UPSC Exam - Page 6 of 9 - Vidhyarthi Darpan

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

NDA/NA(I) Exam 2016 General Ability Test

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

A. inevitable

B. undeniable

C. fatal

D. miserable

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

A. built

B. finalised

C. sketched

D. arranged

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

A. cultivated

B. finished

C. perfected

D. enlarged

Q. 4 He is greatly admired for his_______________ behaviour.

A. decrepit

B. decadent

C. decorative

D. decorous

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

A. remarking

B. saying

C. explaining

D. talking

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

A. against

B. to

C. with

D. for

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

A. discriminate

B. discern

C. distinguish

D. identify

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

A. installed

B. dug

C. pitched

D. established

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

A. divulge

B. divert

C. indulge

D. invert

Questions: 10 – 20

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

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

A. delicate

B. sturdy

C. quick

D. clumsy

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

A. rural

B. rude

C. irrational

D. indifferent

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

A. arrogance

B. boldness

C. skillfulness

D. cunning

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

A. significant

B. small

C. unruly

D. noisy

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

A. occupied

B. inattentive

C. engaged

D. absent

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

A. following

B. previous

C. first

D. last

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

A. clever

B. wild

C. incorrect

D. discriminating

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

A. violent

B. mild

C. bad

D. continuous

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

A. Individually

B. Obviously

C. Clearly

D. Collectively

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

A. charming

B. ugly

C. small

D. unnoticeable

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

A. repeated

B. irrational

C. occasional

D. regular

Questions: 21 – 30

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

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

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

A. (a)

B. (b)

C. (c)

D. (d)

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

A. (a)

B. (b)

C. (c)

D. (d)

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

A. (a)

B. (b)

C. (c)

D. (d)

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

A. (a)

B. (b)

C. (c)

D. (d)

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

A. (a)

B. (b)

C. (c)

D. (d)

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

A. (a)

B. (b)

C. (c)

D. (d)

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

A. (a)

B. (b)

C. (c)

D. (d)

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

A. (a)

B. (b)

C. (c)

D. (d)

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

A. (a)

B. (b)

C. (c)

D. (d)

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

A. (a)

B. (b)

C. (c)

D. (d)

Questions: 31 – 40

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

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

enthusiasm

A. carried aloft

B. carried down

C. carried away

D. No improvement

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

A. rose another two feet

B. arisen another two feet

C. would raise another two feet

D. no improvement

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

A. seldom

B. hardly

C. ever

D. no improvement

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

A. whom are graduates

B. whose are graduates

C. whom are only graduates

D. no improvement

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

A. has rained

B. rains

C. rained

D. no improvement

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

A. notice of

B. notice from

C. notice to

D. no improvement

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

A. big

B. tall

C. long

D. no improvement

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

A. stand at

B. stand on

C. stand up

D. no improvement

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

A. how to tell stories

B. telling stories

C. to narrate stories

D. no improvement

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

A. shall be waiting on

B. shall have been waiting

C. shall wait

D. no improvement

Questions: 41 – 50

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

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

A. dangerous

B. terrifying

C. mild

D. very loud

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

A. usual

B. durable

C. commendable

D. some

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

A. at rest

B. idle

C. quiet

D. impatient

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

A. scarcity

B. availability

C. plenty

D. absence

Q. 45 The servants ‘retired’ to their quarters

A. entered

B. went away

C. ran away

D. mobilised

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

A. sensitive

B. strategic

C. immediate

D. expert

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

A. dispute

B. disagree

C. distinguish

D. differ

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

A. depressed

B. weakened

C. worried

D. defeated

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

A. welcome

B. sincere

C. good

D. praiseworthy

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

A. rebuke

B. sympathy

C. indifference

D. remorse

Questions: 51 – 55

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

Code:

(a) Both the Statements are individually true and Statement II is the correct explanation of Statement I.

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

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

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

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

different hydrocarbons

A. (a)

B. (b)

C. (c)

D. (d)

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

Statement II: Rate of evaporation is high in Red Sea

A. (a)

B. (b)

C. (c)

D. (d)

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

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

A. (a)

B. (b)

C. (c)

D. (d)

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

Statement II: The soil of humid tropics is highly fertile

A. (a)

B. (b)

C. (c)

D. (d)

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

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

A. (a)

B. (b)

C. (c)

D. (d)

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

A. X=Y

B. X=13.6Y

C. Y=13.6X

D. None of the above

Q. 57 Density of water is

A. maximum of 0⁰ C

B. minimum of 0⁰ C

C. maximum of 4⁰ C

D. minimum of -4⁰ C

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

A. red phosphorous

B. black phosphorous

C. white phosphorous

D. scarlet phosphorous

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

A. ripening of fruits

B. curdling of milk

C. freezing of water

D. digestion of food

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

1. Nitrogen oxide(NOₓ)

2. carbon monoxide(CO)

3. carbon dioxide(CO₂)

4. benzene

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

A. 1 and 4 only

B. 1 and 2 only

C. 1,2 and 3 only

D. 1,2 and 4 only

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

1. Rishikesh

2. New delhi

3. Patna

4. Bhubaneswar

Select the correct answer using the code given below:

A. 4-3-1-2

B. 4-1-3-2

C. 3-4-2-1

D. 3-2-1-4

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

A. F

B. 2F

C. 4F

D. F/4

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

A. lose one-fourth of its total energy

B. lose one-fourth of its potential energy

C. gain one-fourth of its potential energy

D. gain three-fourth of its total energy

Q. 64 Soap is sodium or potassium salt of

A. Stearic acid

B. Oleic acid

C. Palmitic acid

D. All of the above

Q. 65 Mass of a particular amount of substance

1. is the amount of matter present in it

2. does not vary from place to place

3. changes with change in gravitational force

Select the correct answer using the code given below:

A. 1,2,3

B. 1,2 only

C. 2,3 only

D. 1 only

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

1. Pesticide residues

2. lead

3. metanil yellow

4. mercury

Select the correct answer using the code given below:

A. 1,2 only

B. 1,2,4 only

C. 3,4 only

D. 1,2,3,4 only

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

A. Sapt Kosi Valley

B. Jhelum Valley

C. Alakananda Valley

D. Teesta Valley

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

A. Shiwalik Range

B. deccan plateau

C. greater himalaya

D. aravalli range

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

A. momentum of B will be double that of A

B. momentum of A will be double that of B

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

D. momentum of both A and B will be equal

Q. 70 During solar eclipse

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

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

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

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

Q. 71 The S.I unit of acceleration is

A. ms⁻¹

B. ms⁻²

C. cms⁻²

D. kms⁻²

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

A. 12

B. 6

C. 10

D. 14

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

A. 2Mg(s)+O₂(g)->2MgO(s)

B. S(s)+O₂->SO₂(g)

C. 2HgO(s)->2Hg(l)+O₂(g)

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

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

1. steel utensils

2. Plastic coffee mugs

3. Aluminium utensils

4. Plastic water storage bottles

Select the correct answer using the code given below:

A. 1 only

B. 1,2 only

C. 2,4 only

D. 1,2,3 only

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

A. godavari

B. krishna

C. kavery

D. mahanadi

Q. 76 Consider the following statements:

1. Rajmahal highlands consist of lava flow deposits

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

Which of the statements given below is/are correct?

A. 1 only

B. 2 only

C. both 1,2

D. neither 1 nor 2

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

A. real and magnified

B. virtual and magnified

C. real and reduced

D. virtual and reduced

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

A. real,inverted and magnified

B. real, erect and magnified

C. virtual, inverted and reduced

D. virtual, erect and magnified

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

A. tidal energy

B. geothermal energy

C. solar energy

D. biomass energy

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

A. N₂O

B. N₂O₃

C. NO₂

D. N₂O₅

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

A. sodium bicarbonate(sodium hydrogen carbonate)

B. sodium carbonate

C. potassium bicarbonate(potassium hydrogen carbonate)

D. potassium carbonate

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

1. DNA is the hereditary material of all living organisms

2. All segments of DNA code for synthesis of proteins

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

4. DNA is also found in mitochondria

select the correct answer using the code given below:

A. 1,2,3 only

B. 3,4 only

C. 1,3,4 only

D. 4 only

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

A. geographical survey of India

B. archaeological survey of India

C. survey of India

D. National atlas and thematic mapping organisation

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

A. dresden line

B. durand line

C. maginot line

D. 38th parallel

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

A. 40 cm

B. 60 cm

C. 80 cm

D. 120 cm

Q. 86 The brightness of a tar depends on its

A. size and temperature only

B. size and distance from the earth

C. size, temperature and mass

D. size, temperature and distance from the earth

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

A. condensation

B. evaporation

C. sublimation

D. diffusion

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

A. mixture of carbon monoxide and hydrogen

B. mixture of carbon monoxide and nitrogen

C. mixture of carbon dioxide and water vapour

D. mixture of carbon monoxide and water vapour

Q. 89 Which of the following statements are correct?

In honey bees

1. Males are haploid

2. workers are sterile and diploid

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

4. honey is collected/made by males

select the correct answer using the code given below:

A. 1,2,3,4

B. 2,3 only

C. 1,2,3 only

D. 1,4 only

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

1. narmada

2. Mahanadi

3. Tapti

4. Son

select the correct answer using the code given below:

A. 1,2 only

B. 2 only

C. 1,3,4 only

D. 1,2,4 only

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

1. vernal equinox occurs on march 21

2. summer solstice occurs on december 22

3. autumnal equinox occurs on september 23

winter solstice occurs on june 21

A. 1 only

B. 1.3 only

C. 2,4 only

D. 1,2,3 only

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

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

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

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

D. the water does not freeze at all

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

A. 0.5 A

B. 2 A

C. 4 A

D. 5 A

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

A. less than 2 ohm

B. more than 2 ohm but less than 4 ohm

C. 4 ohm

D. 14 ohm

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

A. Solution ‘A’

B. Solution ‘B’

C. Solution ‘C’

D. Solution ‘D’

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

A. CuO

B. Al₂O₃

C. Fe₂O₃

D. Na₂O

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

2. high HDL level.

3. high VLDL level.

4, high LDL level.

Select the correct answer using the code piven below :

(a) Land2only –

(b) 1,2 and 4 only

(c)

(d)

A. 1,2 only

B. 1,2,4 only

C. 3 and 4 only

D. 1, 2 and 8 only

Q. 98 Spruce and Cedar are tree varieties of

A. Equatorial forest

B. Temperate, coniferous forest

C. Monsoon forest

D. Temperate deciduous forest

Q. 99 ‘Sal’ tree is a

A. Tropical evergreen tree

B. Tropical semi-evergreen tree

C. Dry deciduous tree

D. Moist deciduous tree

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

A. Liquid < Gas < Solid

B. Solid < Liquid < Gas

C. Gas < Liquid < Solid

D. Solid < Gas < Liquid

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

A. strength of the intermolecular forces of attraction

B. strength of the intermolecular forces of repulsion

C. molecular mass

D. molecular size

Q. 102 Consider the circuit in the diagram:

The equivalent resistance of the circuit will be

A. 12 Ω

B. 8(11/2) Ω

C. 9(1/11) Ω

D. 24/25 Ω

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

A. Hg

B. Al

C. Mg

D. Fe

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

A. 1,3,4 only

B. 3,4 only

C. 2 and 4 only

D. 2 only

Q. 105 Consider the following statements :

1. All Echinoderms are not marine.

2. Sponges are exclusively marine.

3. Insects are found in all kinds of habitats.

4. Many primates are arboreal.

Which of the statements given above is/are correct ?

