 If A and B are two invertible square matrices of same order, then what is (AB)⁻¹ equal to?

A. B⁻¹ A⁻¹

B. A⁻¹ B⁻¹

C. B⁻¹ A

D. A⁻¹ B

Q. 19 What is the solution of the of equation given if a+b+c=0 ?

A. x=a

B. x=[√3(a²+b²+c²)]/√2

C. x=[√2(a²+b²+c²)]/√3

D. x=0

Q. 20 What should be the value of x so that the matrix does not have an inverse?

A. 16

B. -16

C. 8

D. -8

Q. 21 The system of equations

2x + y – 3z = 5,

3x – 2y + 2z = 5 and

5x – 3y – z = 16

A. is inconsistent

B. is consistent, with a unique solution

C. is consistent, with infinitely many solutions

D. has its solution lying along x-axis in three-dimensional space

Q. 22 Which one of the following is correct in respect of the cube roots of unity?

A. They are collinear

B. They lie on a circle of radius √3

C. They form an equilateral triangle

D. None of the above

Q. 23 If u, v and w (all positive) are the pᵗʰ, qᵗʰ and rᵗʰ terms of a GP, then the determinant of the given matrix is?

A. 0

B. 1

C. (p-q)(q-r)(r-p)

D. ln u x ln v x ln w

Q. 24 Let the coefficient of the middle term of the binomial expansion of (1+x)²ⁿ be α and those of two middle terms of the binomial expansion of (1+x)²ⁿ⁻¹ be β and γ. Which one of the following relations is correct?

A. α > β + γ

B. α < β + γ

C. α = β + γ

D. α = βγ

Q. 25 Let A = {x ∈ R : – 1 ≤ x ≤ 1},

B = y ∈ R : – 1 ≤ y ≤ 1} and S be the

subset of A x B, defined by

S = [(x, y) ∈ A x B : x² + y² = 1]

Which one of the following is correct?

A. S is a one-one function from A into B

B. S is a many-one function from A into B

C. S is a bijective mapping from A into B

D. S is not a function

Q. 26 Let Tᵣ be the rth term of an AP for r=1, 2, 3, … . If for some distinct positive integers u and v we have Tᵤ=1/ᵥ and Tᵥ=1/ᵤ, then what is Tᵤᵥ equal to?

A. (uv)⁻¹

B. u⁻¹+v⁻¹

C. 1

D. 0

Q. 27 Suppose f(x) is such a quadratic expression that it is positive for all real x.

If g(x) = f(x) + f'(x) + f”(x), then for any real x

A. g(x) < 0

B. g(x) > 0

C. g(x) = 0

D. g(x) ≥ 0

Q. 28 Consider the following in respect of matrices A, B, and C of same order:

1. (A + B + C)’ = A’ + B’ + C’

2. (AB)’ = A’B’

3. (ABC) = C’B’A’

Where A’ is the transpose of the matrix A.

Which of the above is correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 29 The sum of the binary numbers (11011)₂, (10110110)₂ and (10011x0y)₂ is the binary number (101101101)₂. What are the values of x and y?

A. x = 1, y = 1

B. x = 1, y = 0

C. x = 0, y = 1

D. x = 0, y = 0

Q. 30 Let matrix B be the adjoint of a square matrix A, l be the identity matrix of same order as A. If k (≠0) is the determinant of the matrix A, then what is AB equal to?

A. l

B. kl

C. k²l

D. (1/k)l

Q. 31 If (0.2)ⁿ = 2 and log₁₀2 = 0.3010, then what is the value of n to the nearest tenth?

A. -10.0

B. -0.5

C. -0.4

D. -0.2

Q. 32 The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is

A. 45360

B. 30240

C. 27216

D. 15120

Q. 33 What is the determinant of the matrix?

A. (x – y) (y – z) (z – x)

B. (x – y) (y – z)

C. (y – z) (z – x)

D. (z – x)² (x + y + z)

Q. 34 As given in the picture, if A, B and C are angles of a triangle then which one of the following is correct?

A. The triangle ABC is isosceles

B. The triangle ABC is equilateral

C. The triangle ABC is scalene

D. No conclusion can be drawn with regard to the nature of the triangle

Q. 35 Consider the following in respect of matrices A and B of same order:

1. A² – B² = (A + B)(A – B)

2. (A – I)(I + A) = O ⇔ A² = 1

where I is the identity matrix and O is the null matrix.

Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 36 What is 2 tanθ/1 + tan²θ equal to?

A. cos 2θ

B. tan 2θ

C. sin 2θ

D. cosec 2θ

Q. 37 If sec (θ – a), sec θ and sec (θ + a) are in AP, where cos a ≠ 1, then what is the value of sin²θ + cos a?

A. 0

B. 1

C. -1

D. 1/2

Q. 38 If A + B + C = 180°, then what is sin 2A – sin 2C equal to?

A. -4 sin A sin B sin C

B. -4 cos A sin B cos C

C. -4 cos A cos B sin C

D. -4 sin A cos B cos C

Q. 39 A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the

balloon is 48°. If the height of the balloon above the bridge is 122 m, then what is the length of the bridge?

A. 122 sin 48° m

B. 122 tan 42° m

C. 122 cos 48° m

D. 122 tan 48° m

Q. 40 A is an angle in the fourth quadrant. It satisfies the trigonometric equation 3 (3 – tan²A – cot A)² = 1. Which one of the following is the value of A?

A. 300°

B. 315°

C. 330°

D. 345°

Q. 41 The top of a hill observed from the top and bottom of a building of height h is at angles of elevation π/6 and π/3 respectively. What is the height of the hill?

A. 2h

B. 3h/2

C. h

D. h/2

Q. 42 What is/are the solution(s) of the trigonometric equation cosec x + cot x = √3, where 0 < x < 2π ?

A. 5π/3 only

B. π/3 only

C. π only

D. π, π/3, 5π/3

Q. 43 If θ=π/8, then what is the value of

(2cosθ+1)¹⁰(2cos2θ-1)¹⁰(2cosθ-1)¹⁰(2cos4θ-1)¹⁰?

A. 0

B. 1

C. 2

D. 4

Q. 44 If cos α and cos β (0<α<β<π) are the roots of the quadratic equation 4x²-3=0, then what is the value of sec α and sec β?

A. -4/3

B. 4/3

C. 3/4

D. -3/4

Q. 45 Consider the following values of x:

1. 8

2. -4

3. 1/6

4. -1/4

Which of the above values of x is/are the solution(s) of the equation tan⁻¹(2x)+tan⁻¹(3x)=π/4 ?

A. 3 only

B. 2 and 3 only

C. 1 and 4 only

D. 4 only

Q. 46 If the second term of a GP is 2 and the sum of its infinite terms is 8, then the GP is

A. 8, 2, 1/2, 1/8

B. 10, 2, 2/5, 2/25

C. 4, 2, 1, 1/2, 1/2²

D. 6, 3, 3/2, 3/4

Q. 47 If a, b, c are in AP or GP or HP, then a -b/b – c is equal to

A. b/a or 1 or b/c

B. c/a or c/b or 1

C. 1 or a/b or a/c

D. 1 or a/b or c/a

Q. 48 What is the sum of all three-digit numbers that can be formed using all the digits 3, 4 and 5, when repetition of digits is not allowed?

A. 2664

B. 3882

C. 4044

D. 4444

Q. 49 The ratio of roots of the equations ax²+bx+c=0 and px²+qx+r=0 are equal. If D₁ and D₂ are respective discriminants, then what is D₁/D₂ equal to?

A. a²/p²

B. b²/q²

C. c²/r²

D. None of the above

Q. 50 If A=sin²θ+cos⁴θ, then for all real θ, which one of the following is correct?

A. 1≤ A ≤ 2

B. 3/4 ≤ A ≤ 1

C. 13/16 ≤ A ≤ 1

D. 3/4 ≤ A ≤ 13/16

Q. 51 The equation of a circle whose end points of a diameter are (x₁,y₁) and (x₂,y₂) is

A. (x-x₁)(x-x₂)+(y-y₁)(y-y₂)=x²+y²

B. (x-x₁)²+(y-y₁)²=x₂y₂

C. x²+y²+2x₁x₂+2y₁y₂=0

D. (x-x₁)(x-x₂)+(y-y₁)(y-y₂)=0

Q. 52 The second degree equation x² + 4y² – 2x – 4y + 2 = 0 represents

A. A point

B. An ellipse of semi-major axis 1

C. An ellipse with eccentricity √3/2

D. None of the above

Q. 53 The angle between the two lines lx+my+n=0 and l’x+m’y+n’=0 is given by tan⁻¹θ. What is θ equal to?

A. |lm’-l’m/ll’-mm’|

B. |lm’+l’m/ll’+mm’|

C. |lm’-l’m/ll’+mm’|

D. |lm’+l’m/ll’+mm’|

Q. 54 Consider the following statements:

1. The distance between the lines y=mx+c₁ and y=mx+c₂ is |c₁-c₂|/[√1+m²]

2. The distance between the lines ax+by+c₁=0 and ax+by+c₂=0 is |c₁-c₂|/[√a²+b²]

3. The distance between the lines x=c₁ and x=c₂ is |c₁-c₂|

Which of the above statements are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 55 What is the equation of straight line passing through the point of intersection of the lines x/2 + y/3 = 1 and x/3 + y/2 = 1, and parallel to the line 4x + 5y – 6 = 0 ?

A. 20x + 25y – 54 = 0

B. 25x + 20y – 54 = 0

C. 4x + 5y – 54 = 0

D. 4x + 5y – 45 = 0

Q. 56 What is the distance of the point (2, 3, 4) from the plane 3x – 6y + 2z + 11 = 0?

A. 1 unit

B. 2 units

C. 3 units

D. 4 units

Q. 57 Coordinates of the points O, P ,Q and R are respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram who two adjacent sides LK and LM are each of length √2. What are the values of m and n respectively?