A. 1,3,4 only

B. 3,4 only

C. 2,4 only

D. 3 only

Q. 106 Areas which are engines for economic growth

supported by quality infrastructure and complemented by an attractive fiscal package

are known as

A. Export Processing Zones

B. Duty Free Tariff Zones

C. Special Economic Zones

D. Technology Parks

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

A. South-Western border along Arabian Sea

B. Coromandel Coast

C. North-Eastern Frontier

D. North-Western India

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

A. 625 m

B. 1250 m

C. 2500 m

D. 50 m

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

A. 70 kg

B. 35 kg

C. 140 kg

D. zero

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

A. 2000 J

B. 4000 J

C. 8000 J

D. 1000 J

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

A. Benzene

B. Hexane

C. Naphthalene

D. Anthracene

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

A. (a)

B. (b)

C. (c)

D. (d)

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

A. Dhrian

B. Daurs

C. Dhoros

D. Dhaya

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

A. force

B. momentum

C. work done

D. energy

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

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

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

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

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

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

select the correct answer using the code given below:

A. 1,2,3 only

B. 1,2 only

C. 1,4 only

D. 2 only

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

A. nuclear energy

B. potential energy

C. electrical energy

D. chemical energy

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

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

A. 25 km and 60 km

B. 95 km and 35 km

C. 60 km and 25 km

D. 85 km and 35 km

Q. 119 Jelep La pass is located in

A. punjab himalayas

B. sikkim himalayas

C. kumaon himalayas

D. kashmir himalayas

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

A. 1

B. 2

C. 3

D. 4

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

A. (a)

B. (b)

C. (c)

D. (d)

Q. 122 Consider the following statements :

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

2. Jammu and Kashmir has been given special status under Article 370 of the Constitution of India.

Which of the statements given above is/are correct ?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 123 The Speaker of the Lok Sabha may resign his office by writing, addressed to the

A. President of India

B. Prime Minister of India

C. Vice President of India

D. Deputy Speaker of the Lok Sabha

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

A. Shantha Sinha

B. Kuilaah Satyarent

C. Aruna Roy

D. Anil Agarwal

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

1. Ensuring financial inclusion of the poor

2. Enhancing financial literacy

3. Provision for accidental insurance to account holders

4. Allowing bank accounts with zero balance

Select the correct answer using the code given” below:

A. 1 and 4 only

B. 1,2 and 3 only

C. 2 and 4 only

D. 1,2,3 and 4

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

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

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

below :

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

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

Development strategy ?

A. Development of capital goods industries

B. Major involvement of the State in the economy

C. Industrial deregulation and disinvestment in the public sector

D. Enhancing the scope and importance of the public sector

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

A. faster, sustainable and more inclusive growth

B. modernisation of industries and strengthiening infrastructure

C. enhancing agricultural and rural incomes

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

requirements, health and family planning

Q. 129 Nabhah sparsam diptam is the motto of

A. central industrial security force

B. indian air force

C. ISRO

D. indian navy

Q. 130 Consider the following statements:

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

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

A. 1 only

B. 2 only

C. both 1,2

D. neither 1 nor 2

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

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

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

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

Select the correct answer using the code given below:

A. 1 only

B. 2,3 only

C. 1,2 only

D. 1,2,3 only

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

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

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

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

Select the correct answer using the code given below:

A. 1,2 only

B. 2 only

C. 1,2,3

D. 3 only

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

A. bhutan

B. myanmar

C. nepal

D. singapore

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

A. Tommy Robredo

B. Fabio Fognini

C. Roger Federer

D. Pablo Cuevas

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

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

B. right to acquire, hold and disperse of property

C. right to practice any profession

D. right to form co-operative societies

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

A. character act, 1813

B. character act, 1833

C. charles wood’s education despatch, 1854

D. indian councils act, 1861

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

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

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

Which of the statements given above is/are correct ?

A. 1 only

B. 2 only

C. Both l and 2

D. Neither 1 nor 2

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

A. Jaintia Hills, Meghalaya

B. Koriya, Chhattisgarh

C. Angul, Odisha

D. Bardhaman, West Bengal

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

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

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

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

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

Select the correct answer using the code given below :

A. 2 only

B. 1, 2 and 3 only

C. 4 only

D. 1 and 4 only

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

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

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

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

society.

Select the correct answer using the code given below:

A. 3 only

B. 1,2 and 3

C. 1 and 3 only

D. 1 only

Q. 141 Division of labour often involves

1. specialized economic activity.

2. highly distinct productive roles.

3. involving everyone in many of the same activities.

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

Select the correct answer using below:

A. 1, 3 and 4 only

B. 1, 2 and 4 only

C. 3 only

D. 2 and 4 only

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

A. Chandi Prasad Bhatt

B. Narendra Dabholkar

C. G.D. Agrawal

D. Kailash Satyarthi

Q. 143 Consider the following statements :

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

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

Which of the statements given above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 144 Consider the following statements about Sufism in India

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

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

Which of the statements above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

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

1. Henry David Thoreau

2. John Ruskin

3. John Milton

4. Jainism

Select the correct answer using the a given below :

A. 1 only

B. 1,2 and 3 only

C. 1, 2 and 4 only

D. 2 and 4 only

Q. 146 Consider the following statements:

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

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

Which of the statements Shown above is/are correct ?

A. 1 only

B. 2 only

C. both 1,2

D. neither 1 nor 2

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

1. Permission of 100 percent FDI in automotive sector

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

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

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

Select the correct answer using the code given below:

A. 1 only

B. 2,4 only

C. 1,2 only

D. 1,2,3 only

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

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

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

Select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

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

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

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

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

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

Select the correct answer using the code given below:

A. 1 only

B. 1,2 only

C. 2,3 only

D. 1,2,3,4

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

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

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

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

4. To organize international conferences

select the correct answer using the code given below:

A. 1 only

B. 1,2,4 only

C. 2 only

D. 1,2,3 only

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

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

NDA/NA(II) Exam 2016 Mathematics

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

A. 21

B. 23

C. 32

D. 36

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

A. (0, 2)

B. (2, 3)

C. (3, 4)

D. (–2, 0)

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

1. A ∩ B {X∈ R : –2 < x < 1}

2. A \ B = {x ∈R : –7 < x < –2}

Select the correct answer using the code given below:

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

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

A. 1/10

B. 2/5

C. 8/5

D. 1/40

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

A. 1

B. 3ω

C. 3ω²

D. 0

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

A. z = 1+ i

B. |z| = 2

C. z = 1 – i

D. | z| = 1

Q. 7 Is equal to?

A. a

B. b

C. c

D. d

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

A. 3

B. 4

C. 5

D. 6

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

A. 0

B. 1/2

C. √3/2

D. 1

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

A. -2 < k < 2

B. -5 < k < 3

C. -3 < k < 5

D. -1 < k < 3

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

A. 1

B. 2

C. 3

D. 5

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

A. 1

B. 2

C. 4

D. infinitely many

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

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

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

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

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

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

A. 96

B. 48

C. 32

D. no number can be formed

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

A. ⁵²C₄

B. ⁵¹C₅

C. ⁵³C₄

D. ⁵²C₅

Questions: 16 – 18

Consider the following for the next three items that follow:

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

Q. 16 what is the value of ab?

A. 10

B. 9

C. 8

D. 6

Q. 17 what is the value of xyz?

A. 120

B. 105

C. 90

D. cannot be determined

Q. 18 what is the value of pqr?

A. 35/243

B. 81/35

C. 243/35

D. cannot be determined

Questions: 19 – 20

Consider the following for the next two items that follow:

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

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

A. 8/5

B. 9/5

C. 2

D. 11/5

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

A. -4

B. -6

C. -8

D. -10

Questions: 21 – 22

Consider the following for the next two items that follows:

Q. 21 What is the value of c?

A. -1

B. 34

C. 35

D. 50

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

A. 62

B. 63

C. 65

D. 68

Questions: 23 – 24

Consider the following for the next two items that follows:

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

Q. 23 how many possible values can n have?

A. one

B. two

C. three

D. infinitely many

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

A. 160⁰ only

B. 195⁰ only

C. either 160⁰ or 195⁰

D. neither 160⁰ nor 195⁰

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

A. -1

B. 0

C. 1

D. 2

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

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

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

1. They have no solution, if k =15

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

3. They have unique solution, if k = 25

select the correct answer using the code given below:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

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

1. AB(A⁻¹B⁻¹) is a unit matrix.

2. (AB)⁻¹ = A⁻¹ ⁻B¹

Select the correct answer usin the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 29 which of the following is correct?

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

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

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

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

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

A. (11110011)₂

B. (11101011)₂

C. (11110101)₂

D. (11011011)₂

Questions: 31 – 32

Consider the following for the next two items that follow :

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

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

A. a² < 1/ 2

B. a² < 1/2

C. a²≤ 1/2

D. a²≥ 1/2

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

A. a² < 1/2

B. a² > 1/2

C. a² > 1

D. a² ε (1/3, 1/2 ) only

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

A. 1

B. ω

C. ω²

D. iω, where i = √-1

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

A. 10

B. 12

C. 15

D. none of the above

Questions: 35 – 36

consider the following for the next two items that follow

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

= μ

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

A. λ=5 and μ≠ 9

B. λ=5 and μ = 9

C. λ= 9 and μ = 5

D. λ=9 and μ ≠ 5

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

A. λ=5 and μ = 9

B. λ≠5 and μ = 7 only

C. λ≠9 and μ has any real value

D. λ has any real value and μ ≠ 9

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

A. 2100

B. 2120

C. 2240

D. 3331

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

A. 8

B. 9

C. 10

D. 11

Questions: 39 – 40

consider the following for the next two items that follow:

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

roots positive where α > 0 and β > 0

Q. 39 what is the value of α?

A. 1/2

B. 1

C. 2

D. 4

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

A. 1

B. 2

C. 4

D. 6

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

1. 4 sin 2A cos² (A/2)

2. 2 sin 2A(sin A/2 + cos A/2)²

3. 8 sin A cos A cos² (A/2)

select the correct answer using the code given below:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

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

A. 1/16

B. 1/8

C. 1/4

D. 1/2

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

A. 0

B. 1

C. 2

D. 4

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

A. 1/2

B. 1/2 + 1/2√2

C. 1/2 – 1/2√2

D. 1/8

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

A. x² + y² – z²

B. x ² – y² – z²

C. x² – y² + z²

D. x² + y² + z²

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

A. 0.81

B. 0.56

C. 0.48

D. 0.28

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

A. (h cot q)/(cot q – cot p)

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

C. (2h tan p)/(tan p – tan q)

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

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

A. [√(3+√5)+√(5-√5)]/4

B. [√(3+√5)+√(5+√5)]/4

C. [√(3-√5)+√(5-√5)]/4

D. [√(3+√5)-√(5-√5)]/4

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

A. 4500/√3

B. [4500(√3-1)]/√3

C. 4500√3

D. [4500(√3+1)]/√3

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

A. √3

B. -√3

C. √2 – 1

D. 1-√2

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

A. (0,2√3) only

B. (3,-√3) only

C. (0,2√3) or (3,-√3)

D. neither (0,2√3) nor (3,-√3)

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

A. 2x+4y-11=0

B. 2x-4y-5=0

C. 2x-4y-11=0

D. x-y+1=0

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

A. 3 units

B. 5 units

C. 3√3 units

D. 5√2 units

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

A. x²/25 – y²/20 = 1

B. x²/40 – y²/20 =1

C. x²/40 – y²/30 =1

D. x²/30 – y²/25 = 1

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

A. IaI < 2

B. IaI < √2

C. IaI < 1

D. IaI < 1/ √2

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

A. 4x + 3y + 2 = 0

B. 4x – y + 2 = 0

C. 4x – 3y – 2 = 0

D. 4x – 3y + 2 = 0

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

1. 3a – 4b – 4 = 0

2. 8a + 6b + 11= 0

3. 8a + 6b – 9 = 0

select the correct answer using the code given below:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

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

A. 5 units

B. 6 units

C. 8 units

D. 10 units

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

A. (1,3)

B. (2,0)

C. (0,2)

D. (1,1)

Q. 60 What is the eccentricity of rectangular hyperbola?

A. √2

B. √3

C. √5

D. √6

Questions: 61 – 62

Consider the following for the next two items that follows:

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

Q. 61 consider the following:

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

2. PQ is of length more than 8 units

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

which of the above statemnets are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Q. 62 Consider the following:

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

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

which of the above statements is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Questions: 63 – 64

consider the following for the next two items that follows:

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

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

A. <1,4,3>

B. <-1,-4,3>

C. <1,-4,3>

D. <1,-4,-3>

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

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

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

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

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

Questions: 65 – 66

Consider the following for the next two items that follows:

Q. 65 What is equal to vector c ?

A. a

B. b

C. c

D. d

Q. 66 Which of the following equations are correct?

A. a

B. b

C. c

D. d

Questions: 67 – 68

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

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

A. a

B. b

C. c

D. d

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

A. a

B. b

C. c

D. d

Q. 69 which of the following is correct?

A. a

B. b

C. c

D. d

Q. 70 which of the following is correct?

A. a

B. b

C. c

D. d

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

A. (-∞,0)

B. (0,∞)

C. 0< x < 1

D. x > 1

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

A. 1 only

B. 3 only

C. 2 and 3 only

D. 1 and 3 only

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

A. A

B. B = (x ∈ ℝ: x ≥0 )

C. C = (x ∈ ℝ: x ≤0 )

D. D = ℝ

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

A. it has local maximum at x = 0

B. it has local maximum at x = 0

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

D. it has maximum value 1

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

A. 4/3 square units

B. 8/3 square units

C. 4 square units

D. 16/3 square units

Questions: 76 – 77

Consider the following function for the next two items that follows

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

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

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

select the correct answer using the code given below.

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 77 which of the following statements are correct?

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

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

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

select the correct answer using code given below

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Questions: 78 – 80

consider the following for the next three items that follow:

let f(x) = {I x I – I x-1I}²

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

A. 0

B. 2x-1

C. 4x-2

D. 8x-4

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

A. 0

B. 2x-1

C. 4x-2

D. 8x-4

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

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

2. f”(-2) + f”(0.5) + f”(3) = 4

select the correct answer by using the code given below

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Questions: 81 – 83

consider the following for the next three items that follow:

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

Q. 81 which of the following statements is correct?

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

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

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

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

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

A. a

B. b

C. c

D. d

Q. 83 which of the following statements are correct?

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

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

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

select the correct answer using the code given below:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 nd 3

Questions: 84 – 85

Consider the following for the next two items that follow

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

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

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

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

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

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

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

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

select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Questions: 86 – 87

Consider the following for the next two items that follow:

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

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

straight line?

A. (0,2)

B. (-2,-8)

C. (-7,2)

D. (1,10)

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

A. √10/2

B. √10/5

C. 1/√10

D. √5/4

Questions: 88 – 90

Consider the following for the next three items that follow:

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

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

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

select the correct answer

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

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

A. -1

B. 0

C. 1

D. 2

Q. 90 which of the following statements are correct ?

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

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

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

select the correct answer:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Q. 91 choose the correct option

A. 2 f(1)

B. 0

C. 2f(-1)

D. 4f(1)

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

A. √(x⁴+x²+1)/x + c

B. √(x⁴-1/x²+1)/x + c

C. √(x⁴+1/x²+1)/x + c

D. √(x⁴-x²+1)/x + c

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

A. 1,1

B. 1,2

C. 2,1

D. 2,2

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

A. circle

B. parabola

C. ellipse

D. hyperbola

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

A. 3 only

B. -1 only

C. both -1 and 3

D. neither -1 nor 3

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

A. 1

B. 2

C. 3

D. cannot be determined

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

A. (y-x dy/dx)² = 1-(dy/dx)²

B. (y+x dy/dx)² = 1+(dy/dx)²

C. (y-x dy/dx)² = 1+(dy/dx)²

D. (y+x dy/dx)² = 1-(dy/dx)²

Q. 98 Function in figure is equal to

A. ( x + sec x) eˢᶦⁿ ˣ + c

B. ( x – sec x) eˢᶦⁿ ˣ + c

C. ( x + tan x) eˢᶦⁿ ˣ + c

D. ( x – tan x) eˢᶦⁿ ˣ + c

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

A. 1/4

B. 1/2

C. 1

D. 2

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

A. -232/5

B. -116/5

C. 116/5

D. 232/5

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

A. 1/72

B. 1/8

C. 7/72

D. 25/216

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

A. 1-(1/4)²

B. (1/4)⁷

C. (3/4)⁷

D. 1-(3/4)⁷

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

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

A. 0.98

B. 0.91

C. 0.70

D. 0.49

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

A. m(1+n) = 1

B. n(m+1) = 1

C. m=1

D. mn = 1

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

A. 209/343

B. 134/343

C. 149/343

D. 60/343

Q. 106 consider the following statements:

1. the mean and median are equal in symmetric distribution

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

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

bounded by the frequency polygon and horizontal axis

choose the correct one from the below

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

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

A. mean and median

B. median and mode

C. mode only

D. mean and mode

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

Σx=130,Σy=220,Σx² = 2288, Σy² = 5506

what is the line of regression of y on x?

A. y=0.91x + 8.74

B. y=1.02x + 8.74

C. y=1.02x – 7.02

D. y=0.91x – 7.02

Q. 109 from the data choose the correct option:

A. a

B. b

C. c

D. d

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

1. class intervals need not be mutually exclusive

2. class intervals should be exhaustive

3. class intervals need not be of equal width

choose correct statements

A. 1 and 2 only

B. 2 and 3only

C. 1 and 3 only

D. 1,2 and 3

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

A. 1/1024

B. 243/1024

C. 1023/1024

D. 781/1024

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

A. 3/7

B. 3/4

C. 1/3

D. 4/7

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

A. 0.06

B. 0.16

C. 0.84

D. 0.94

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

A. 1/4

B. 2/3

C. 3/4

D. 1/24

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

A. a

B. b

C. c

D. d

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

A. 41.0

B. 41.5

C. 42.0

D. 42.5

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

A. 0.4

B. 0.5

C. 0.6

D. 0.7

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

A: no head appears

B: exactly one head appears

C: at least two heads appear

which one of the following is correct?

A. (A U B) ∩ (A U C) = B U C

B. (A ∩ B’) U (A ∩ C’) =B’ U C’

C. A ∩ (B’ U C’) = A U B U C

D. A ∩ (B’ U C’) = B’ ∩ C’

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

A. 17/18

B. 11/12

C. 1/12

D. 1/18

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

A. 1/3

B. 1/4

C. 1/5

D. 1/6

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

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

NDA/NA(I) Exam 2016 Mathematics

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

A. 60°

B. 90°

C. 120°

D. 150°

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

A. * is reflexive but not transitive and symmetric

B. * is transitive but not reflexive and symmetric

C. * is symmetric and reflexive but not transitive

D. * is symmetric but not reflexive and transitive

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

A. | p | < 4

B. | p | ≤ 4

C. | p | > 4

D. | p | ≥ 4

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

A. π

B. π/2

C. π/3

D. π/4

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

A. ln( (1 – x)/(1 + x) )

B. ln( (2 + x)/(1 – x) )

C. tan⁻¹(1 – x)/(1 + x) )

D. tan⁻¹(1 + x)/(1 – x) )

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

A. [0, 1)

B. [0, 1]

C. (0, 1)

D. (0, 1]

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

A. 12 square units

B. 15 square units

C. 20 square units

D. 30 square units

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

A. 2 + √2

B. 2 – √2

C. 2√2

D. √2

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

A. 1

B. 2

C. 3

D. 4

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

A. 0

B. 1

C. 2

D. 3

Q. 11 Consider the function f(θ) = 4( sin² θ + cos⁴ θ ). Consider the following statements : 1. f(θ) = 2 has no solution. 2. f(θ) = 7/2 has a solution. Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 12 Consider the curves f(x) = x|x| – 1 and g(x) = { 3x/2, x>0 and 2x, x≤0}. Where do the curves intersect?

A. At (2, 3) only

B. At (-1, -2) only

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

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

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

A. 17/6 square units

B. 8/3 square units

C. 2 square units

D. 1/3 square units

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

A. One

B. Two

C. Three

D. Four

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

A. One

B. Two

C. Three

D. Four

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

A. 1/6

B. 1/3

C. 5/18

D. 5/36

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

A. 37/72

B. 2/3

C. 17/72

D. 37/144

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

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

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

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

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

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

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

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

C. f(x) is increasing in (-∞, 1) and decreasing in (1, ∞)

D. f(x) is decreasing in (-∞, 1) and increasing in (1, ∞)

Q. 20 Consider the function f(x) = | x – 1 | + x² where x ∈ ℝ. Which one of the following statements is correct?

A. f(x) has local minima at more than one point in (-∞, ∞)

B. f(x) has local maxima at more than one point in (-∞, ∞)

C. f(x) has local minima at one point only in (-∞, ∞)

D. f(x) has neither local minima nor maxima in (-∞, ∞)

Q. 21 Consider the function f(x) = | x – 1 | + x² where x ∈ ℝ. What is the area of region bounded by x-axis, the curve y = f(x) and the two ordinates x = 1/2 and x = 1?

A. 5/12 square unit

B. 5/6 square unit

C. 7/6 square units

D. 2 square units

Q. 22 Consider the function f(x) = | x – 1 | + x² where x ∈ ℝ. What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates x = 1 and x = 3/2?

A. 5/12 square unit

B. 7/12 square unit

C. 2/3 square unit

D. 11/12 square unit

Q. 23 Consider the following statements:

1. The sequence { a₂ₙ } is in AP with common difference zero.

2. The sequence {a₂ₙ₊₁} is in AP with common difference zero. Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. neither 1 nor 2

Q. 24 What is aₙ₋₁ – aₙ₋₄ equal to?

A. -1

B. 0

C. 1

D. 2

Q. 25 Consider the equation x + |y| = 2y. Which of the following statements are not correct?

1. y as a function of x is not defined for all real x.

2. y as a function of x is not continuous at x = 0

3.y as a function of x is differentiable for all x.

Select the correct answer using the code given below

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 26 Consider the equation x + |y| = 2y. Which of the following statements are not correct? What is the derivative of y as a function of x with respect to x for x < 0?

A. 2

B. 1

C. 1/2

D. 1/3

Q. 27 Consider the lines y = 3x, y = 6x and y = 9. What is the area of the triangle formed by these lines?

A. 27/4 square units

B. 27/2 square units

C. 19/4 square units

D. 19/2 square units

Q. 28 Consider the lines y = 3x, y = 6x and y = 9 The centroid of the triangle is at which one of the following points?

A. (3, 6)

B. (3/2, 6)

C. (3, 3)

D. (3/2, 9)

Q. 29 Consider the function: f(x) = (x – 1)²(x + 1)(x – 2)³ . What is the number of points of local minima of the function f( x )?

A. None

B. One

C. Two

D. Three

Q. 30 Consider the function: f(x) = (x – 1)²(x + 1)(x – 2)³ . What is the number of points of local maxima of the function f(x)?

A. none

B. One

C. Two

D. Three

Q. 31 Let f(x) and g(x) be twice differentiable functions on [0, 2] satisfying f’ ‘(x) = g’ ‘(x), f'(1) = 4, g'(1) = 6, f(2) = 3 and g(2) = 9. Then what is f(x) – g(x) at x = 4 equal to?

A. -10

B. -6

C. -4

D. 2

Q. 32 Consider the curves y =| x – 1 | and |x| = 2. What is/are the point(s) of intersection of the curves?

A. (-2, 3) only

B. (2, 1) only

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

D. neither (-2, 3) nor (2, 1)

Q. 33 Consider the curves y =| x – 1 | and |x| = 2. What is the area of the region bounded by the curves and x-axis?

A. 3 square units

B. 4 square units

C. 5 square units

D. 6 square units

Q. 34 What is the value of f'(0)?

A. p³

B. 3 p³

C. 6 p³

D. -6 p³

Q. 35 What is the value of p for which f’ ‘(0) = 0?

A. -1/6 or 0

B. -1 or 0

C. -1/6 or 1

D. -1 or 1

Q. 36 Consider a triangle ABC which cos A + cos B + cos C = √3 sin π/3. What is the value of sin(A/2).sin(B/2).sin(C/2)?

A. 1/2

B. 1/4

C. 1/8

D. 1/16

Q. 37 Consider a triangle ABC which cos A + cos B + cos C = √3 sin π/3. What is the value of cos((A+B)/2).cos((B+C)/2).cos((C+A)/2)?

A. 1/4

B. 1/2

C. 1/16

D. None of the above

Q. 38 Given that tanα and tanβ are the roots of the equation x² + bx + c = 0 with b≠0. What is tan(α + β) equal to?

A. b(c – 1)

B. c(b – 1)

C. c(b – 1)^(-1)

D. b(c – 1)^(-1)

Q. 39 Given that tanα and tanβ are the roots of the equation x² + bx + c = 0 with b≠0. What is sin(α + β) secα secβ equal to?

A. b

B. -b

C. c

D. -c

Q. 40 Consider the two circles (x – 1)² + (y – 3)² = r² and x² + y² – 8x + 2y + 8 =0. What is the distance between the centres of the two circles?

A. 5 units

B. 6 units

C. 8 units

D. 10 units

Q. 41 Consider the two circles (x – 1)² + (y – 3)² = r² and x² + y² – 8x + 2y + 8 =0. If the circles intersect at two distinct points, then which one of the following is correct?

A. r = 1

B. 1 < r < 2

C. r = 2

D. 2 < r < 8

Q. 42 Consider the two lines x + y + 1 = 0 and 3x + 2y + 1 = 0. What is the equation of the line passing through the point of intersection of the given lines and parallel to x-axis?

A. y + 1 = 0

B. y – 1 = 0

C. y – 2 = 0

D. y + 2 = 0

Q. 43 Consider the two lines x + y + 1 = 0 and 3x + 2y + 1 = 0. What is the equation of the line passing through the point of intersection of the given lines and parallel to y-axis?

A. x + 1 = 0

B. x – 1 = 0

C. x – 2 = 0

D. x + 2 = 0

Q. 44 Consider the equation k sin x + cos2x = 2k – 7. If the equation possesses a solution, then what is the minimum value of k?