A. 6, 2

B. 1, 3

C. 3, 1

D. None of the above

Q. 58 The line x-1/2 = y-2/3 = z-3/4 is given by

A. x+y+z=6, x+2y-3z=-4

B. x+2y-2z=-1, 4x+4y-5z-3=0

C. 3x+2y-3z=0, 3x-6y+3z=-2

D. 3x+2y-3z=-2, 3x-6y+3z=0

Q. 59 Consider the following statements:

1. The angle between the planes

2x-y+z=1 and x+y+2z=3 is π/3.

2. The distance between the planes

6x-3y+6z+2=0 and

2x-y+2z+4=0 is 10/9

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. 60 Consider the following statements:

Statement I: If the line segment joining the points P(m, n) and Q(r, s) subtends an angle α at the origin, then cos α = ms-nr/[√(m²+n²)(r²+s²)]

Statement II: In any triangle ABC, it is true that a²=b²+c²-2bc cos A

Which one of the following is correct in respect of the above two statements?

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

B. Both Statement I and Statement II are true, but Statement II is not the correct

explanation of Statement I

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

D. Statement I is false, but Statement II is true

Q. 61 What is the area of the triangle with vertices (x₁, 1/x₁), (x₂, 1/x₂), (x₃, 1/x₃)?

A. |(x₁-x₂)(x₂-x₃)(x₃-x₁)|

B. 0

C. |(x₁-x₂)(x₂-x₃)(x₃-x₁)/x₁x₂x₃|

D. |(x₁-x₂)(x₂-x₃)(x₃-x₁)/2x₁x₂x₃|

Q. 62 If y-axis touches the circle

x²+y²+gx+fy+e/4=0, then the normal at this point intersects the circle at the point

A. (-g/2, -f/2)

B. (-g, -f/2)

C. (-g/2, f)

D. (-g, -f)

Q. 63 Let |a̅|≠0, |b̅|≠0

(a̅+b̅).(a̅+b̅)=|a̅|²+|b̅|²

holds if and only if

Note: a̅ and b̅ represent vector sign

A. a̅ and b̅ are perpendicular

B. a̅ and b̅ are parallel

C. a̅ and b̅ are inclined at an angle of 45°

D. a̅ and b̅ are anti-parallel

Q. 64 if r̅=xî+yĵ+zk̂, then what is r̅.(î+ĵ+k̂) equal to?

Note: r̅ represents the vector sign.

A. x

B. x+y

C. -(x+y+z)

D. (x+y+z)

Q. 65 A unit vector perpendicular to each of the vectors 2î-ĵ+k̂ and 3î-4ĵ-k̂ is

A. (1/√3)î+(1/√3)ĵ-(1/√3)k̂

B. (1/√2)î+(1/2)ĵ-(1/2)k̂

C. (1/√3)î-(1/√3)ĵ-(1/√3)k̂

D. (1/√3)î+(1/√3)ĵ+(1/√3)k̂

Q. 66 if |a̅|=3, |b̅|=4, and |a̅-b̅|=5, then what is the value of |a̅+b̅|?

Note: a̅, b̅ represent the vector sign.

A. 8

B. 6

C. 5√2

D. 5

Q. 67 Let a̅, b̅ and c̅ be three mutually perpendicular vectors each of unit magnitude. If A̅=a̅+b̅+c̅, B̅=a̅-b̅+c̅ and C̅=a̅-b̅-c̅, then which one of the following is correct?

Note: A̅, B̅, C̅, a̅, b̅ and c̅ represent the vector sign.

A. |A̅|>|B̅|>|C̅|

B. |A̅|=|B̅|≠|C̅|

C. |A̅|=|B̅|=|C̅|

D. |A̅|≠|B̅|≠|C̅|

Q. 68 What is (a̅-b̅)×(a̅+b̅) equal to?

Note: a̅ and b̅ represent the vector sign.

A. 0̅

B. a̅×b̅

C. 2(a̅×b̅)

D. |a̅|²-|b̅|²

Q. 69 A spacecraft located at î+2ĵ+3k̂ is subjected to a force λk̂ by firing a rocket. The spacecraft is subjected to a moment of magnitude

A. λ

B. √3λ

C. √5λ

D. None of the above

Q. 70 In a triangle ABC, if taken in order, consider the given statements.

How many of the statements given in the image are correct

A. One

B. Two

C. Three

D. Four

Q. 71 Let the slope of the curve y=cos⁻¹(sin x) be tan θ. Then the value of θ in the interval (0, π) is

A. π/6

B. 3π/4

C. π/4

D. π/2

Q. 72 If f(x)=(√x-1)/x-4 defines a function on ℝ, then what is its domain?

A. (-∞, 4)⋃(4, ∞)

B. [4, ∞)

C. (1, 4)⋃(4, ∞)

D. [1, 4)⋃(4, ∞)

Q. 73 Which one of the following is correct in respect of the function?

A. It is not continuous at x=0

B. It is continuous at every x

C. It is not continuous at x=π

D. It is continuous at x=0

Q. 74 For the function f(x) = |x-3|, which one of the following is not correct ?

A. The function is not continuous at x = -3

B. The function is continuous at x = 3

C. The function is differentiable at x = 0

D. The function is differentiable at x = -3

Q. 75 If the function f(x)=2x-sin⁻¹x/2x+tan⁻¹x is continuous at each point in its domain, then what is the value of f(0) ?

A. -1/3

B. 1/3

C. 2/3

D. 2

Q. 76 If f(x)=(√25-x²), then what is the given matrix equal to?

A. -1/√24

B. 1/√24

C. -1/4√3

D. 1/4√3

Q. 77 If y=tan⁻¹(5-2tan√x/2+5tan√x), then what is dy/dx equal to?

A. -1/2√x

B. 1

C. -1

D. 1/2√x

Q. 78 Which one of the following is correct in respect of the function f(x)=x sin x + cos x + ½ cos²x?

A. It is increasing in the interval (0, π/2)

B. It remains constant in the interval (0, π/2)

C. It is decreasing in the interval (0, π/2)

D. It is decreasing in the interval (π/4, π/2)

Q. 79 What is the given matrix equal to?

A. √2

B. 2√2

C. 1/√2

D. -1/2√2

Q. 80 A function f : A→R is defined by the equation f(x)=x²-4x+5 where A=(1, 4). What is the range of the function?

A. (2, 5)

B. (1, 5)

C. [1, 5)

D. [1, 5]

Q. 81 What is the given matrix equal to, where [.] is the greatest integer function?

A. b-a

B. a-b

C. 0

D. 2(b-a)

Q. 82 What is the given matrix equal to?

A. 2

B. 3

C. 4

D. 9

Q. 83 What is ∫ sin³ x cos x dx equal to?

Note: where c is the constant of integration.

A. cos⁴x+c

B. sin⁴x+c

C. [(1-sin²x)²/4] + c

D. [(1-cos²x)²/4] + c

Q. 84 What is the given matrix equal to?

A. ln|tan x|+c

B. ln|sec x|+c

C. tan x+c

D. eᵗᵃⁿ ˣ+c

Q. 85 What is the given matrix equal to?

A. 0

B. -π/4

C. -π/2

D. π/2

Q. 86 In which one of the following intervals is the function f(x)=x²-5x+6 decreasing?

A. (∼∞, 2]

B. [3, ∞)

C. (∼∞, ∞)

D. (2, 3)

Q. 87 The differential equation of the family of curves y=p cos (ax)+ q sin (ax), where p, q are arbitrary constants is

A. (d²y/dx²) – a²y = 0

B. (d²y/dx²) – ay = 0

C. (d²y/dx²) + ay = 0

D. (d²y/dx²) + a²y = 0

Q. 88 The equation of the curve passing through the point (-1, -2) which satisfies dy/dx=-x²-1/x³, is

A. 17x²y-6x²+3x⁵-2=0

B. 6x²y+17x²+2x⁵-3=0

C. 6xy-2x²+17x⁵+3=0

D. 17x²y+6xy-3x⁵+5=0

Q. 89 What is the order of the differential equation whose solution is y=a cos x + b sin x + ce⁻ⁿ + d, where a, b, c and d are arbitrary constants?

A. 1

B. 2

C. 3

D. 4

Q. 90 What is the solution of the differential equation ln(dy/dx)=ax+by?

Note: where c is an arbitrary constant

A. aeᵃˣ + beᵇʸ = c

B. (1/a)eᵃˣ +(1/b)eᵇʸ = c

C. aeᵃˣ + be⁻ᵇʸ = c

D. (1/a)eᵃˣ + (1/b)e⁻ᵇʸ = c

Q. 91 If u=eⁱ ⁿ sin bx and v=eⁱ ⁿ cos bx, then what is u(du/dx)+v(dv/dx) equal to?

A. a e²ⁱ ⁿ

B. (a²+b²)eⁱ ⁿ

C. ab e²ⁱ ⁿ

D. (a+b)eⁱ ⁿ

Q. 92 If y=sin(ln x), then which one of the following is correct?

A. (d²y/dx²) + y = 0

B. d²y/dx²=0

C. x²(d²y/dx²)+x(dy/dx)=0

D. x²(d²y/dx²)-x(dy/dx)=0

Q. 93 A flower-bed in the form of a sector has been fenced by a wire of 40 m length. If the flowerbed has the greatest possible area, then what is the radius of the sector?

A. 25 m

B. 20 m

C. 10 m

D. 5 m

Q. 94 What is the minimum value of [x(x-1)+1]¹⁄³, where 0≤x≤1 ?

A. (3/4)¹⁄³

B. 1

C. 1/2

D. (3/8)¹⁄³

Q. 95 If y=|sin x||ˣ|, then what is the value of dy/dx at x=-π/6 ?

A. [2⁻π/⁶ (6 ln 2 – √3π)] / 6

B. [2π/⁶ (6 ln 2 + √3π)] / 6

C. [2⁻π/⁶ (6 ln 2 + √3π)] / 6

D. [2π/⁶ (6 ln 2 – √3π)] / 6

Q. 96 What is d√(1-sin2x)/dx equal to, where π/4

A. cos x + sin x

B. -(cos x+ sin x)

C. ±(cos x + sin x)

D. None of the above

Q. 97 What is ∫ dx/a²sin²x+b²cos²x equal to?

Note: where c is the constant of integration

A. c+1/ab tan⁻¹(a tan x/b)

B. c-1/ab tan⁻¹(b tan x/a)

C. c+1/ab tan⁻¹(b tan x/a)

D. None of the above

Q. 98 According to the matrix given, let f(x+y)=f(x)f(y) and f(x)=1+xg(x)φ(x). Then what is f'(x) equal to?

A. 1+abf(x)

B. 1+ab

C. ab

D. abf(x)

Q. 99 What is solution of the differential equation dx/dy=x+y+1/x+y-1 ?

Note: where c is an arbitrary constant.

A. y-x+4ln(x+y)=c

B. y+x+2ln(x+y)=c

C. y-x+ln(x+y)=c

D. y+x+2ln(x+y)=c

Q. 100 What is the matrix given equal to?

A. -1/2

B. -1/3

C. -2

D. -3

Q. 101 If two dices are thrown and at least one of the dice shows 5, then the probability that the sum is 10 or more is

A. 1/6

B. 4/11

C. 3/11

D. 2/11

Q. 102 The correlation coefficient computed from a set of 30 observations is 0.8. Then the percentage of variation not explained by linear regression is

A. 80%

B. 20%

C. 64%

D. 36%

Q. 103 The average age of a combined group of men and women is 25 years. If the average age of the group of men is 26 years and that of the group of women is 21 years, then the percentage of men and women in the group is respectively

A. 20, 80

B. 40, 60

C. 60, 40

D. 80, 20

Q. 104 If sin β is the harmonic mean of sin α and cos α, and sin θ is the arithmetic mean of sin α and cos α, then which of the following is/are correct?

1. √2 sin (α+π/4)sinβ = sin 2α

2. √2 sin θ = cos (α-π/4)

Select the correct answer using the code below:

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 105 Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If P(B) = 1.5 P(A) and P(C) = 0.5 P(B), then P(A) is equal to

A. 3/4

B. 4/13

C. 2/3

D. 1/2

Q. 106 In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25%, 35% and 40% of the factory’s total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X?

A. 5/39

B. 14/39

C. 20/39

D. 34/39

Q. 107 8 coins are tossed simultaneously. The probability of getting at least 6 heads is

A. 7/64

B. 57/64

C. 37/256

D. 229/256

Q. 108 Three groups of children contain 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys. One child is selected at random from each group. The probability that the three selected consist of 1 girl and 2 boys is

A. 13/32

B. 9/32

C. 3/32

D. 1/32

Q. 109 Consider the following statements:

1. If 10 is added to each entry on a list, then the average increases by 10.

2. If 10 is added to each entry on a list, then the standard deviation increases by 10.

3. If each entry on a list is doubled, then the average doubles.

Which of the above statements are correct?

A. 1, 2 and 3

B. 1 and 2 only

C. 1 and 3 only

D. 2 and 3 only

Q. 110 The variance of 25 observations is 4. If 2 is added to each observation, then the new variance of the resulting observations is

A. 2

B. 4

C. 6

D. 8

Q. 111 If xᵢ>0, yᵢ>0 (i=1, 2, 3 … n) are the values of two variables X and Y with geometric means P and Q respectively, then the geometric mean of X/Y is

A. P/Q

B. antilog (P/Q)

C. n(logP-logQ)

D. n(logP+logQ)

Q. 112 If the probability of simultaneous occurrence of two events A and B is p and the probability that exactly one of A, B occurs is q, then which of the following is/are correct?

1. P(A̅)+P(B̅)=2-2p-q

2. P(A̅∩B̅)=1-p-q

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. 113 If the regression coefficient of Y on X is -6, and the correlation coefficient between X and Y is -1/2, then the regression coefficient of X on Y would be

A. 1/24

B. -1/24

C. -1/6

D. 1/6

Q. 114 The set of bivariate observations (x₁, y₁), (x₂, y₂) …, (xᵣ, yᵣ) are such that all the values are distinct and all the observations fall on a straight line with non-zero slope. Then the possible values of the correlation coefficient between x and y are

A. 0 and 1 only

B. 0 and -1 only

C. 0, 1 and -1

D. -1 and 1 only

Q. 115 Two integers x and y are chosen with replacement from the set {0, 1, 2, …, 10}. The probability that |x – y| > 5 is

A. 6/11

B. 35/121

C. 30/121

D. 25/121

Q. 116 An analysis of monthly wages paid to the workers in two firms A and B belonging to the same industry gives the result as shown in the table. The average of monthly wage and variance of distribution of wages of all the workers in the firms A and B taken together are

A. Rs 1860, 100

B. Rs. 1750, 100

C. Rs. 1800, 81

D. None of the above

Q. 117 Three dice having digits, 1, 2, 3, 4, 5 and 6 on their faces are marked I, II and III and rolled. Let x, y and z represent the number on die-I, die-II and die-III respectively. What is the number of possible outcomes such that x > y > z ?

A. 14

B. 16

C. 18

D. 20

Q. 118 Which one of the following can be obtained from an ogive?

A. Mean

B. Median

C. Geometric mean

D. Mode

Q. 119 In any discrete series (when all values are not same), if x represents mean deviation about mean and y represents standard deviation, then which one of the following is correct ?

A. y ≥ x

B. y ≤ x

C. x = y

D. x < y

Q. 120 In which one of the following cases would you expect to get a negative correlation?

A. The ages of husbands and wives

B. Shoe size and intelligence

C. Insurance companies’ profits and the number of claims they have to pay

D. Amount of rainfall and yield of crop

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

NDA/NA(II) Exam 2017 Mathematics Previous Year Paper

NDA/NA(II) Exam 2017 Mathematics

Q. 1 If x + log₁₀ (1 + 2ˣ) = x log₁₀ 5 + log₁₀ 6, then x is equal to

A. 2, -3

B. 2 only

C. 1

D. 3

Q. 2 The remainder and the quotient of the binary division (101110)₂ / (110)₂ are respectively

A. (111)₂ and (100)₂

B. (100)₂ and (111)₂

C. (101)₂ and (101)₂

D. (100)₂ and (100)₂

Q. 3 The matrix A has x rows and x + 5 columns. The matrix B has y rows and 11 – y columns. Both AB and BA exists. What are the values of x and y respectively?

A. 8 and 3

B. 3 and 4

C. 3 and 8

D. 8 and 8

Q. 4 If Sₙ = nP + n(n – 1)Q/2, where Sₙ denotes the sum of the first n terms of an AP, then the common difference is

A. P + Q

B. 2P + 3Q

C. 2Q

D. Q

Q. 5 The roots of the equation (q – r)x² + (r – p)x + (p – q) = 0 are

A. (r – p)/(q – r), 1/2

B. (p – q)/(q – r), 1

C. (q – r)/(p – q), 1

D. (r – p)/(p – q), 1/2

Q. 6 If E is the universal set and A = B U C, then the set E – (E – (E – (E – (E – A)))) is same as the set

A. B’ U C’

B. B U C

C. B’ ∩ C’

D. B ∩ C

Q. 7 If A = {x: x is a multiple of 2}, B = {x: x is a multiple of 5} and C = {x: x is a multiple of 10}, then A ∩ (B ∩ C) is equal to

A. A

B. B

C. C

D. {x: x is a multiple of 100}

Q. 8 If α and β are roots of the equation 1 + x + x² = 0, then the given matrix product is equal to

A. a

B. b

C. c

D. d

Q. 9 If lal denotes the absolute value of an integer, then which of the following are correct?

1. labl = lal lbl

2. la + bl <= lal + lbl

3. la – bl >=l lal – lbl l

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. 10 How many different permutations can be made out of the letters of the word

‘PERMUTATION’?

A. 19958400

B. 19954800

C. 19952400

D. 39916800

Q. 11 Answer the questions given in the image.

A. a

B. b

C. c

D. d

Q. 12 The sum of all real roots of the equation lx – 3l² + lx – 3l – 2 = 0 is

A. 2

B. 3

C. 4

D. 6

Q. 13 It is given that the roots of the equation x² – 4x – log₃ P = 0 are real. For this, the minimum value of P is

A. 1/27

B. 1/64

C. 1/81

D. 1

Q. 14 If A is a square matrix, then the value of adj Aᵀ – (adj A)ᵀ is equal to

A. A

B. 2lAl I, where I is the identity matrix

C. null matrix whose order is same as that of A

D. unit matrix whose order is same as that of A

Q. 15 The value of the product 6¹/² x 6¹/⁴ x 6¹/⁸ x 6¹/¹⁶ x … up to infinite terms is

A. 6

B. 36

C. 216

D. 512

Q. 16 The value of the given determinant for all values of θ is

A. 1

B. cos θ

C. sin θ

D. cos 2θ

Q. 17 The number of terms in the expansion of (x + a)¹⁰⁰ + (x – a)¹⁰⁰ after simplification is

A. 202

B. 101

C. 51

D. 50

Q. 18 In the expansion of (1 + x)⁵⁰, the sum of the coefficients of odd powers of x is

A. 2²⁶

B. 2⁴⁹

C. 2⁵⁰

D. 2⁵¹

Q. 19 If a, b, c are real non-zero numbers, then the inverse of the matrix A is

A. a

B. b

C. c

D. d

Q. 20 A person is to count 4500 notes. Let aₙ denote the number of notes he counts in the nth minute. If a1 = a2 = a3 = … = a10 = 150, and a10, a11, a12, …. are in AP with the common difference -2, then the time taken by him to count all the notes is

A. 24 minutes

B. 34 minutes

C. 125 minutes

D. 135 minutes

Q. 21 The smallest positive integer n for which given equation is correct is

A. 1

B. 4

C. 8

D. 16

Q. 22 If we define the relation R on the set N x N as (a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N x N, then the relation is

A. symmetric only

B. symmetric and transitive only

C. equivalence relation

D. reflexive only

Q. 23 If y = x + x² + x³ + … up to infinte terms, where x < 1, then which one of the following is correct?

A. x = y / (1 + y)

B. x = y / (1 – y)

C. x = (1 + y) / y

D. x = (1 – y) / y

Q. 24 If α and β are the roots of the equation 3x² + 2x + 1 = 0, then the equation whose roots are α + β⁻¹ and β + α⁻¹ is

A. 3x² + 8x + 16 = 0

B. 3x² – 8x – 16 = 0

C. 3x² + 8x – 16 = 0

D. x² + 8x + 16 = 0

Q. 25 The value of 1/log₃ e + 1/log₃ e² + 1/log₃ e⁴ + … upto infinite terms is

A. logₑ 9

B. 0

C. 1

D. logₑ 3

Q. 26 A tea party is arranged for 16 people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is

A. 24 x 8! x 8!

B. (8!)³

C. 210 x 8! x 8!

D. 16!

Q. 27 The system of equations kx + y + z = 1, x + ky + z = k and x + y + kz = k² has no solution if k equals

A. 0

B. 1

C. -1

D. -2

Q. 28 If 1.3 + 2.3² + 3.3³ + …. + n.3ⁿ = [(2n – 1)3ᵃ + b] / 4, then a and b are respectively

A. n, 2

B. n, 3

C. n + 1, 2

D. n + 1, 3

Q. 29 In △PQR, ∠R = π/2; If tan (P/2) and tan (Q/2) are the roots of the equation ax² + bx + c = 0, then which on of the following is correct?