A. 1

B. 2

C. 4

D. 6

Q. 45 Consider the equation k sin x + cos2x = 2k – 7. If the equation possesses solution, then what is the maximum value of k?

A. 1

B. 2

C. 4

D. 6

Q. 46 Consider the function f( x ) = (a |ˣ| ⁺ ˣ – 1)/( [x] + x ) where [ . ] denotes the greatest integer function. What is lim x→ 0+ f( x ) equal to?

A. 1

B. ln a

C. 1 = a⁻¹

D. Love does not exist

Q. 47 Consider the function f( x ) = (a |ˣ| ⁺ ˣ – 1)/( [x] + x ) where [ . ] denotes the greatest integer function. What is lim x→ 0- f( x ) equal to?

A. 0

B. ln a

C. 1 – a⁻¹

D. Limit does not exist

Q. 48 Let z₁, z₂ and z₃ be the non-zero complex numbers satisfying z² = iz̅, where i = √-1. What is z₁ + z₂ + z₃ equal to?

A. i

B. -i

C. 0

D. 1

Q. 49 Let z₁, z₂ and z₃ be the non-zero complex numbers satisfying z² = iz̅, where i = √-1. Consider the following statements:

1. z₁.z₂.z₃ is purely imaginary.

2. z₁.z₂ + z₂.z₃ + z₃.z₁ is purely real.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. neither 1 nor 2

Q. 50 Given that logₓ y, log􀀁 x, logᵧ z are in GP, xyz = 64 and x³, y³, z³ are in AP. Which one of the following is correct?

x,y and z are

A. in AP only

B. in GP only

C. in both AP and GP

D. neither in AP nor in GP

Q. 51 Given that logₓ y, log􀀁 x, logᵧ z are in GP, xyz = 64 and x³, y³, z³ are in AP. Which one of the following is correct?

xy, yz and zx are

A. in AP only

B. in GP only

C. in both AP and GP

D. neither in AP nor in GP

Q. 52 Let z be a complex number satisfying | (z – 4)/(z – 8)| = 1 and | z/(z – 2)| = 3/2. What is |z| equal to?

A. 6

B. 12

C. 18

D. 36

Q. 53 Let z be a complex number satisfying | (z – 4)/(z – 8)| = 1 and | z/(z – 2)| = 3/2. What is |(z – 6)/(z + 6)| equal to?

A. 3

B. 2

C. 1

D. 0

Q. 54 A function f(x) is defined as follows: f(x) = { x + π for x∈[ -π, 0); n.cosx for x∈[ 0, π/2]; (x – π)² for x∈( π/2, π] }.

Consider the following statements:

1. The function f(x) is continuous at x = 0.

2. The function f(x) is continuous at x = π/2.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 55 A function f(x) is defined as follows: f(x) = { x + π for x∈[ -π, 0); n.cosx for x∈[ 0, π/2]; (x – π)² for x∈( π/2, π] }.

Consider the following statements:

1. The function f(x) is differentiable at x = 0.

2. The function f(x) is differentiable at x = π/2.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 56 Let α and β ( α < β ) be the roots of the equation s² + bx + c = 0, where b > 0 and c > 0. Consider the following :

1. β < -α

2. β < |α|.

Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 57 Let α and β ( α < β ) be the roots of the equation s² + bx + c = 0, where b > 0 and c > 0. Consider the following :

1. α + β + βα > 0

2. α²β + β²α > 0.

Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 58 Consider a parallelogram whose vertices are A(1,2), B(4,y), C(x,6) and D(3,5) taken in order. What is the value of AC² – BD²?

A. 25

B. 30

C. 36

D. 40

Q. 59 Consider a parallelogram whose vertices are A(1,2), B(4,y), C(x,6) and D(3,5) taken in order. What is the point of intersection of the diagonals?

A. (7/2, 4)

B. (3, 4)

C. (7/2, 5)

D. (3, 5)

Q. 60 Consider a parallelogram whose vertices are A(1,2), B(4,y), C(x,6) and D(3,5) taken in order. What is the area of parallelogram?

A. 7/2 square units

B. 4 square units

C. 11/2 square units

D. 7 square units

Q. 61 Let f: ℝ->ℝ be a function such that f(x) = x³ + x²f'(1) + xf”(2) + f”'(3) for x∈ℝ. What is f(1) equal to?

A. -2

B. -1

C. 0

D. 4

Q. 62 Let f: ℝ->ℝ be a function such that f(x) = x³ + x²f'(1) + xf”(2) + f”'(3) for x∈ℝ. What is f'(1) equal to?

A. -6

B. -5

C. 1

D. 0

Q. 63 Let f: ℝ->ℝ be a function such that f(x) = x³ + x²f'(1) + xf’ ‘(2) + f’ ‘ ‘(3) for x∈ℝ. What is f’ ‘(10) equal to?

A. 1

B. 5

C. 6

D. 8

Q. 64 Let f: ℝ->ℝ be a function such that f(x) = x³ + x²f'(1) + xf”(2) + f”'(3) for x∈ℝ.

Consider the following:

1. f(2) = f(1) – f(0)

2. f’ ‘(2) – f'(1) = 12 .

Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 65 A plane P passes through the line of intersection of the planes 2x – y + 3z = 2, x + y – z =1 and the point (1, 0, 1). What are the direction ratios of the line of intersection of the given planes?

A. <2, -5, -3>

B. <-1, -5, -3>

C. <2, 5, 3>

D. <1, 3, 5>

Q. 66 A plane P passes through the line of intersection of the planes 2x – y + 3z = 2, x + y – z =1 and the point (1, 0, 1). What is the equation of the plane P?

A. 2x + 5y – 2 = 0

B. 5x + 2y – 5 = 0

C. x + z – 2 = 0

D. 2x – y – 2z = 0

Q. 67 A plane P passes through the line of intersection of the planes 2x – y + 3z = 2, x + y – z =1 and the point (1, 0, 1). If the plane P touches the sphere x² + y² + z² = r², then what is r equal to?

A. 2 / √29

B. 4 / √29

C. 5 / √29

D. 1

Q. 68 Consider the function f(x) = | x² – 5x + 6 |. What is tf'(4) equal to?

A. -4

B. -3

C. 3

D. 2

Q. 69 Consider the function f(x) = | x² – 5x + 6 |. What is f’ ‘(2.5) equal to?

A. -3

B. -2

C. 0

D. 2

Q. 70 Let f(x) be the greatest integer functions and g(x) be the modulus function. What is (g ∘ f) (-5/3) – (f ∘ g)(-5/3) equal to?

A. -1

B. 0

C. 1

D. 2

Q. 71 Let f(x) be the greatest integer functions and g(x) be the modulus function. What is (f ∘ f) (-9/5) + (g ∘ g)(-2) equal to?

A. -1

B. 0

C. 1

D. 2

Q. 72 Consider a circle passing through the origin and the points (a, b) and (-b, -a). On which line does the centre of the circle lie?

A. x + y = 0

B. x – y = 0

C. x + y = a + b

D. x – y = a² – b²

Q. 73 Consider a circle passing through the origin and the points (a, b) and (-b, -a). What is the sum of the squares of the intercepts cut off by the circle on the axes?

A. ( a² + b²)/(a² – b²)²

B. 2( a² + b²)/(a – b)²

C. 4( a² + b²)/(a – b)²

D. None of the above

Q. 74 Let â, b̂ be two unit vectors and θ be the angle between them. What is cos(θ/2) equal to?

A. | â – b̂|/2

B. | â + b̂|/2

C. | â – b̂|/4

D. | â + b̂|/4

Q. 75 Let â, b̂ be two unit vectors and θ be the angle between them. What is sin(θ/2) equal to?

A. | â – b̂|/2

B. | â + b̂|/2

C. | â – b̂|/4

D. | â + b̂|/4

Q. 76 Consider the following statements :

1.There exists θ ∈ ( -π/2, π/2) for which tan⁻¹ ( tan θ ) ≠ θ.

2. sin⁻¹ (1/3) – sin⁻¹ (1/5) = sin⁻¹ ( 2√2( √3 – 1)/15) .

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. neither 1 nor 2

Q. 77 Consider the following statements :

1. tan⁻¹ ( x ) + tan⁻¹ (1/x) = π

2. There exist x, y∈[-1, 1], where x≠y such that sin⁻¹ ( x ) + cos⁻¹ ( y ) = π/2.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 78 What are the order and degree respectively of the differential equation whose solution is y = cx + c² – 3c³/² + 2, where c is a parameter?

A. 1, 2

B. 2, 2

C. 1, 3

D. 1, 4

Q. 79 What is ∫ (-2→2) x dx – ∫ (-2→2) [ x ] dx equal to, where [ . ] is the greatest integer function?

A. 0

B. 1

C. 2

D. 4

Q. 80 If ∫ (-2→5) f(x)dx = 4 and ∫ (0→5) { 1 + f(x) }dx = 7 then what is ∫ (-2→0) f(x)dx equal to?

A. -3

B. 2

C. 3

D. 5

Q. 81 If lim x→0 Φ( x ) = a^2, where a ≠ 0, then what is lim x→0 Φ( x/a ) equal to?

A. a²

B. a⁻²

C. -a²

D. -a

Q. 82 What is lim x→0 e⁻¹/ˣ² equal to?

A. 0

B. 1

C. -1

D. Limit does not exist

Q. 83 If A is square matrix, then what is adj(A⁻¹) – (adj A)⁻¹ equal to?

A. 2 |A|

B. Null matrix

C. Unit matrix

D. None of the above

Q. 84 What is the binary equivalent of the decimal number 0.3125?

A. 0.0111

B. 0.1010

C. 0.0101

D. 0.1101

Q. 85 Let R be a relation on the set N of natural numbers defined by ‘nRm ⇔ n is a factor of m’. Then which one of the following is correct?

A. R is reflexive, symmetric but not transitive

B. R is transitive, symmetric but not reflexive

C. R is reflexive, transitive but not symmetric

D. R is an equivalence relation

Q. 86 What is ∫ 0→4π ( | cos x | )dx equal to?

A. 0

B. 2

C. 4

D. 8

Q. 87 What is the number of natural numbers less than or equal to 1000 which are neither divisible by 10 nor 15 nor 25?

A. 860

B. 854

C. 840

D. 824

Q. 88 (a, 2b) is the mid-point of the line segment joining the points (10, 06) and (k, 4). If a – 2b = 7, then what is the value of k?

A. 2

B. 3

C. 4

D. 5

Q. 89 Consider the following statements:

1. If ABC is an equilateral triangle then 3.tan( A + B ).tan C = 1.

2. If ABC is a triangle in which A = 78°, B = 66°, then tan(A/2 + C) < tan A.

3. If ABC is any triangle, then tan( A+B/2 ). sin(C/2) < cos(C/2).

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. 1 and 2

D. 2 and 3

Q. 90 If A = ( cos 12° – cos 36° )( sin 96° + sin 24° ) and B = (sin 60° – sin 12° )( cos 48° – cos 72° ), then what is A/B equal to?

A. -1

B. 0

C. 1

D. 2

Q. 91 What is the mean deviation from the mean of the numbers 10, 9, 21, 16, 24?

A. 5.2

B. 5.0

C. 4.5

D. 4.0

Q. 92 Three dice are thrown simultaneously. What is the probability that the sum on the three faces is at least 5?

A. 17/18

B. 53/54

C. 103/108

D. 215/216

Q. 93 Two independent events A and B have P(A) = 1/3 and P(B) = 3/4. What is the probability that exactly one of the two events A or B occurs?

A. 1/4

B. 5/6

C. 5/12

D. 7/12

Q. 94 A coin is tossed three times. What is the probability of getting head and tail alternatively?

A. 1/8

B. 1/4

C. 1/2

D. 3/4

Q. 95 if the total number of observations is 20, Σ(xi) = 1000 and Σ (xi²) = 84000, then what is the variance of the distribution?

A. 1500

B. 16000

C. 1700

D. 1800

Q. 96 A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is queen of spade?

A. 1/52

B. 1/13

C. 1/4

D. 1/8

Q. 97 If two dice are thrown, then what is the probability that the sum on the two faces is greater than or equal to 4?

A. 13/18

B. 5/6

C. 11/12

D. 35/36

Q. 98 A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired so that there is at least 80% probability that target is hit?