A. a = b + c

B. b = c + a

C. c = a + b

D. b = c

Q. 30 If lz – 4/zl = 2, thn the maximum value of lzl is equal to

A. 1 + √3

B. 1 + √5

C. 1 – √5

D. √5 – 1

Q. 31 The angle of elevation of a stationary cloud from a point 25 m above a lake is 15° and the angle of depression of its image in the lake is 45°. The height of the cloud above the lake level is

A. 25 m

B. 25√3 m

C. 50 m

D. 50√3 m

Q. 32 The value of tan 9° – tan 27° – tan 63° + tan 81° is equal to

A. -1

B. 0

C. 1

D. 4

Q. 33 The value of √3 cosec 20° – sec 20° is equal to

A. 4

B. 2

C. 1

D. -4

Q. 34 Angle α is divided into two parts A and B such that A – B = x and tan A : tan B = p : q. The value of sin x is equal to

A. (p + q) sin α / (p – q)

B. p sin α / (p + q)

C. p sin α / (p – q)

D. (p – q) sin α / (p + q)

Q. 35 The value of sin⁻¹ (3/5) + tan⁻¹ (1/7) is equal to

A. 0

B. π/4

C. π/3

D. π/2

Q. 36 The angles of elevation of the top of a tower from the top and foot of a pole are respectively 30° and 45°. If hₜ is the height of the tower and hₚ is the height of the pole, then which of the following are correct?

1. 2hₜhₚ/(3 + √3) = hₚ²

2. hₜ – hₚ / (√3 + 1) = hₚ/2

3. 2(hₚ + hₜ)/hₚ = 4 + √3

Select the correct answer using the code given below.

A. 1 and 3 only

B. 2 and 3 only

C. 1 and 2 only

D. 1, 2 and 3

Q. 37 In a triangle ABC, a – 2b + c = 0. The value of cot(A/2) cot(C/2) is

A. 9/2

B. 3

C. 3/2

D. 1

Q. 38 √(1 + sin A) = – (sin A/2 + cos A/2) is true if

A. 3π/2 < A < 5π/2 only

B. π/2 < A < 3π/2 only

C. 3π/2 < A < 7π/2

D. 0 < A < 3π/2

Q. 39 In triangle ABC, if (sin² A + sin² B + sin² C) / (cos² A + cos² B + cos² C) = 2 then the triangle is

A. right angled

B. equilateral

C. isosceles

D. obtuse angled

Q. 40 The principal value of sin⁻¹ x lies in the interval

A. (-π/2, π/2)

B. [-π/2, π/2]

C. [0, π/2]

D. [0, π]

Q. 41 The points (a, b), (0, 0), (-a, -b) and (ab, b²) are

A. the vertices of a paralellogram

B. the vertices of a rectangle

C. the vertices of a square

D. colinear

Q. 42 The length of the normal from origin to the plane x + 2y – 2z = 9 is equal to

A. 2 units

B. 3 units

C. 4 units

D. 5 units

Q. 43 If α, β, and γ are the angles which the vector OP (O being the origin) makes with the positive direction of the coordinate axis, then which of the following are correct?

1. cos² α + cos² β = sin² γ

2. sin² α + sin² β = cos² γ

3. sin² α + sin² β + sin² γ = 2

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 44 The angle between the lines x + y – 3 = 0 and x – y + 3 = 0 is α and the acute angle between the lines x – √3y + 2√3 = 0 and √3x – y + 1 = 0 is β. Which one of the following s correct?

A. α = β

B. α > β

C. α < β

D. α = 2β

Q. 45 Let ⃗α = î + 2ĵ – k̂, ⃗β = 2î + ĵ + 3k̂ and ⃗γ = 2î + ĵ + 6k̂ be three vectors. If ⃗α and ⃗β are both perpendicular to the vector ⃗δ and ⃗δ . ⃗γ = 10, then what is the magnitude of ⃗δ?

A. √3 units

B. 2√3 units

C. √3/2 units

D. 1/√3 units

Q. 46 If â and b̂ are two unit vectors, then the vector (â + b̂) x (â x b̂) is parallel to

A. (â – b̂)

B. (â + b̂)

C. (2â – b̂)

D. (2â + b̂)

Q. 47 A force ⃗F = î + 3ĵ + 2k̂ acts on a particle to displace it from the point A(î + 2ĵ – 3k̂) to the point B(3î – ĵ + 5k̂). The work done by the force will be

A. 5 units

B. 7 units

C. 9 units

D. 10 units

Q. 48 For any vector ⃗α, l ⃗α x î l² + l ⃗α x ĵ l² + l ⃗α x k̂ l² is equal to

A. l ⃗α l²

B. 2 l ⃗α l²

C. 3 l ⃗α l²

D. 4 l ⃗α l²

Q. 49 A man running around a racecourse notes that the sum of the distances of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m. The area of the path he encloses is

A. 18π square meters

B. 15π square meters

C. 12π square meters

D. 8π square meters

Q. 50 The distance of the point (1, 3) from the line 2x + 3y = 6, measured parallel to the line 4x + y = 4 is

A. 5/√13 units

B. 3/√17 units

C. √17 units

D. √17/2 units

Q. 51 If the vectors aî + ĵ + k̂, î + bĵ + k̂, î + ĵ + ck̂ (a, b, c ≠ 1) are coplaner, then the value of 1/(1 – a) + 1/(1 – b) + 1/(1 – c) is equal to

A. 0

B. 1

C. a + b + c

D. abc

Q. 52 The point of intersection of the line joining the points (-3, 4, -8) and (5, -6, 4) with the XYplane is

A. (7/3, -8/3, 0)

B. (-7/3, -8/3, 0)

C. (-7/3, 8/3, 0)

D. (7/3, 8/3, 0)

Q. 53 If the angle between the lines whose direction ratios are <2, -1, 2> and is π/4, then the smaller value of x is

A. 52

B. 4

C. 2

D. 1

Q. 54 The position of the point (1, 2) relative to the ellipse 2x² + 7y² = 20 is

A. outside the ellipse

B. inside the ellipse but not at the focus

C. on the ellipse

D. at the focus

Q. 55 The equation of a straight line which cuts off an intercept of 5 units on the negative direction of the y-axis and makes an angle 120⁰ with the positive direction of the x-axis is

A. y + √3x + 5 = 0

B. y – √3x + 5 = 0

C. y + √3x – 5 = 0

D. y – √3x – 5 = 0

Q. 56 The equation of the line passing through the point (2, 3) and the point of intersection of lines 2x – 3y + 7 = 0 and 7x + 4y + 2 = 0 is

A. 21x + 46y – 180 = 0

B. 21x – 46y + 96 = 0

C. 46x + 21y -155 = 0

D. 46x – 21y – 29 = 0

Q. 57 The equation of the ellipse whose center is at the origin, the major axis is along the x-axis with eccentricity 3/4 and latus rectum 4 units is

A. x²/1024 + 7y²/64 = 1

B. 49x²/1024 + 7y²/64 = 1

C. 8x²/1024 + 49y²/64 = 1

D. x²/1024 + y²/64 = 1

Q. 58 The equation of the circle which passes through the points (1, 0), (0, -6) and (3, 4) is

A. 4x² + 4y² + 142x + 47y + 140 = 0

B. 4x² + 4y² – 142x – 47y + 138 = 0

C. 4x² + 4y² – 142x + 47y + 138 = 0

D. 4x² + 4y² + 150x – 49y + 138 = 0

Q. 59 A variable plane passes through a fixed point (a, b, c) and cuts the axes in A, B and C respectively. The locus of the center of the sphere OABC, O being the origin, is

A. x/a + y/b + z/c = 1

B. a/x + b/y + c/z = 1

C. a/x + b/y + c/z = 2

D. x/a + y/b + z/c = 2

Q. 60 The equation of the plane passing through the line of intersection of the planes x + y + z = 1, 2x + 3y + 4z = 7 and perpendicular to the plane x – 5y + 3z = 5 is given by

A. x + 2y + 3z – 6 = 0

B. x + 2y + 3z + 6 = 0

C. 3x + 4y + 5z – 8 = 0

D. 3x + 4y + 5z + 8 = 0

Q. 61 The inverse of the function y = 5ˡⁿ ˣ is

A. x = y¹/ˡⁿ ⁵, y > 0

B. x = yˡⁿ ⁵, y > 0

C. x = y¹/ˡⁿ ⁵, y < 0

D. x = 5 ln y, y > 0

Q. 62 Which one is correct in respect of the given function?

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

B. f(x) is continuous as well as differentiable at x = 0

C. f(x) is discontinuous at x = 0

D. None of the above

Q. 63 Answer as per instructions given in the image.

A. – y²tan x / (1 – y ln(cos x))

B. y²tan x / (1 + y ln(cos x))

C. y²tan x / (1 – y ln(sin x))

D. y²sin x / (1 + y ln(sin x))

Q. 64 Consider the following:

1. x + x² is continuous at x = 0.

2. x + cos 1/x is discontinuous at x = 0.

3. x² + cos 1/x is continuous at x = 0.

Which of the above are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 65 Consider the following statements:

1. dy/dx at a point on the curve gives the slope of the tangent at that point.

2. If a(t) denotes acceleration of a particle, then ∫a(t) dt + c gives a velocity of the particle.

3. If s(t) gives a displacement of a particle at a time t, then ds/dt gives its acceleration at that instant.

Which of the above statement(s) is/are correct?

A. 1 and 2 only

B. 2 only

C. 1 only

D. 1, 2 and 3

Q. 66 If y = sec⁻¹ [(x + 1)/(x – 1)] + sin⁻¹ [(x – 1)/(x + 1)], then dy/dx is equal to

A. 0

B. 1

C. (x – 1)/(x + 1)

D. (x + 1)/(x – 1)

Q. 67 What is ∫ tan⁻¹ (sec x + tan x) dx equal to?

A. πx/4 + x²/4 + c

B. πx/2 + x²/4 + c

C. πx/4 + πx²/4 + c

D. πx/4 – x²/4 + c

Q. 68 Which one of the following is correct in respect of the derivative of the function, i.e. f'(x)?

A. f'(x) = 2x for 0<x≤1

B. f'(x) = -2x for 0<x≤1

C. f'(x) = -2x for 0<x<1

D. f'(x) = 0 for 0<x<∞

Q. 69 Which one of the following is correct in respect of the function f(x) = x(x – 1)(x + 1)?

A. The local maximum value is larger than local minimum value.

B. The local maximum value is smaller than local minimum value.

C. The function has no local maximum.

D. The function has no local minimum.

Q. 70 Consider the following statements:

1. A derivative of f(x) may not exist at some point.

2. A derivative of f(x) may exist finitely at some point.

3. A derivative of f(x) may be infinite (geometrically) at some point.

Which of the above statement(s) are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 71 The maximum value of (ln x)/x is

A. e

B. 1/e

C. 2/e

D. 1

Q. 72 The function f(x) = lxl – x³ is

A. odd

B. even

C. both even and odd

D. neither even nor odd

Q. 73 Answer as per instructions given in the image.

A. l₁ ≠ l₂

B. d/dx(l₃) = l₂

C. ∫ l₃ dx = l₂

D. l₃ = l₂

Q. 74 The general solution of dy/dx = (ax + h)/(by + k) represents a circle only when

A. a = b = 0

B. a = -b ≠ 0

C. a = b ≠ 0, h = k

D. a = b ≠ 0

Q. 75 Answer as per instructions given in the image.

A. l = 1, m = 1

B. l = 2/π, m = ∞

C. l = 2/π, m = 0

D. l = 1, m = ∞

Q. 76 Answer as per instructions given in the image.

A. 8

B. 4

C. 2

D. 0

Q. 77 The area bounded by the curve lxl + lyl = 1 is

A. 1 square unit

B. 2√2 square units

C. 2 square units

D. 2√3 square units

Q. 78 If x is any real number, then x²/(1 + x⁴) belongs to which one of the following intervals?

A. (0, 1)

B. (0, 1/2]

C. (0, 1/2)

D. [0, 1]

Q. 79 The left hand derivative of f(x) = [x] sin (πx) at x = k; where k is an integer and [x] is the greatest integer function; is

A. (-1)ᵏ (k – 1)π

B. (-1)ᵏ⁻¹ (k – 1)π

C. (-1)ᵏ (kπ)

D. (-1)ᵏ⁻¹ (kπ)

Q. 80 If f(x) = x/2 – 1, then on the interval [0, π] which one of the following is correct?

A. tan [f(x)], where [.] is the greatest integer function, and 1/f(x) are both continuous

B. tan [f(x)], where [.] is the greatest integer function, and f⁻¹(x) are both continuous

C. tan [f(x)], where [.] is the greatest integer function, and 1/f(x) are both discontinuous

D. tan [f(x)], where [.] is the greatest integer function, is discontinuous but 1/f(x) is

continuous

Q. 81 Answer as per instructions given in the image.

A. 3 and 2

B. 2 and 2

C. 2 and 3

D. 1 and 3

Q. 82 If y = cos⁻¹ (2x/(1 + x²)), then dy/dx is equal to

A. -2/(1 + x²) for all lxl < 1

B. -2/(1 + x²) for all lxl > 1

C. 2/(1 + x²) for all lxl < 1

D. None of the above

Q. 83 The set of all points, where the function f(x) = √(1 – e⁻ˣ²) is differentiable is

A. (0, ∞)

B. (-∞, ∞)

C. (-∞, 0) U (0, ∞)

D. (-1, ∞)

Q. 84 Match List – I with List – II and select the correct answer using the code given.

A. A – 2, B – 3, C – 1, D – 4

B. A – 2, B – 3, C – 4, D – 1

C. A – 3, B – 2, C – 1, D – 4

D. A – 3, B – 2, C – 4, D – 1

Q. 85 If f(x) = x(√x – √(x – 1)), then f(x) is

A. continuous but not differentiable at x = 0

B. differentiable at x = 0

C. not continuous at x = 0

D. None of the above

Q. 86 Which one of the given graphs represent the function f(x) = x/x’, x ≠ 0?

A. a

B. b

C. c

D. d

Q. 87 Answer as per instructions given in the image.

A. 251

B. 250

C. 1

D. 0

Q. 88 Answer as per instructions given in the image.

A. x (ln x)⁻¹ + c

B. x (ln x)⁻² + c

C. x (ln x) + c

D. x (ln x)² + c

Q. 89 A cylindrical jar without a lid has to be constructed using a given surface area of a metal sheet. If the capacity of the jar is to be maximum, then the diameter of the jar must be k times the height of the jar. The value of k is

A. 1

B. 2

C. 3

D. 4

Q. 90 The value of given function is

A. π/4

B. π/2

C. π/2√2

D. π/√2

Q. 91 Let g be the greatest integer function. Then the function f(x) = (g(x)² – g(x)) is discontinuous at

A. all integers

B. all integers except 0 and 1

C. all integers except 0

D. all integers except 1

Q. 92 The differential equation of minimum order by eliminating the arbitraty constants A and C in the equation y = A [sin (x + C) + cos (x + C)] is

A. y” + (sin x + cos x)y’ = 1

B. y” = (sin x + cos x)y’

C. y” = (y’)² + sin x cos x

D. y” + y = 0

Q. 93 Consider the following statements:

Statement I – x > sin x for all x > 0

Statement II – f(x) = x – sin x is an increasing function for all x > 0

Which one of the following is correct in respect of the above statements?

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

B. Both I and II are true and II is not the correct explanation of I

C. I is true but II is false

D. I is false but II is true

Q. 94 Answer as per instructions given in the image.

A. y = x/(∅(x) + c)

B. y = ∅(x)/x + c

C. y = (∅(x) + c) / x

D. y = ∅(x) / (x + c)

Q. 95 If f(x) = (4x + x⁴) / (1 + 4x³) and g(x) = ln [(1 + x)/(1 – x)], then what is the value of f ∘ g [(e – 1)/(e + 1)] equal to?

A. 2

B. 1

C. 0

D. 1/2

Q. 96 Answer as per the instructions given in the image.

A. (α – β)(β γ)(α – γ)

B. (α – β)(β γ)(γ – α)

C. (α – β)(β γ)(γ – α)(α + β + γ)

D. 0

Q. 97 Answer as per the instructions given in the image.

A. a

B. b

C. c

D. d

Q. 98 Answer as per the instructions given in the image.

A. A² = -2A

B. A² = -4A

C. A² = -3A

D. A² = 4A

Q. 99 Geometrically Re (z² – i) = 2, where i = √-1 and Re is the real part, represents

A. Circle

B. Ellipse

C. Rectangular Hyperbola

D. Parabola

Q. 100 Answer as per instructions given in the image.

A. 0

B. 1

C. pa + qb + rc

D. pa + qb + rc + a + b + c

Q. 101 A committee of two people is selected from two men and two women. The probability that the committee will have exactly one woman is

A. 1/6

B. 2/3

C. 1/3

D. 1/2

Q. 102 Let a die be loaded in such a way that even faces are twice likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed?

A. 1/3

B. 2/3

C. 4/9

D. 5/9

Q. 103 Let the sample space consist of non-negative integers up to 50, X denotes the numbers which are multiples of 3 and Y denote odd numbers. Which of the following is/are correct?

1. P(X) = 8/25

2. P(Y) = 1/2

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. 104 For two events A and B, let P(A) = 1/2, P (A U B) = 2/3 and P (A ∩ B) = 1/6. What is P(A̅ ∩ B) equal to?

A. 1/6

B. 1/4

C. 1/3

D. 1/2

Q. 105 Consider the following statements:

1. The coefficient of variation depends on the unit of measurement fo the variable.

2. A range is a measure of dispersion.

3. Mean deviation is least when measured about the median.

Which of the above statements are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 106 Given that the arithmetic mean and standard deviation of a sample of 15 observations are 24 and 0 respectively. Then which one of the following is the arithmetic mean of the smallest five observations in the data?

A. 0

B. 8

C. 16

D. 24

Q. 107 Which one of the following can be considered as an appropriate pair of values of the regression coefficient of y on x and regression coefficient of x on y?