A. 5

B. 6

C. 7

D. None of the above

Q. 99 For two mutually exclusive events A and B, P(A) = 0.2 and P(A’∩B) 0.3. What is P(A| (A U B)) equal to?

A. 1/2

B. 2/5

C. 2/7

D. 2/3

Q. 100 What is the probability of 5 Sundays in the month of December?

A. 1/7

B. 2/7

C. 3/7

D. None of the above

Q. 101 if m is the geometric mean of (y/z)ˡᵒᵍ ⁽ʸᶻ⁾ , (z/x)ˡᵒᵍ ⁽ᶻˣ⁾ and (x/y)ˡᵒᵍ ⁽ˣʸ⁾ then what is the value of m?

A. 1

B. 3

C. 6

D. 9

Q. 102 A point is chosen at random inside a rectangle measuring 6 inches by 5 inches. What is the probability that the randomly selected point is at least one inch from the edge of the rectangle?

A. 2/3

B. 1/3

C. 1/4

D. 2/5

Q. 103 The mean of the series x₁, x₂, …, xₙ is X’. If x₂ is replaced by λᵢ then what is the new mean?

A. X’ – x₂ + λ

B. (X’ – x₂ – λ)/n

C. (X’ – x₂ + λ)/n

D. (nX’ – x₂ + λ)/n

Q. 104 For the data 3,5,1,6,5,9,2,8,6 the mean, median and mode are x, y and z respectively. Which one of the following is correct?

A. x = y ≠ z

B. x ≠ y = z

C. x ≠ y ≠ z

D. x = y = z

Q. 105 Consider the following statements in respect of a histogram :

1. The total area of the rectangles in a histogram is equal to the total area bounded by the corresponding frequency polygon and the x-axis.

2. When class intervals are unequal in a frequency distribution, the area of the rectangle is proportional to the frequency.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 106 A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times?

A. 1/2

B. 3/8

C. 1/4

D. 1/8

Q. 107 What is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets?

A. 60

B. 120

C. 500

D. 1000

Q. 108 If one root of the equation (l – m)x² + l.x + 1 = 0 is double the other and l is real, then what is the greatest value of m?

A. -9/8

B. 9/8

C. -8/9

D. 8/9

Q. 109 What is the number of four-digit decimal numbers (<1) in which no digit is repeated?

A. 3024

B. 4536

C. 5040

D. None of the above

Q. 110 What is a vector of unit length orthogonal to both the vectors î + ĵ + k̂ and 2 î + 3 ĵ -k̂?

A. (-4 î + 3 ĵ – k̂)/√26

B. (-4 î + 3 ĵ + k̂)/√26

C. (-3 î + 2 ĵ – k̂)/√14

D. (-3 î + 2 ĵ +k̂)/√14

Q. 111 If a̅, b̅ and c̅ are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then which one of the following is correct?

A. a̅ + b̅ + c̅ = 0̅

B. a̅ + b̅ + c̅ = unit vector

C. a̅ + b̅ = c̅

D. a̅ = b̅ + c̅

Q. 112 What is the area of the parallelogram having diagonals 3î + ĵ – 2k̂ and î – 3ĵ + 4k̂?

A. 5√5 square units

B. 4√5 square units

C. 5√3 square units

D. 15√2 square units

Q. 113 Consider the following in respect of the matrix A.

1. A² = -A

2. A³ = 4A .

Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 114 Which of the following determine have value zero? Select the correct answer using the code given below.

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 115 What is the acute angle between the lines represented by the equations y – √3 x – 5 = 0 and √3 y – x + 6 = 0?

A. 30°

B. 45°

C. 60°

D. 75°

Q. 116 The system of linear equations kx + y + z = 1, x + ky + z = 1 and x + y + kz = 1 has a unique solution under which one of the following conditions?

A. k ≠ 1 and k ≠ -2

B. k ≠ 1 and k ≠ 2

C. k ≠ -1 and k ≠ -2

D. k ≠ -1 and k ≠ -2

Q. 117 What is the number of different messages that can be represented by three 0’s and two 1’s?

A. 10

B. 9

C. 8

D. 7

Q. 118 If log(base a) (ab) = x, then what is log(base b)(ab) equal to?

A. 1/x

B. x/(x+1)

C. x/(1-x)

D. x/(x-1)

Q. 119 If y = log₁₀x + logₓ10 + logₓx + log₁₀10 then what is (dy/dx)ₓ₌₁₀ equal to?

A. 10

B. 2

C. 1

D. 0

Q. 120 Suppose ω₁ and ω₂ are two distinct cube roots of unity different from 1. Then what is (ω₁ – ω₂)² equal to?

A. 3

B. 1

C. -1

D. -3

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

NDA/NA(II) Exam 2015 Mathematics Previous Year Paper

NDA/NA(II) Exam 2015 Mathematics

Q. 1 Let X be the set of all persons living in Delhi. The persons a and b in X are said to be related if the difference in their ages is at most 5 years. The relation is

A. an equivalence relation

B. reflexive and transitive but not symmetric

C. symmetric and transitive but not reflexive

D. reflexive and symmetric but not transitive

Q. 2 The matrix A will have inverse for every real number x except for

A. x = (11±√5)/2

B. x = (9±√5)/2

C. x = (11±√3)/2

D. x = (9 ±√3)/2

Q. 3 If the value of the determinant is positive, where a≠b≠c, then value of abc

A. cannot be less than 1

B. is greater than -8

C. is less than -8

D. must be greater than 8

Q. 4 consider the following statements respect of the determinant where α,β are complementary angles

1. The value of the determinant is 1/√2 cos(α-β)/2

2. the minimum value of the determinant is 1/√2

which of the above statements is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 5 What is (1000000001)₂ – (0.0101)₂ equal to ?

A. (512.6775)₁₀

B. (512.6875)₁₀

C. (512.6975)₁₀

D. (512.0909)₁₀

Q. 6 If A is the matrix, then the matrix X for which 2X + 3A = 0 holds true is:

A. a

B. b

C. c

D. d

Q. 7 If z₁ and z₂ are complex numbers with Iz₁I = Iz₂I, then which of the following is/are correct?

1. z₁ = z₂

2. real part of z₁ = real part of z₂

3. imaginary part of z₁ = imaginary part of z₂

select the correct answer using the code given below.

A. 1 only

B. 2 only

C. 3 only

D. none

Q. 8 If A and B are two matrices given, then which of the following is/are correct?

1. A and B are commute

2. AB is a null matrix

select the correct answer using the code given below.

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 9 The number of real roots of the equation x² – 3IxI + 2 = 0 is

A. 4

B. 3

C. 2

D. 1

Q. 10 If the sum of roots of the equation ax² + bx + c=0 is equal to the sum of their squares, then

A. a²+b² = c²

B. a² + b² = a+ b

C. ab + b² = 2ac

D. ab – b² = 2ac

Q. 11 If A ={xεR: x²+6x-7<0} and B = {xεR:x²+9x+14>0}, then which of the following is/are correct?

1. )A∩B) = (-2,1)

2. (A∖B)=(-7,-2)

select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 12 A, B,C and D are four sets such that A∩B = C ∩ D =φ.consider the following:

1. A U C and B U D are always disjoint.

2.A ∩ C and B ∩ D are always disjoint.

which of the above statements is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 13 If A is an invertible matrix of order n and k is any positive real number, then the value of [det(KA)]⁻¹ det A

A. k⁻ⁿ

B. k⁻¹

C. kⁿ

D. nk

Q. 14 The value of the infinite product 6½ x 6½ x 6⅜ x 6¼ x… is

A. 6

B. 36

C. 216

D. ∞

Q. 15 If the roots of the equation x² – nx + m = 0 differ by 1, then

A. n²-4m-1=0

B. n²+4m-1=0

C. m²+4n+1=0

D. m²-4n-1=0

Q. 16 If different words are formed with all the letters of the ‘AGAIN’ and are arranged alphabetically among themselves as in a dictionary among themselves as in a dictionary, the word at the 50th place will be

A. NAAGI

B. NAAIG

C. IAAGN

D. IAANG

Q. 17 The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, is

A. 165

B. 364

C. 1001

D. 1365

Q. 18 In the expression of (√x + 1/3x²)¹⁰ the value of constant team (independent of x ) is

A. 5

B. 8

C. 45

D. 90

Q. 19 The value of sin² 5⁰ + sin² 10⁰ + sin² 15⁰ +sin² 20⁰ +…+sin² 90⁰ is

A. 7

B. 8

C. 9

D. 19

Q. 20 On simplifying (sin³ A + sin 3A)/sin A + (cos³ A – cos 3A)/cos A, we get

A. sin 3A

B. cos 3A

C. sin A + cos A

D. 3

Q. 21 The value of tan(2 tan⁻¹ 1/5 – π/4) is

A. -7/17

B. 5/16

C. 5/4

D. 7/17

Q. 22 Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15⁰ with the horizontal. The distance between the poles is approximately equal to

A. 36.3 m

B. 37.3 m

C. 38.3 m

D. 39.3 m

Q. 23 If g(x) = 1/f(x) and f(x) = x, x ≠ 0, then which one of the following is correct?

A. f(f(f(g(g(f(x)))))) = g(g(f((g(f(x)))))

B. f(f(g(g(g(f(x))))) = g(g(f(g(f(x)))))

C. f(g(f(g(g(g(f(x))))) = g(g(f(g(f(x)))))

D. f(f(f(g(g(f(x))))) = f(f(f(g(f(x))))

Q. 24 consider the following :

1. sin⁻¹ 4/5 + sin⁻¹ 3/5 = π/2

2. tan⁻¹ √3 + tan⁻¹ 1 = -tan⁻¹ (2+π√3)

which of the above is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 25 If A is an orthogonal matrix of order 3 and B, then which of the following is/are correct?

1.IABI = ± 47

2. AB = BA

select the correct answer using the code given below

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 26 If a,b,c are the sides of a Δ ABC, then (refer figure) where p > 1 a

A. always negative

B. always positive

C. always zero

D. positive if 1<p<2 and negative p>2

Q. 27 Id a,b,c are real number, then the value of the determinant is

A. 0

B. (a-b)(b-c)(c-a)

C. (a+b+c)²

D. (a+b+c)³

Q. 28 If the point z₁ = 1+i where i = √-1 is the reflection of a point z₂ = x+iy in the line iz̅-iz = 5, then the point z₂ is

A. 1+4i

B. 4 + i

C. 1-i

D. -1-i

Q. 29 If sin x + sin y= a and cos x + cos y = b, then tan² (x+y)/2+tan² (x-y)/2 is equal to

A. (a⁴ + b⁴+4b²)/(a²b²+b⁴)

B. (a⁴-b⁴+4b²)/(a²b²+b⁴)

C. (a⁴-b⁴+4a²)/(a²b²+a⁴)

D. none of the above

Q. 30 A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. from a point on the field , the angles of elevation of the bottom and tip of the flag staff are 30⁰ and 45⁰ respectively. Which of the following gives the best approximation to the height of the tower?

A. 3.90 m

B. 4.00 m

C. 4.10 m

D. 4.25 m

Questions: 31 – 33

For the next three items that follow:

consider the expansion of (1+x)²ⁿ⁺¹

Q. 31 If the coefficients of x^r and x^(r+1) are equal in the expansion, then r is equal to

A. n

B. (2n-1)/2

C. (2n+1)/2

D. n+1

Q. 32 The average of the coefficients of the two middle terms in the expansion is

A. A

B. B

C. C

D. D

Q. 33 The sum of the coefficients of all the terms in the expansion is

A. 2²ⁿ⁻¹

B. 4ⁿ⁻¹

C. 2 x 4ⁿ

D. none of the above

Q. 34 The nth term of A.P is (3+n)/4, then the sum of first 105 terms is

A. 270

B. 735

C. 1409

D. 1470

Q. 35 A polygon has 44 diagonals. The number of its side sides:

A. 11

B. 10

C. 8

D. 7

Q. 36 If p,q,r are in one geometric progression and a,b,c are in another geometric progression then ap, bq, cr are in

A. arithmatic progression

B. geometric progression

C. harmonic progression

D. none of the above

Questions: 37 – 38

For the next two items that follow:

consider a triangle ABC satisfying 2a sin² (C/2)+2c sin² (A/2) = 2a+2c-3b

Q. 37 The sides of the triangle are in

A. G.P

B. A.P

C. H.P

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

Q. 38 sin A, sin B, sin C are in

A. G.P

B. A.P

C. H.P

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

Q. 39 If the p=tan(-11π/6), q=tan (21π/6) and r = cot(283π/6), then which of the following is/are correct?

1. The value of p x r is 2.

2. p,q and r are in G.P.

select the correct answer using the code given below.