A. (1, 1)

B. (-1, 1)

C. (-1/2, 2)

D. (1/3, 10/3)

Q. 108 Let A and B be two events with P(A) = 1/3, P(B) = 1/6 and P(A ∩ B) = 1/12. What is P(BlA̅) equal to?

A. 1/5

B. 1/7

C. 1/8

D. 1/10

Q. 109 In a binomial distribution, the mean is 2/3 and the variance is 5/9. What is the probability that X = 2?

A. 5/36

B. 25/36

C. 25/216

D. 25/54

Q. 110 The probability that a ship safely reaches a port is 1/3. The probability that out of 5 ships, at least 4 ships would arrive safely is

A. 1/243

B. 10/243

C. 11/243

D. 13/243

Q. 111 What is the probability that at least two persons out of a group of three persons were born in the same month (disregard year)?

A. 33/144

B. 17/72

C. 1/144

D. 2/9

Q. 112 It is given that X̅ = 10, Y̅ = 90, σₓ = 3, σᵧ = 12 and rₓᵧ = 0.8. The regression equation of X on Y is

A. Y = 3.2X + 58

B. X = 3.2Y + 58

C. X = -8 + 0.2Y

D. Y = -8 + 0.2X

Q. 113 If P(B) = 3/4, P (A ∩ B ∩ C̅) = 1/3 and P (A̅ ∩ B ∩ C̅) = 1/3, then what is P (B ∩ C) equal to?

A. 1/12

B. 3/4

C. 1/15

D. 1/9

Q. 114 In constructing a pie diagram to the above data, the radii of the circles are to be chosen by which one of the given ratios?

A. 1 : 1

B. 10 : 9

C. 100 : 91

D. 5 : 4

Q. 115 If a variable takes values 0, 1, 2, 3, ……., n with frequencies 1, C(n, 1), C(n, 2), C(n, 3),……, C(n, n) respectively, then the arithmetic mean is

A. 2n

B. n + 1

C. n

D. n/2

Q. 116 In a multiple-choice test, an examinee either knows the correct answer with probability p, or guesses with probability 1 – p. The probability of answering a question correctly is 1/m, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is

A. mp / (1 + mp)

B. mp / (1 + (m – 1)p)

C. (m – 1)p / (1 + (m – 1)p)

D. (m – 1)p / (1 + mp)

Q. 117 If x₁ and x₂ are positive quantities, then the condition for the difference between the arithmetic mean and the geometric mean to be greater than 1 is

A. x₁ + x₂ > 2√(x₁x₂)

B. √x₁ + √x₂ > √2

C. l√x₁ – √x₂l > √2

D. x₁ + x₂ < 2√((x₁x₂) + 1)

Q. 118 Consider the following statements:

1. Variance is unaffected by the change of origin and change of scale.

2. A coefficient of variance is independent of the unit of observations.

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. 119 Five sticks of length 1, 3, 5, 7 and 9 feet are given. Three of these sticks are selected at random. What is the probability that the selected sticks can form a triangle?

A. 0.5

B. 0.4

C. 0.3

D. 0

Q. 120 The coefficient of correlation when coefficients of regression are 0.2 and 1.8 is

A. 0.36

B. 0.2

C. 0.6

D. 0.9

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

NDA/NA(I) Exam 2018 Mathematics Previous Year Paper

NDA/NA(I) Exam 2018 Mathematics

Q. 1 If n ∈ N, then 121ⁿ – 25ⁿ + 1900ⁿ – (-4)ⁿ is divisible by which one of the following ?

A. 1904

B. 2000

C. 2002

D. 2006

Q. 2 If n = (2017)!, then what is 1/log₂n + 1/log₃n + 1/log₄n + … + 1/log₂₀₁₇n equals to

A. 0

B. 1

C. n/2

D. n

Q. 3 In the expansion of (1 + x)⁴³, if the coefficients of (2r + 1)th and (r + 2)th terms are equal, then what is the value of r(r ≠ 1)?

A. 5

B. 14

C. 21

D. 22

Q. 4 What is the principal argument of (-1 -i), where i = √-1?

A. π/4

B. -π/4

C. -3π/4

D. 3π/4

Q. 5 Let α and β be real numbers and z be a complex number. If z² + αz + β = 0 has two distinct non-real roots with Re(z) = 1, then it is necessary that

A. β ∈ ( -1, 0)

B. |β| = 1

C. β ∈ (1, ∞)

D. β ∈ (0, 1)

Q. 6 Let A and B be subsets of X and C = (A ∩ B’) ∪ (A’ ∩ B), where A’ and B’ are complements of A and B respectively in X. What is C equals to?

A. (A ∪ B’) – (A ∩ B’)

B. (A’ ∪ B) – (A’ ∩ B)

C. (A ∪ B) – (A ∩ B)

D. (A’ ∪ B’) – (A’ ∩ B’)

Q. 7 How many numbers between 100 and 1000 can be formed with the digits 5, 6, 7, 8, 9, if the repetition of digits is not allowed?

A. 3⁵

B. 5³

C. 120

D. 60

Q. 8 The number of non-zero integral solutions of the equation |1 – 2i|^x = 5^x is

A. Zero (No solution)

B. One

C. Two

D. Three

Q. 9 If the ratio of AM to GM of two positive numbers a and b is 5 : 3, then a : b is equal to

A. 3 : 5

B. 2 : 9

C. 9 : 1

D. 5 : 3

Q. 10 If the coefficient of a^m and a^n in the expansion of (1 + a)^m+n are α and β, then which one of the following is correct?

A. α = 2β

B. α = β

C. 2α = β

D. α = (m + n)β

Q. 11 If x + log₁₅(1 + 3^x) = x log₁₅5 + log₁₅ 12, where x is an integer, then what is x equal to?

A. -3

B. 2

C. 1

D. 3

Q. 12 How many four-digit numbers divisible by 10 can be formed using 1, 5, 0, 6, 7 without repetition of digits?

A. 24

B. 36

C. 44

D. 64

Questions: 13 – 14

In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.

Q. 13 What is the number of students who are good in either Hindi or Mathematics but not in English?

A. 99

B. 107

C. 125

D. 150

Q. 14 What is the number of students who are good in Hindi and Mathematics but not in English?

A. 18

B. 12

C. 10

D. 8

Q. 15 If If α and β are different complex numbers with |α| = 1, then what is |α – β|/|1 – αβ̅| equals to?

A. |β̅|

B. 2

C. 1

D. 0

Q. 16 The equation |1 – x| + x² = 5 has

A. a rational root and an irrational root

B. two rational roots

C. two irrational roots

D. no real roots

Q. 17 The binary number expression of the decimal number 31 is

A. 1111

B. 10111

C. 11011

D. 11111

Q. 18 What is i¹⁰⁰⁰ + i¹⁰⁰¹ + i¹⁰⁰² + i¹⁰⁰³ equal to (where i = √-1) ?

A. 0

B. i

C. -1

D. 1

Q. 19 What is 1/log₂N + 1/log₃N + 1/log₄N + … + 1/log₁₀₀N equal to (N ≠ 1)?

A. 1/log₁₀₀₁N

B. 1/log₉₉₁N

C. 99/log₁₀₀₁N

D. 99/log₉₉₁N

Q. 20 The modulus-amplitude form of √3 + i, where i = √-1 is

A. 2(cosπ/3 + i sinπ/3)

B. 2(cosπ/6 + i sinπ/6)

C. 2(cosπ/3 + i sinπ/3)

D. 2(cosπ/6 + i sinπ/6)

Q. 21 What is the number of non-zero terms in the expansion of (1 + 2√3 x)¹¹ + (1 – 2√3x)¹¹(after simplification)?

A. 4

B. 5

C. 6

D. 11

Q. 22 What is the greatest integer among the following by which the number 5⁵ + 7⁵ is divisible?

A. 6

B. 8

C. 11

D. 12

Q. 23 If x = 1 – y + y² – y³ + ….. up to finite terms, where |y| < 1, then which one of the following is correct?

A. x = 1/(1 + y)

B. x = 1/(1 – y)

C. x = y/(1 + y)

D. x = y/(1 – y)

Q. 24 What is the inverse of the matrix (among (a), (b), (c), (d)) given in figure?

A. (a)

B. (b)

C. (c)

D. (d)

Q. 25 If A is a 2 x 3 matrix and AB is a 2 x 5 matrix then B must be a

A. 3 x 5 matrix

B. 5 x 3 matrix

C. 3 x 2 matrix

D. 5 x 2 matrix

Q. 26 A is a matrix given in figure and A² – kA – I₂ = 0, where I₂ is the 2 x 2 identity matrix, then what is the value of k?

A. 4

B. -4

C. 8

D. -8

Q. 27 What is the number of triangles that can be formed by choosing the vertices from a set of 12 points in a plane, seven of which lie on the same straight line?

A. 185

B. 175

C. 115

D. 105

Q. 28 What is C(n, r) + 2C(n, r – 1) + C(n, r – 2) equal to?

A. C(n + 1, r)

B. C(n – 1, r + 1)

C. C(n, r + 1)

D. C(n + 2, r)

Q. 29 Let [x] denote the greatest integer function. What is the number of solutions of the equation x² – 4x + [x] = 0 inthe interval [0, 2] ?

A. Zero (No solution)

B. One

C. Two

D. Three

Q. 30 A survey of 850 students in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance?

A. 40

B. 45

C. 50

D. 55

Q. 31 What is the sum of all two-digit numbers which when divided by 3 leave 2 as the remainder?

A. 1565

B. 1585

C. 1635

D. 1655

Q. 32 If 0 < a < 1, the value of log₁₀a is negative. This is justified by

A. Negative power of 10 is less than 1

B. Negative power of 10 is between 0 and 1

C. Negative power of 10 is positive

D. Negative power of 10 is negative

Q. 33 The third term of a GP is 3. What is the product of the first five terms?

A. 216

B. 226

C. 243

D. Cannot be determined due to insufficient data

Q. 34 If x, 3/2, z are in AP; x, 3, z are in GP; then which one of the following will be in HP?

A. x, 6, z

B. x, 4, z

C. x, 2, z

D. x, 1, z

Q. 35 What is the value of the sum given in the figure:

A. i

B. 2i

C. -2i

D. 1 + i

Q. 36 If sin x = 1/√5, sin y = 1/√10 where 0 < x < π/2, 0 < y < π/2, 0 < y < π/2, then what is (x + y) equal to?

A. π

B. π/2

C. π/4

D. 0

Q. 37 What is (sin 5x – sin 3x)/(cos 5x + cos 3x) equal to?

A. sin x

B. cos x

C. tan x

D. cot x

Q. 38 What is sin 105° + cos 105° equal to?

A. sin 50°

B. cos 50°

C. 1/√2

D. 0

Q. 39 In a triangle ABC if a = 2, b = 3 and sinA = 2/3 what is angle B equal to?

A. π/4

B. π/2

C. π/3

D. π/6

Q. 40 What is the principal value of sin⁻¹(sin2π/3)?

A. π/4

B. π/2

C. π/3

D. 2π/3

Q. 41 If x, x- y and x + z are the angles of a triangle (not an equilateral triangle) such that tan (x – y), tan x and tan (x + y) are in GP, then what is x equal to?