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 40 The number of ways in which 3 holiday tickets can be given to 20 employees of an organization if each employee is eligible for any one or more of the tickets, is

A. 1140

B. 3420

C. 6840

D. 8000

Q. 41 What is the sum of n terms of the series √2+√8+√18+√32+…?

A. [n(n-1)]/√2

B. √2n(n+1)

C. [n(n+1)]/√2

D. [n(n-1)]/2

Q. 42 The coefficient of x⁹⁹ in the expansion of (x-1)(x-2)(x-3)…(x-100) is

A. 5050

B. 5000

C. -5050

D. -5000

Q. 43 zz̅+(3-i)+(3+i)z̅+1=0 represents a circle with

A. centre (-3,-1) and radius 3

B. centre (-3,1) and radius 3

C. centre (-3,-1) and radius 4

D. centre (-3,1) and radius 4

Q. 44 The number of 3 digit even numbers that can be found from the digits 0,1,2,3.4 and 5 repetition of digits being out allowed is

A. 60

B. 56

C. 52

D. 48

Q. 45 If log₈ m + log₈ 1/6 = 2/3, then m is equal to

A. 24

B. 18

C. 12

D. 3

Q. 46 The area of the figure formed by the lines ax+by+c=0, ax-by-c=0,ax+by-c=0 and ax-by-c=0 is

A. c²/ab

B. 2c²/ab

C. c²/2ab

D. c²/4ab

Q. 47 If a line is perpendicular to the line 5x-y=0 and forms a triangle of area 5 square units with co-ordinate axes, then its equation is

A. x+5y±5√2=0

B. x-5y±5√2=0

C. 5x+y±5√2=0

D. 5x-y±5√2=0

Q. 48 Consider any point P on the ellipse x²/25 + y²/9 = 1 in the first quadrant. Let r and s represent its distances from (4,0) and (-4,0) respectively, then (r+s) is equal to

A. 10 unit

B. 9 unit

C. 8 unit

D. 6 unit

Q. 49 A straight line x=y+2 touches the circle 4(x²+y²)=r². The value of r is

A. √2

B. 2√2

C. 2

D. 1

Q. 50 The three lines 4x+4y=1,8x-3y=2,y=0 are

A. the sides of an isosceles triangle

B. concurrent

C. mutually perpendicular

D. the sides of an equilateral triangle

Q. 51 The line 3x+4y-24=0 intersects the x-axis at A and y-axis at B. Then the circumcentre of the triangle OAB where O is the origin is

A. (2,3)

B. (3,3)

C. (4,3)

D. none of the above

Q. 52 The eccentricity of the hyperbola 16x²-9y²=1 is

A. 3/5

B. 5/3

C. 4/5

D. 5/4

Q. 53 The product of the perpendiculars from the two points (±4,0) to the line 3x cos φ +5y sin φ =15 is

A. 25

B. 16

C. 9

D. 8

Q. 54 If the centre of the circle passing through the origin is (3,4), then the intercepts cut off by the circle on x-axis and y-axis respectively are

A. 3 unit and 4 unit

B. 6 unit and 4 unit

C. 3 unit and 8 unit

D. 6 unit and 8 unit

Q. 55 The lines 2x=3y=-z and 6x=-y=-4z

A. are perpendicular

B. are parallel

C. intersect at an angle 45⁰

D. intersect at an angle 60⁰

Q. 56 Two straight lines passing through the point A(3,2) cut the line 2y=x+3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ is

A. 7x+y-21=0

B. x+7y+21=0

C. 2x+y-8=0

D. x+2y+8=0

Q. 57 The radius of the sphere 3x²+3y²+3z²-8x+4y+8z-15=0 is

A. 2

B. 3

C. 4

D. 5

Q. 58 The direction ratios of the line perpendicular to the lines with direction ratios<1,-2,-2>and <0,2,1> are

A. <2,-1,2>

B. <-2,1,2>

C. <2,1,-2>

D. <-2,-1,-2>

Q. 59 What are the co-ordinates of the foot of the perpendicular drawn from the point (3,5,4) on the plane z=0

A. (0,5,4)

B. (3,5,0)

C. (3,0,4)

D. (0,0,4)

Q. 60 The lengths of the intercepts on the co-ordinate axes made by the plane 5x+2y+z-13=0 are

A. 5,2,1 unit

B. 13/5, 13/2, 13 unit

C. 5/13, 2/13, 1/13 unit

D. 1,2,5 unit

Q. 61 The area of the square, one of whose diagonals is 3î+4j is

A. 12 square unit

B. 12.5 square unit

C. 25 square unit

D. 156.25 square unit

Q. 62 ABCD is a parallelogram and P is the point of intersection of the diagonals. If the O is the origin, then

A. a

B. b

C. c

D. d

Q. 63 If b̅ and c̅ are the position vectors of the point B and C respectively, then the position vector of the point D such that

A. 4(c̅ – b̅)

B. -4(c̅ – b̅)

C. 4c̅-3 b̅

D. 4c̅ + b̅

Q. 64 If the position vector a̅ of the point (5,n) is such that I a̅I=13, then the value/values of n can be

A. ±8

B. a±12

C. 8 only

D. 12 only

Q. 65 If Ia̅I = 2 and I b̅ I = 3, them Ia̅ x b̅ I² + Ia̅.b̅I² is equal to

A. 72

B. 64

C. 48

D. 36

Q. 66 Consider the following inequilities in the respect of vectors a̅ and b̅:

1.I a̅ + b̅ I ≤ I a̅ I + I b̅ I

2. I a̅ – b̅ I ≥ a̅ I – I b̅ I

Which of the above is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 67 If the magnitude of difference of two unit vectors is √3 , then the magnitude of sum of the two vectors is

A. 1/2 unit

B. 1 unit

C. 2 unit

D. 3 unit

Q. 68 If the vectors αî + αĵ + γk̂, î + k̂, and γî + γĵ + βk̂ lie on a plane, where α, β, and γ are distinct non-negative numbers, then γ is

A. Arithmetic mean of α and β

B. geometric mean of α and β

C. Harmonic mean of α and β

D. none of the above

Q. 69 The vectors a̅, b̅, c̅ and d̅ are such that a̅ x b̅ = c̅ x d̅. Which of the following is/are correct?

1.(a̅ – d̅) x (b̅ – d̅) = 0

2. (a̅ x d̅) x (c̅ x d̅) = 0

select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 70 The value of the integral where a+b=0 is

A. 2b-a sin (b-a)

B. a+3b cos(b-a)

C. sin a – (b-a)cos b

D. 0

Q. 71 If f(x)=√(25-x)², the what is the value is equal to?

A. 1/5

B. 1/24

C. √24

D. -1/√24

Q. 72 consider the function

f(x) = { ax-2, for -2< x < -1

-1, for -1 ≤ x ≤ 1

a+2(x-1)², for 1 < x < 2

what is the value of a for which f(x) is continuous ar x = -1 and x = 1?

A. -1

B. 1

C. 0

D. 2

Q. 73 The function f(x) = (1-sin x+cos x)/(1+sin x+cos x) is not defined at x= π. The value of f(π) so that f(x) is continuous at x=π is

A. -1/2

B. 1/2

C. -1

D. 1

Q. 74 consider the following functions:

1. f(x) = { 1/x is x ≠ 0

0 if x=0

2. f(x) = { 2x+5 if x> 0

x²+2x+5 if x ≤ 0

which of the above is/are derivable at x =0?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 75 The domain of the function f(x) = 1/√(IxI-x) is

A. [0,∞]

B. (-∞,0)

C. [1,∞)

D. (-∞,0]

Q. 76 consider the following statements :

1. The function f(x)= x² + 2 cos x is increasing in the interval (0,π)

2. The function f(x) = ln (√( 1 + x² ) – x ) is decreasing in the interval (-∞,∞)

which of the above statements is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 77 The derivative of ln(x+sin x) with respect to (x+cos x) is

A. (1+cos x)/(x+sin x)(1-sin x)

B. (1-cos x)/(x+sin x)(1+sin x)

C. (1-cos x)/(x-sin x)(1+cos x)

D. (1+cos x)/(x-sin x)(1-cos x)

Q. 78 If y = cot⁻¹ [(√(1+sin x)+√(1-sin x))/(√(1+sin x)-√(1-sin x))] where 0 < x < π/2, then dy/dx is equal to

A. 1/2

B. 2

C. sin x+cos x

D. sin x-cos x

Q. 79 The function f(x) = x/e^x is monotonically increasing if

A. x < 0 only

B. x > 2 only

C. 0 < x < 2

D. x ∈(-∞,0) U (2,∞)

Q. 80 If x^a .y^b = (x-y)^(a+b), then the value of dy/dx – y/x is equal to

A. a/b

B. b/a

C. 1

D. 0

Q. 81 If f: R—> R, g:R—> R be two functions given by

f(x) = 2x-3 and g(x) = x³+5, then (fog)⁻¹(x) is equal to

A. [(x+7)/2]⅓

B. [(x-7)/2]⅓

C. [(x – 7/2)]⅓

D. [(x + 7/2)]⅓

Q. 82 If 0 < a < b, then the value of

A. IbI – I a I

B. I a I – I b I

C. I b I/I a I

D. 0

Q. 83 the value of the integral is equal to

A. 8/15

B. 16/15

C. 32/15

D. 0

Q. 84 If f(x) = sin(e^(x-2)-1)/ln (x-1), then

A. -2

B. -1

C. 0

D. 1

Q. 85 Consider the following statements:

1. f(x) = ln x is an increasing function on (0,∞)

2. f(x) = e^x – x (ln x) is an increasing function on (1,∞).

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 86 If s = √(t² + 1), then d²s / d²t is equal to

A. 1/s

B. 1/s²

C. 1/s³

D. 1/s⁴

Q. 87 Consider the following statements:

statement 1: the function f : R—> R such that f(x) = x³ for all x R is one-one.

statement 2: f(a) = f(b) ⇒ a = b for all a,b ε R if the function f is one-one.

which of the following is correct in respect of the above statement?

A. both the statements are true and statement 2 is the correct explanation of statement 1.

B. both the statements are true and statement 2 is not the correct explanation of statement 1

C. statement 1 is true but statement 2 is false

D. statement 1 is false but statement 2 is true

Q. 88 ∫ dx/1+e^-x is equal to

where c is the constant of integration

A. 1+e^x+c

B. ln(1+e^-x)+c

C. ln(1+e^x)+c

D. 2 ln(1+e^-x)+c

Q. 89 The value of integration

A. 0

B. 2/3

C. 2

D. -2

Q. 90 The area bounded by the coordinate axes and the curve √x + √y = 1, is

A. 1 square unit

B. 1/2 square unit

C. 1/3 square unit

D. 1/6 square unit

Questions: 91 – 92

for the next two items that follow

consider the function f(x) = (1/x)^(2x^2), where x > 0

Q. 91 At what value of x does the function attain maximum value?

A. e

B. √e

C. 1/√e

D. 1/e

Q. 92 The maximum value of the function is

A. e

B. e^(2/e)

C. e^(1/e)

D. 1/e

Questions: 93 – 94

For the next two items that follow

consider f'(x) = x²/2 -kx+1 such that f(0) = 0 and f(3) = 15.

Q. 93 The value of k is

A. 5/3

B. 3/5

C. -5/3

D. -3/5

Q. 94 f”(-2/3) is equal to

A. -1

B. 1/3

C. 1/2

D. 1

Q. 95 For the next two items that follow

f(x) = -2x³ – 9x² -12x + 1

The function f(x) is an increasing function in the interval

A. (-2,-1)

B. (-∞,-2)

C. (-1,2)

D. (-1,∞)

Q. 96 For the next two items that follow

f(x) = -2x³ – 9x² -12x + 1

The function f(x) is a decreasing function in the interval

A. (-2,-1)

B. (-∞,-2) only

C. (-1,2) only

D. (-1,∞) U (-1, ∞)

Questions: 97 – 98

For the next two items that follow:

consider the integrals

Q. 97 which one of the following is correct?

A. A = 2B

B. B = 2A

C. A = B

D. A = 3B

Q. 98 What is the value of B?

A. π/4

B. π/2

C. 3π/4

D. π

Questions: 99 – 100

consider the function for the next two items that follow

f(x) = { -2 sin x if x ≤ -π/2

A sin x + B is -π/2 < x < π/2

cos x if x ≥ π/2

which is continuous everywhere.

Q. 99 The value of A is

A. 1

B. 0

C. -1

D. -2

Q. 100 The value of B is

A. 1

B. 0

C. -1

D. -2

Q. 101 The degree of the differential equation dy/dx – x = (y-x dy/dx)⁻⁴ is

A. 2

B. 3

C. 4

D. 5

Q. 102 The solution of dy/dx = √(1-x²-y² + x²y²) is

A. sin⁻¹ y = sin⁻¹ x + c

B. 2 sin⁻¹ y = √(1-x²)+ sin⁻¹ x+ c

C. 2 sin⁻¹ y = x√(1-x²)+ sin⁻¹ x + c

D. 2 sin⁻¹ y = x√(1-x²)+ cos⁻¹ x + c

Q. 103 The differential equation of the family of circles passing through the origin and having centres on the x-axis is

A. 2xy dy/dx = x²-y²

B. 2xy dy/dx = y²-x²

C. 2xy dy/dx = x²+y²

D. 2xy dy/dx+x²+y²=0

Q. 104 The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a,0) where a > 0, are respectively

A. 1,1

B. 2,1

C. 1,2

D. 2,2

Q. 105 f(xy) = f(x) + f(y) is true for all

A. polynomial functions f

B. trigonometric functions f

C. exponential functions f

D. logarithmic functions f

Q. 106 Three digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that product is odd?

A. 2/3

B. 7/48

C. 5/42

D. 5/108

Q. 107 Two events A and B are such that P(not B) = 0.8, P(A U B) = 0.5 and p(A/B)=0.4. Then P(A) is equal to

A. 0.28

B. 0.32

C. 0.38

D. none of the above

Q. 108 If mean and variance of a Binomial variate X are 2 and 1 respectively , then the probability that X takes a value greater than 1 is

A. 2/3

B. 4/5

C. 7/8

D. 11/16

Q. 109 Seven unbiased coins are tossed 128 times . In how many throws would you find at least three heads?

A. 99

B. 102

C. 103

D. 104

Q. 110 A coin is tossed five times. What is the probability that heads are observed more than three times?

A. 3/16

B. 5/16

C. 1/2

D. 3/32

Q. 111 The geometric mean of the observations x1,x2,x3……… xn is G1. The geometric mean of the observations y1,y2,y3 ….. yn is G2 . The geometric mean of observations is x1/y1 , x2/y2 , x3/y3………….. xn/yn is

A. G1G2

B. ln(G1G2)

C. G1/G2

D. ln(G1/G2)

Q. 112 the arithmetic mean of 1,8,27,64 upto n terms is given by

A. n(n+1)/2

B. n(n+1)²/2

C. n(n+1)²/4

D. n²(n+1)²/4

Q. 113 An unbiased coin is tossed until the first head appears or until four tosses are completed, whichever happens earlier. Which of the following statements is / are correct?

1. The probability that no head is observed is 1/16.

2. The probability that the experiment ends with three tosses is 1/8.

Select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 114 If x∈[ 0 , 5 ] , then what is the probability that x² – 3x + 2 ≥0 ?

A. 4/5

B. 1/5

C. 2/5

D. 3/5

Q. 115 A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black is

A. 5/24

B. 13/24

C. 1/4

D. 2/3

Q. 116 A problem in statistics is given to three students A B and C whose chances of solving it independently are 1/2 , 1/3 and 1/4 respectively . The probability that the problem will be solved is

A. 1/12

B. 11/12

C. 1/2

D. 3/4

Q. 117 An insurance company insured 2000 scooter drivers , 4000 car drivers and 5000 truck drivers. The probabilities of an accident involving a scooter driver , a car driver and a truck driver are 0.01,0.03 and 0.15 respectively. One of the insured persons meets with an accident. The probability that the person is a scooter driver is

A. 1/52

B. 3/52

C. 15/52

D. 19/52

Q. 118 A coin is tossed 5 times . The probability that tail appears an odd number of times is

A. 1/2

B. 1/3

C. 2/5

D. 1/5

Q. 119 The regression coefficients of a bivariate distribution are -0.64 and -0.36. Then the correlation coefficient of the distribution is

A. 0.48

B. -0.48

C. 0.50

D. -0.50

Q. 120 What is the probability that the sum of any two different single digit natural numbers is a prime number?

A. 5/27

B. 7/18

C. 1/3

D. none of the above

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

NDA/NA(I) Exam 2015 Mathematics Previous Year Paper

NDA/NA(I) Exam 2015 Mathematics

Q. 1 Let X be the set of all persons living in a city, Persons x, in y in X are said to be related as x < y if y is at least 5 years older than x. Which one of the following is correct?

A. The relation is an equivalence relation on X

B. The relation is transitive but neither reflexive nor symmetric

C. The relation is reflexive but neither transitive nor symmetric

D. The relation is symmetric but neither transitive not reflexive

Q. 2 Which one of the following matrices is an elementary matrix?

A. (a)

B. (b)

C. (c)

D. (d)

Q. 3 Consider the following statements in respect of the given equation : (x^2 + 2)^2 + 8 x^2 = 6 x ( x^2 + 2) . Given : 1.) All the roots of the equation are complex. 2.) The sum of all the roots of the equation is 6. 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. 4 In solving a problem that reduces to a quadratic equation, one student makes a mistake in the constant term and obtains 8 and 2 for roots. Another student makes a mistake only in the coefficient of first-degree term and finds -9 and -1 for roots. The correct equation is

A. x^2 – 10 x + 9 = 0

B. x^2 + 10 x + 9 = 0

C. x^2 – 10 x + 16 = 0

D. x^2 – 8 x -9 = 0

Q. 5 What is A + 3 A^(-1) equal to?

A. 3I

B. 5I

C. 7I

D. None of the above

Q. 6 In a class of 60 students, 45 students like music, 50 students like dancing, 5 students like neither. Then the number of students in the class who like both music and dancing is

A. 35

B. 40

C. 50

D. 55

Q. 7 If log [base 10]( 2 ), log [base 10]( 2^x – 1 ) and log [base 10]( 2^x + 3 ) are three consecutive terms of an AP, then the value of x is

A. 1

B. log [base 5]( 2 )

C. log [base 2]( 5 )

D. log [base 10] (5)

Q. 8 The Matrix A is

A. symmetric

B. skew – symmetric

C. Hermitian

D. skew – Hermitian

Q. 9 Let Z be the set of integers and aRb, where a, b ∈ Z if and only if ( a – b ) is divisible by 5.

Consider the following statements :

1. The relation R partitions Z into five equivalent classes.

2. Any two equivalent classes are either equal or disjoint

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 not 2

Q. 10 If z = -2( 1 + 2i ) / 3 + i where i = √-1, then the argument θ( -Π < θ ≤ Π ) of z is

A. 3Π/4

B. Π/4

C. 5Π/6

D. -3Π/4

Q. 11 If m and n are the roots of the equation ( x + p )( x + q ) – k = 0, then the roots of the equation ( x – m )( x – n ) + k = 0 are

A. p and q

B. 1/p and 1/q

C. -p and -q

D. p + q and p – q

Q. 12 What is the sum of the series 0.5 + 0.55 + 0.555 + … to n terms?

A. 5/9[ n – ( 2/9)( 1 – 1/(10^n) ) ]

B. 1/9[ 5 – ( 2/9)( 1 – 1/(10^n) ) ]

C. 1/9[ n – ( 5/9)( 1 – 1/(10^n) ) ]

D. 5/9[ n – ( 1/9)( 1 – 1/(10^n) ) ]

Q. 13 If 1, ω, ω^2 are the cube roots of unity, then the value of ( 1 + ω )( 1 + ω^2 )( 1 + ω^4 )( 1 + ω^8 ) is

A. -1

B. 0

C. 1

D. 2

Q. 14 Let A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Then the number of subsets of A containing exactly two elements is

A. 20

B. 40

C. 45

D. 90

Q. 15 What is the square root of i, where i = √-1

A. ( 1 + i )/2

B. ( 1 – i )/2

C. ( 1 + i )/√2

D. None of the above

Q. 16 The decimal number (127.25)(decimal) , when converted to binary number, takes the form

A. ( 1 1 1 1 1 1 1 . 1 1)(binary)

B. ( 1 1 1 1 1 1 0 . 0 1)(binary)

C. ( 1 1 1 0 1 1 1 . 1 1)(binary)

D. ( 1 1 1 1 1 1 1 .0 1)(binary)

Q. 17 Consider the following in respect of two non-singular matrices A and B of same order :

1. det( A + B ) = det A + det B

2. ( A + B )^(-1) = A^(-1) + B^(-1) . Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 18 If X, A and B satisfy the equation AX = B, then the matrix A is equal to:

A. (a)

B. (b)

C. (c)

D. (d)

Q. 19 The equation given in figure equals to

A. ⁿ⁺²C₁

B. ⁿ⁺²Cₙ

C. ⁿ⁺³Cₙ

D. ⁿ⁺²Cₙ₋₁

Q. 20 How many words can be formed using all the letters of the word ‘NATION’ so that all the three vowels should never come together?

A. 354

B. 348

C. 288

D. None of the above

Q. 21 ( x^3 – 1 ) can be factorized as : ( where ω is one of the cube roots of unity. )

A. ( x- 1 )( x – ω )( x + ω^2 )

B. ( x- 1 )( x – ω )( x – ω^2 )

C. ( x- 1 )( x + ω )( x + ω^2 )

D. ( x- 1 )( x + ω )( x – ω^2 )

Q. 22 What is { [sin Π/6 + i( 1 – cos Π/6 )] / [sin Π/6 – i( 1 – cos Π/6 )] }^3 where i = √-1, equal to ?

A. 1

B. -1

C. i

D. -i

Q. 23 For given A, B and C matrices. If AB = C, then what is A² equal to?

A. (a)

B. (b)

C. (c)

D. (d)

Q. 24 The value of A is

A. x + y

B. x – y

C. xy

D. 1 + x + y

Q. 25 If A = { x : x is a multiple of 3 } and B = { x : x is a multiple of 4 } and C = { x : x is multiple of 12 }, then which one of the following is a null set?

A. ( A \ B ) ∪ C

B. ( A \ B ) \ C

C. ( A ∩ B ) ∩ C

D. ( A ∩ B ) \ C

Q. 26 If ( 1 1 1 0 1 0 1 1)(binary) is converted to decimal system, then the resulting number is

A. 235

B. 175

C. 160

D. 126

Q. 27 What is the real part of (sin x + i cos x )^3 where i = √-1?

A. -cos 3x

B. -sin 3x

C. sin 3x

D. cos 3x

Q. 28 then E(α) E(β) is equal to

A. E(αβ)

B. E(α – β)

C. E(α + β)

D. – E(α + β)

Q. 29 Let A = { x, y, z} and B = { p, q, r, s}. What is the number of distinct relations from B to A?

A. 4096

B. 4094

C. 128

D. 126

Q. 30 If 2p + 3q = 18 and 4p² + 4pq – 3q² – 36 = 0. Then what is (2p + q) equal to?

A. 6

B. 7

C. 10

D. 20

Q. 31 Let θ be a positive angle. If the number of degrees in θ is divided by the number of radians in θ, then an irrational number 180 / Π results. If the number of degrees in θ is multiplied by the number of radians in θ, then an irrational number 125π / 9 results. The angle θ must be equal to

A. 30°

B. 45°

C. 50°

D. 60°

Q. 32 In a triangle ABC, a = (1 + √3 ) cm, b = 2 cm and angle C = 60°. Then the other two angles are

A. 45° and 75°

B. 30° and 90°

C. 105° and 15°

D. 100° and 20°

Q. 33 Let α be the root of the equation 25cos² θ + 5cos θ – 12 = C, where Π/2 < α < Π. What is tan α equal to?

A. -3 / 4

B. 3 / 4

C. – 4 / 3

D. – 4 / 5

Q. 34 Let α be the root of the equation 25cos² θ + 5cos θ – 12 = C, where Π/2 < α < Π. What is sin 2α equal to?

A. 24 / 25

B. -24 / 25

C. -5 / 12

D. -21 / 25

Q. 35 The angle of elevation of the top of a tower from a point of 20 m away from its base is 45°. What is the height of the tower?

A. 10 m

B. 20 m

C. 30 m

D. 40 m

Q. 36 The equation tan^(-1)( 1 + x ) + tan^(-1)( 1 – x ) = Π/2 is satisfied by

A. x = 1

B. x = -1

C. x = 0

D. x = 1/2

Q. 37 The angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances 49 m and 36 m are 43° and 47° respectively. What is the height of the tower?