A. π/4

B. π/3

C. π/6

D. π/2

Q. 42 ABC is a triangle inscribed in a circle with centre O. Let α = ∠BAC, where 45° < α < 90°. Let β = ∠BOC. Which one of the following is correct?

A. cos β = (1 – tan²α)/(1 + tan²α)

B. cos β = (1 + tan²α)/(1 – tan²α)

C. cos β = 2tanα/(1 + tan²α)

D. sin β = 2sin²α

Q. 43 If a flag-staff of 6 m height placed on the top of a tower throws a shadow of 2√3m along the ground, then what is the angle that the sun makes with the ground?

A. 60°

B. 45°

C. 30°

D. 15°

Q. 44 What is tan⁻¹(1/4) + tan⁻¹(3/5) equal to

A. 0

B. π/4

C. π/3

D. π/2

Q. 45 A spherical balloon of radius r subtends an angle α at the eye of an observer, while the angle of elevation of its centre is β. What is the height of the centre of the balloon (neglecting the height of the observer)?

A. r sin β/sin(α/2)

B. r sin β/sin(α/4)

C. r sin(β/2)/sinα

D. r sin α/ sin(β/2)

Q. 46 If [sin(x + y)]/[sin(x – y) = (a + b)/(a – b), then what is tan x/tan y equal to?

A. a/b

B. b/a

C. (a + b)/(a – b)

D. (a – b)/(a + b)

Q. 47 If sinα + sinβ = 0 = cosα + cosβ, where 0 < β < α < 2π, then which one of the following is correct?

A. α = π – β

B. α = π + β

C. α = 2π – β

D. 2α = π + 2β

Q. 48 Suppose cos A is given. If only one value of cos(A/2) is possible, then A must be

A. An odd multiple of 90°

B. A multiple of 90°

C. An odd multiple of 180°

D. A multiple of 180°

Q. 49 If cosα + cosβ + cosγ = 0, where 0 < α ≤ π/2, 0 < β ≤π/2, 0 < γ ≤ π/2, then what is the value of sinα + sinβ + sinγ?

A. 0

B. 3

C. 5√2/2

D. 3√2/2

Q. 50 The maximum value of sin(x + π/5) + cos(x + π/5), where x ∈ (0, π/2), is attained at

A. π/20

B. π/15

C. π/10

D. π/2

Q. 51 What is the distance between the points which divide the line segment joining (4, 3) and (5, 7) internally and externally in the ratio 2 : 3?

A. 12√17/5

B. 13√17/5

C. √17/5

D. 6√17/5

Q. 52 What is the angle between the straight lines (m² – mn)y = (mn + n²)x + n³ and (mn + m²)y = (mn – n²)x + m³, where m > n?

A. tan⁻¹(2mn)/(m² + n²)

B. tan⁻¹(4m²n²)/(m⁴ – n⁴)

C. tan⁻¹(4m²n²)/(m⁴ + n⁴)

D. 45°

Q. 53 What is the equation of the straight line cutting off an intercept 2 from the negative direction of y-axis and inclined at 30° with the positive direction of x-axis?

A. x – 2√3y – 3√2 = 0

B. x + 2√3y – 3√2 = 0

C. x + √3y – 2√3 = 0

D. x – √3y – 2√3 = 0

Q. 54 What is the equation of the line passing through the point of intersection of the lines x + 2y – 3 = 0 and 2x – y + 5 = 0 and parallel to he line y – x + 10 = 0?

A. 7x – 7y + 18 – 0

B. 5x – 7y + 18 = 0

C. 5x – 5y + 18 = 0

D. x – y + 5 = 0

Q. 55 Consider the following statements:

1. The length p of the perpendicular from the origin to the line ax + by = c satisfies the relation p² = c²/(a² + b²).

2. The length p of the perpendicular from the origin to the line x/a + y/b = 1 satisfies the relation 1/p² = 1/a² + 1/b².

3. The length p of the perpendicular from the origin to the line y = mx + c satisfies the relation 1/p² = (1 + m² + c²)/c².

A. 1, 2 and 3

B. 1 only

C. 1 and 2 only

D. 2 only

Q. 56 What is the equation of the ellipse whose vertices are (±5, 0) and foci are at (±4, 0)?

A. x²/25 + y²/9 = 1

B. x²/16 + y²/9 = 1

C. x²/25 + y²/16 = 1

D. x²/9 + y²/25 = 1

Q. 57 What is the equation of the straight line passing through the point (2, 3) and making an intercept on the positive y-axis equal to twice its intercept on the positive x-axis?

A. 2x + y = 5

B. 2x + y = 7

C. x + 2y = 7

D. 2x – y = 1

Q. 58 Let the coordinates of the points A, B, C be (1, 8, 4), (0, -11, 4) and (2, -3, 1) respectively. What are the coordinates of the point D which is the foot of the perpendicular from A on BC?

A. (3, 4, -2)

B. (4, -2, 5)

C. (4, 5, -2)

D. (2, 4, 5)

Q. 59 What is the equation of the plane passing through the points (-2, 6, -6), (-3, 10, -9) and (-5, 0, -6)?

A. 2x – y – 2z = 2

B. 2x + y + 3z = 3

C. x + y + z = 6

D. x – y – z = 3

Q. 60 A sphere of constant radius r through the origin intersects the coordinate axes in A, B and C. What is the locus of the centroid of the triangle ABC?

A. x² + y² + z² = r²

B. x² + y² + z² = 4r²

C. 9(x² + y² + z²) = 4r²

D. 3(x² + y² + z²) = 2r²

Q. 61 The coordinates of the vertices P, Q and R of a triangle PQR are (1, -1, 1), (3, -2, 2) and (0, 2, 6) respectively. If ∠RQP = θ, then what is ∠PQR equal to?

A. 30° + θ

B. 45° – θ

C. 60° – θ

D. 90° – θ

Q. 62 The perpendiculars that fall from any point of the straight line 2x + 11y = 5 upon the two straight lines 24x + 7y = 20 and 4x – 3y = 2 are

A. 12 and 4 respectively

B. 11 and 5 respectively

C. Equal to each other

D. Not equal to each other

Q. 63 The equation of the line, when the portion of it intercepted between the axes is divided by the point (2, 3) in the ratio of 3 : 2 is

A. Either x + y = 4 or 9x + y = 12

B. Either x + y = 5 or 4x + 9y = 30

C. Either x + y = 4 or x + 9y = 12

D. Either x + y = 5 or 9x + 4y = 30

Q. 64 What is he distance between the straight lines 3x + 4y = 9 and 6x + 8y = 15?

A. 3/2

B. 3/10

C. 6

D. 5

Q. 65 What is the equation to the sphere whose centre is at (-2, 3, 4) and radius is 6 units?

A. x² + y² + z² + 4x – 6y – 8z = 7

B. x² + y² + z² + 6x – 4y – 8z = 7

C. x² + y² + z² + 4x – 6y – 8z = 7

D. x² + y² + z² + 4x + 6y + 8z = 7

Q. 66 If a̅ and b̅ are vectors such that | a̅ | = 2, | b̅ | = 7 and a̅ x b̅ = 3î + 2ĵ + 6k̂, then what is the acute angle between a̅ and b̅? ( ̅ denotes vector )

A. 30°

B. 45°

C. 60°

D. 90°

Q. 67 Let p̅ and q̅ be the position vectors of the points P and Q respectively with respect to origin O. The points R and S divide PQ internally and externally respectively in the ratio 2 : 3. If O̅R̅ and O̅S̅ are perpendicular, them which one of the following is correct? ( ̅ denotes vector )

A. 9p² = 4q²

B. 4p² = 9q²

C. 9p = 4q

D. 4p = 9q

Q. 68 What is the moment about the point î + 2ĵ – k̂ of a force represented by 3î + k̂ acting through the point 2î – ĵ + 3k̂?

A. -3î + 11ĵ + 9k̂

B. 3î + 2ĵ + 9k̂

C. 3î + 4ĵ + 9k̂

D. î + ĵ + k̂

Q. 69 If a⁻ + 2b⁻ + 3c⁻ = 0⁻ and a⁻ x b⁻ + b⁻ x c⁻ + c⁻ x a⁻ = λ(b⁻ x c⁻), then what is the value of λ?

A. 2

B. 3

C. 4

D. 6

Q. 70 If the vectors k̅ and A̅ are parallel to each other, then what is kk̅ x A̅ equal? ( ̅ denotes vector )

A. k²A̅

B. 0̅

C. -k²A̅

D. A̅

Q. 71 Which one of the following is correct in respect of the function f : R → R⁺ defined as f(x) = |x + 1|?

A. f(x²) = [f(x)]²

B. f(|x|) = |f(x)|

C. f9x + y) = f(x) + f(y)

D. None of the above

Q. 72 Suppose f : R → R is defined by f(x) = x²/(1 + x²). What is the range of the function?

A. [0, 1)

B. [0, 1]

C. (0, 1]

D. (0, 1)

Q. 73 If f(x) = |x| + |x – 1|, then which one of the following is correct?

A. f(x) is continuous at x = 0 and x = 1

B. f(x) is continuous at x = 0 but not at x = 1

C. f(x) is continuous at x = 1 but not at x = 0

D. f(x) is neither continuous at x = 0 nor at x = 1

Q. 74 Consider the function given in figure. What is f'(0) equal to ?

A. 0

B. 1

C. -1

D. It does not exist

Q. 75 What is the area of the region bounded by the parabolas y² = 6(x – 1) and y² = 3x?

A. √6/3

B. 2√6/3

C. 4√6/3

D. 5√6/3

Questions: 76 – 78

Three sides of a trapezium are each equal to 6 cm. Let α ∈ (0, π/2) be the angle between a pair of adjacent sides.

Q. 76 If the area of the trapezium is the maximum possible, then what is α equals to?

A. π/6

B. π/4

C. π/3

D. 2π/5

Q. 77 If the area of the trapezium is maximum, what is the length of the fourth side?

A. 8 cm

B. 9 cm

C. 10 cm

D. 12 cm

Q. 78 What is the maximum area of the trapezium?

A. 36√3 cm²

B. 30√3 cm²

C. 27√3 cm²

D. 24√3 cm²

Q. 79 What is the value of the given equation (given in the figure)?

A. (e^π + 1)/2

B. (e^π – 1)/2

C. e^π + 1

D. (e^π + 1)/4

Q. 80 If f(x) = (x² – 9)/(x² – 2x – 3), x ≠ 3 is continuous at x = 3, then which one of the following is correct?

A. f(3) = 0

B. f(3) = 1.5

C. f(3) = 3

D. f(3) = -1.5

Q. 81 What is the value of the equation given in the figure?

A. (e + 1)/4

B. (e² + 1)/4

C. (e – 1)/4

D. (e² – 1)/4

Q. 82 What is the value of the equation given in the figure (where [.] is the greatest integer function)?

A. √2 – 1

B. 1 – √2

C. 2(√2 – 1)

D. √3 – 1

Q. 83 What is the maximum value of 16 sin θ – 12 sin²θ?

A. 3/4

B. 4/3

C. 16/3

D. 4

Q. 84 If f : R → S defined by

f(x) = 4 sin x – 3 cos x + 1 is onto, then what is S equal to?

A. [-5, 5]

B. (-5, 5)

C. (-4, 6)

D. [-4, 6]

Q. 85 For f to be a function, what is the domain of f, if f(x) = 1/(√|x| – x) ?

A. (-∞, 0)

B. (0, ∞)

C. (-∞, ∞)

D. (-∞, 0]

Q. 86 What is the solution of the differential equation x dy – y dx = 0 ?

A. xy = c

B. y = cx

C. x + y = c

D. x – y = c

Q. 87 What is the derivative of the function

f(x) = e^tan x + ln(sec x) – e^ln x at x = π/4?

A. e/2

B. e

C. 2e

D. 4e

Q. 88 Which one of the following differential equations has a periodic solution? (where μ > 0)

A. d²x/dt² + μx = 0

B. d²x/dt² – μx = 0

C. x(dx/dt) + μt = 0

D. dx/dt + μxt = 0

Q. 89 What is the period of the function f(x) = sin x?

A. π/4

B. π/2

C. π

D. 2π

Q. 90 What is the value of the equation given in figure?

A. ln(2^x – 1) + C

B. ln(1 – 2^-x)/ln 2 + C

C. ln(2^-x – 1)/2 ln 2 + C

D. ln(1 + 2^-x)ln 2 + C

Q. 91 The order and degree of the differential equation y² = 4a(x – a), where ’a’ is an arbitrary constant, are respectively

A. 1, 2

B. 2, 1

C. 2, 2

D. 1, 1

Q. 92 What is the value of the equation given in figure?

A. 1/√2 + ln(1/√2)

B. 1/√2

C. 0

D. √2

Q. 93 What are the values of a and b according to the two equations given in the figure?

A. -1, 1

B. 1, 1

C. 0, 0

D. 2, -2

Q. 94 What is the value of the equation given in the figure?

A. 1/110

B. 1/132

C. 1/148

D. 1/240

Q. 95 What is lim(x→0) tanx/sin 2x equal to?

A. 1/2

B. 1

C. 2

D. Limit does not exist

Q. 96 What is lim(h→0) [(√2x + 3h) – (√2x)]/2h equal to?

A. 1/2√2x

B. 3/√2x

C. 3/2√2x

D. 3/4√2x

Q. 97 If f(x) is an even function, where f(x) ≠ 0, then which one of the following is correct?

A. f'(x) is an even function

B. f'(x) is an odd function

C. f'(x) may be an even or odd function depending on the type of function

D. f'(x) is a constant function

Q. 98 If y = e^x^2 sin 2x, what is dy/dx at x = π equal to?

A. (1 + π)e^π^2

B. 2πe^π^2

C. 2e^π^2

D. e^π^2

Q. 99 What is the solution of (1 + 2x)dy – (1 – 2y)dx = 0?

A. x – y – 2xy = c

B. y – x – 2xy = c

C. y + x – 2xy = c

D. x + y + 2xy = c

Q. 100 What are the order and degree, respectively, of the differential equation

(d³y/dx³)² = y⁴ + (dy/dx)⁵ ?

A. 4, 5

B. 2, 3

C. 3, 2

D. 5, 4

Q. 101 In a Binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials?

A. 80/243

B. 40/243

C. 20/243

D. 10/243

Q. 102 Consider the following statements:

1. P(A̅ U B) = P(A̅) + P(B) – P(A̅ ∩ B)

2. P(A ∩ B̅) = P(B) – P(A ∩ B)

3. P(A ∩ B) = P(B) P(A|B)

Which of the above statements are correct?

A. 1 and 2 only

B. 1 and 3 only

C. 2 and 3 only

D. 1, 2 and 3

Q. 103 If the correlation coefficient between x and y is 0.6, covariance is 27 and variance of y is 25, then what is the variance of x?

A. 9/5

B. 81/25

C. 9

D. 81

Q. 104 The probabilities that a student will solve Question A and Question B are 0.4 and 0.5 respectively. What is the probability that he solves at least one of the two questions?

A. 0.6

B. 0.7

C. 0.8

D. 0.9

Q. 105 Let x̅ be the mean of x₁, x₂, x₃, ….., xn. If xi = a + cyi for some constants a and c, then what will be the mean of y₁, y₂, y₃, ….., yn?

A. a + cx̅

B. a – (1/c)x̅

C. (1/c)x̅ – a

D. (x̅ – a)/c

Q. 106 Consider the following statements:

1. If the correlation coefficient rₓᵧ = 0, then the two lines of regression are parallel to each other.

2. If the correlation coefficient rₓᵧ = +1, then the two lines of regression are perpendicular to each other.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 107 If 4x – 5y + 33 = 0 and 20x – 9y = 1-7 are two lines of regression, then what are the values of x̅ and y̅ respectively

A. 12 and 18

B. 18 and 12

C. 13 and 17

D. 17 and 13

Q. 108 Consider the following statements:

1. Mean is independent of change in scale and change in origin.

2. Variance is independent of change in scale but not in origin.

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. 109 Consider the following statements:

1. The sum of deviations from mean is always zero

2. The sum of absolute deviations is minimum when taken around median.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 110 What is the median of the numbers

4.6, 0, 9.3, -4.8, 7.6, 2.3, 12.7, 3.5, 8.2, 6.1, 3.9, 5.2?

A. 3.8

B. 4.9

C. 5.7

D. 6.0

Q. 111 In a test in Mathematics, 20% of the students obtained “first class”. If the data are represented by a Pie-Chart, what is the central angle corresponding to “first class”?

A. 20°

B. 36°

C. 72°

D. 144°

Q. 112 The mean and standard deviation of a set of values are 5 and 2 respectively. If 5 is added to each value, then what is the coefficient of variation for the new set of values?

A. 10

B. 20

C. 40

D. 70

Q. 113 A train overs the first 5 km of its journey at a speed of 30 km/hr and the next 15 km at a speed of 45 km/hr. What is the average speed of the train?

A. 35 km/hr

B. 37.5 km/hr

C. 39.5 km/hr

D. 40 km/hr

Q. 114 Two fair dice are rolled. What is the probability of getting a sum of 7?

A. 1/36

B. 1/6

C. 7/12

D. 5/12

Q. 115 If A and B are two events such that 2P(A) = 3P(B), WHERE 0 < P(A) < P(B) < 1, then which one of the following is incorrect?

A. P(A∣B) < P(B∣A) < P(A∩B)

B. P(A∩B) < P (B∣A) < P (A∣B)

C. P(B∣A) < P(A∣B) < P(A∩B)

D. P(A∩B) < P(A∣B) < P(B∣A)

Q. 116 A box has ten chits numbered 0, 1, 2, 3, ….., 9. First, one chit is drawn at random and kept aside. From the remaining, a second chit is drawn at random. What is the probability that the second chit drawn is “9” ?

A. 1/10

B. 1/9

C. 1/90

D. None of the above

Q. 117 One bag contains 3 white and 2 black balls, another bag contains 5 white and 3 black balls. If a bag is chosen at random and a ball is drawn from it, what is the chance that it is white?

A. 3/8

B. 49/80

C. 8/13

D. 1/2

Q. 118 Consider the following in respect of two events A and B:

1. P(A occurs but nit B) = P(A) – P(B) if B ⊂ A

2. P(A alone or B alone occurs) = P(A) + P(B) – P(A ∩ B)

3. P(A ∪ B) = P(A) + P(B) if A and B are mutually exclusive

Which of the above is/are correct?

A. 1 only

B. 1 and 3 only

C. 2 and 3 only

D. 1 and 2 only

Q. 119 A committee of three has to be chosen from a group of 4 men and 5 women. If the selection is made at random, what is the probability that exactly two members are men?

A. 5/14

B. 1/21

C. 3/14

D. 8/21

Q. 120 The standard deviation σ of the first N natural numbers can be obtained using which one of the following formula?

A. σ = (N² – 1)/12

B. σ = √(N² – 1)/12

C. σ = √(N – 1)/12

D. σ = √(N² – 1)/6N

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

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