A. 40 m

B. 43 m

C. 45 m

D. 47 m

Q. 38 ( 1 – sin A + cos A )² is equal to

A. 2( 1 – cos A )( 1 + sin A )

B. 2( 1 – sin A )( 1 + cos A )

C. 2( 1 – cos A )( 1 – sin A )

D. None of the above

Q. 39 What is cos θ/( 1 + tanθ ) + sinθ/( 1 – cotθ ) equal to ?

A. sinθ – cosθ

B. sinθ + cosθ

C. 2sinθ

D. 2cosθ

Q. 40 Consider x = 4 tan^(-1) ( 1 / 5 ), y = tan^(-1) ( 1 / 70 ) and z = tan^(-1) ( 1/99 ). What is x equal to?

A. tan^(-1) ( 60/119 )

B. tan^(-1) ( 120/119 )

C. tan^(-1) ( 90/169 )

D. tan^(-1) ( 170/169 )

Q. 41 Consider x = 4 tan^(-1) ( 1 / 5 ), y = tan^(-1) ( 1 / 70 ) and z = tan^(-1) ( 1/99 ). What is x – y equal to?

A. tan^(-1) ( 828/845 )

B. tan^(-1) ( 8287/8450 )

C. tan^(-1) ( 8281/8450 )

D. tan^(-1) ( 8287/8471 )

Q. 42 Consider x = 4 tan^(-1) ( 1 / 5 ), y = tan^(-1) ( 1 / 70 ) and z = tan^(-1) ( 1/99 ). What is x – y – z equal to ?

A. Π/2

B. Π/3

C. Π/6

D. Π/4

Q. 43 Consider the triangle ABC with vertices A(-2, 3), B(2, 1) and C(1, 2). What is the circumcentre of the triangle ABC?

A. ( -2, -2)

B. ( 2, 2)

C. ( -2, 2)

D. ( 2, -2)

Q. 44 Consider the triangle ABC with vertices A(-2, 3), B(2, 1) and C(1, 2). What is the centroid of the triangle ABC?

A. ( 1/3, 1 )

B. ( 1/3, 2 )

C. ( 1, 2/3 )

D. ( 1/2, 3 )

Q. 45 Consider the triangle ABC with vertices A(-2, 3), B(2, 1) and C(1, 2). What is foot of the altitude from the vertex A of the triangle ABC?

A. ( 1, 4)

B. ( -1, 3)

C. ( -2, 4)

D. ( – 1, 4)

Q. 46 The point on the parabola y^2 = 4ax nearest to the focus has its abscissa

A. x = 0

B. x = a

C. x = a/2

D. x = 2a

Q. 47 A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is

A. 3/4

B. 4/3

C. 1/3

D. 3

Q. 48 The hyperbola (x / a)^2 – (y / b)^2 = 1 passes through the point ( 3√5, 1 ) and the length of its latus rectum is 4/3 units. The length of the conjugate axis is

A. 2 units

B. 3 units

C. 4 units

D. 5 units

Q. 49 The perpendicular distance between the straight lines 6x + 8y + 15 = 0 and 3x + 4y + 9 = 0 is

A. 3/2 unit

B. 3/10 unit

C. 3/4 unit

D. 2/7 unit

Q. 50 The area of a triangle, whose vertices are (3, 4), (5, 2) and the point of intersection of the lines x = a and y = 5, is 3 square units. What is the value of a?

A. 2

B. 3

C. 4

D. 5

Q. 51 The length of perpendicular from the origin to a line is 5 units and the line makes an angle 120° with the positive direction of x-axis. The equation of the line is

A. x + √3y = 5

B. √3 + y = 10

C. √3x – y = 10

D. None of the above

Q. 52 The equation of the line joining the origin to the point of intersection of the lines x/a + y/b = 1 and x/b + y/a = 1 is

A. x – y = 0

B. x + y = 0

C. x = 0

D. y= 0

Q. 53 The projections of a directed line segment on the coordinate axes are 12, 4, 3 respectively. What is the length of the line segment?

A. 19 units

B. 17 units

C. 15 units

D. 13 units

Q. 54 The projections of a directed line segment on the coordinate axes are 12, 4, 3 respectively. What are the direction cosines of the line segment?

A. < 12/13, 4/13, 3/13 >

B. < 12/13, – 4/13, 3/13 >

C. < 12/13, -4/13, -3/13 >

D. < -12/13, -4/13, 3/13 >

Q. 55 From the point P(3, -1, 11), a perpendicular is drawn on the line L given by the equation x/2 = (y – 2)/3 = (z – 3)/4. Let Q be the foot of the perpendicular. What are the direction ratios of the line segment PQ?

A. < 1, 6, 4 >

B. < -1, 6, -4 >

C. < -1, -6, 4 >

D. < 1, -6, 4 >

Q. 56 From the point P(3, -1, 11), a perpendicular is drawn on the line L given by the equation x/2 = (y – 2)/3 = (z – 3)/4. Let Q be the foot of the perpendicular.What is the length of the line segment PQ?

A. √47 units

B. 7 units

C. √53 units

D. 8 units

Q. 57 A triangular plane ABC with the centroid (1, 2, 3) cuts the coordinate axes at A,B,C respectively. What are the intercepts made by the plane ABC on the axes?

A. 3,, 6, 9

B. 1, 2, 3

C. 1, 4, 9

D. 2, 4, 6

Q. 58 A triangular plane ABC with the centroid (1, 2, 3) cuts the coordinate axes at A,B,C respectively. What is the equation of the plane ABC?

A. x + 2y + 3z = 1

B. 3x + 2y + z = 3

C. 2x + 3y + 6z = 18

D. 6x + 3y + 2z = 18

Q. 59 A point P(1, 2, 3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes. What is the length of one of the diagonals of the cuboid?

A. √10 units

B. √14 units

C. 4 units

D. 5 units

Q. 60 A point P(1, 2, 3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes. What is the equation of the plane passing through P(1, 2, 3) and parallel to xy-plane?

A. x + y = 3

B. x – y = -1

C. z = 3

D. x + 2y + 3z = 14

Q. 61 If G(x) = √(25 – x²) , then what is lim x→1 (G(x) – G(1)) / (x – 1) equal to?

A. – 1/ 2√6

B. 1 / 5

C. – 1 / √6

D. 1 / √6

Q. 62 Consider the following statements: 1. y = ( e^x + e^(-x))/ 2 is an increasing function on [0, ∞). 2. y = ( e^x – e^(-x))/ 2 is an increasing function on (-∞, ∞). Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. neither 1 nor 2

Q. 63 For each non-zero real number x, let f(x) = x / |x|. The range of f is

A. a null set

B. a set consisting of only one element

C. a set consisting of two elements

D. a set consisting of infinitely many elements

Q. 64 Consider the following statements: 1. f(x) = [ x ], where [.] is the greatest integer function, is discontinuous at x = n, there n ∈ Z. 2. f(x) = cot x is discontinuous at x = n.Π, where n ∈ Z. 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. 65 What is the derivative of y with respect to tan^(-1)x?

A. 0

B. 1/2

C. 1

D. x

Q. 66 If f(x) = loge( (1 + x)/(1 – x) ), g(x) = (3x + x^3)/(1 + 3x^2) and g∘f(t) = g( f(t) ), then what is g∘f( (e – 1)/(e + 1)) equal to

A. 2

B. 1

C. 0

D. 1/2

Q. 67 Given a function f(x) = -1 if x ≤ 0, ax + b if 0 < x < 1; 1 if x ≥ 1 where a, b are constants. The function is continuous everywhere. What is the value of a?

A. -1

B. 0

C. 1

D. 2

Q. 68 Given a function f(x) = -1 if x ≤ 0, ax + b if 0 < x < 1; 1 if x ≥ 1 where a, b are constants. The function is continuous everywhere. What is the value of b?

A. -1

B. 1

C. 0

D. 2

Q. 69 Consider the following functions : 1. f(x) = x^3, x ∈ ℝ. 2. f(x) = sin x, 0 < x < 2Π. 3. f(x) = e^x , x ∈ ℝ. Which of the above functions have inverse defined on their ranges

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 70 The integral ∫( 1 /( acosx + bsinx) )dx is of the form (1 / r) [ tan( x+a/ 2 ) ].. what is r equal to?

A. a^2 + b^2

B. √( a^2 + b^2 )

C. a + b

D. √( a^2 – b^2 )

Q. 71 The integral ∫( 1 /( acosx + bsinx) )dx is of the form (1 / r) [ tan( x+a/ 2 ) ]. What is a equal to?

A. tan^(-1) ( a / b )

B. tan^(-1) ( b / a )

C. tan^(-1) ( a + b / a – b )

D. tan^(-1) ( a – b / a + b )

Q. 72 Consider the function f(x) = ( x^2 – 1)/ ( x^2 + 1 ), where x ∈ ℝ. At what value of x does f(x) attain minimum value?

A. -1

B. 0

C. 1

D. 2

Q. 73 Consider the function f(x) = ( x^2 – 1)/ ( x^2 + 1 ), where x ∈ ℝ. What is the minimum value of f(x)?

A. 0

B. 1/2

C. -1

D. 2

Q. 74 Consider the function, f(x) = { acosx / Π – 2x if x ≠ Π/2; 3 if x = Π/2 } which is continuous at x = Π/2, where ‘a’ is a constant. What is the value of a ?

A. 6

B. 3

C. 2

D. 1

Q. 75 Consider the function, f(x) = { acosx / Π – 2x if x ≠ Π/2; 3 if x = Π/2 } which is continuous at x = Π/2, where ‘a’ is a constant. What is lim x→0 f(x) equal to?

A. 0

B. 3

C. 3/Π

D. 6/Π

Q. 76 Consider the line x = √(3y) and the circle x^2 + y^2 = 4. What is the area of the region in the first quadrant enclosed by the x-axis, the line x = √3 and the circle?

A. Π/3 – √3/2

B. Π/2 – √3/2

C. Π/3 – 1/2

D. None of the above

Q. 77 Consider the line x = √(3y) and the circle x^2 + y^2 = 4. What is the area of the region in the first quadrant enclosed by the x-axis, the line x = √3y and the circle?

A. Π/3

B. Π/6

C. Π/3 = √3/2

D. None of the above

Q. 78 Consider the curves y = sin x and y = cos x. What is the area of the region bounded by the above two curves and the lines x = 0 and x = Π/4 ?

A. √2 – 1

B. √2 + 1

C. √2

D. 2

Q. 79 Consider the curves y = sin x and y = cos x. What is the area of the region bounded by the above two curves and the lines x = Π/4 and x = Π/2 ?

A. √2 – 1

B. √2 + 1

C. 2√2

D. 2

Q. 80 Consider the function f( x ) = 0.75 x^4 – x^3 – 9x^2 + 7. What is the maximum value of the function?

A. 1

B. 3

C. 7

D. 9

Q. 81 Consider the function f( x ) = 0.75 x^4 – x^3 – 9x^2 + 7. Consider the following statements :
(1) The function attains local minima at x = -2 and x = 3.

(2) The function increases in the interval (-2, 0). Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. neither 1 nor 2

Q. 82 Consider the parametric equation x = a(1 – t²) / (1 – t²), y = 2at / (1 – t²). What does the equation represent?

A. It represents a circle of diameter a

B. It represents a circle of radius a

C. it represents a parabola

D. None of the above

Q. 83 Consider the parametric equation x = a(1 – t²) / (1 – t²), y = 2at / (1 – t²). What is dy/dx equal to?

A. y/x

B. – y/x

C. x/y

D. – x/y

Q. 84 Consider the parametric equation x = a(1 – t²) / (1 – t²), y = 2at / (1 – t²). What is d²y / dx² equal to?

A. (a / y)^2

B. (a / x)^2

C. – (a / y)^2

D. – a^2 / y^3

Q. 85 Consider the following statements : 1. The general solution of dy/dx = f(x) + x is of the form y = g(x) + c, where c is an arbitrary constant. 2. The degree of (fy/dx)^2 = f(x) is 2. Which fo the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 86 What is ∫( 1 / √( x^2 + a^2 ) ) equal to? ( where c is the constant of integration. )

A. ln| ( x + √(x^2 + a^2) )/ a | + c

B. ln| ( x – √(x^2 + a^2) )/ a | + c

C. ln| ( x^2 + √(x^2 + a^2) )/ a | + c

D. None of the above

Q. 87 Consider the integral Im, where m is a positive integer. What is I1 equal to?

A. 0

B. 1/2

C. 1

D. 2

Q. 88 Consider the integral I(m), where m is a positive integer. What is I2 + I3 equal to?

A. 4

B. 2

C. 1

D. 0

Q. 89 Consider the integral I(m), where m is a positive integer. What is Im equal to?

A. 0

B. 1

C. m

D. 2m

Q. 90 Consider the integral I(m), where m is a positive integer. Consider the following : 1.) I( m ) – I( m – 1) is equal to 0. 2.) I(2m) > Im. Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 91 Given that d/dx( ( 1 + x^2 + s^4 )/( 1 + x + x^2 ) ) = Ax + B. What sis the value of A?

A. -1

B. 1

C. 2

D. 4

Q. 92 Given that d/dx( ( 1 + x² + s⁴ )/( 1 + x + x² ) ) = Ax + B. What is the value of B?

A. -1

B. 1

C. 2

D. 4

Q. 93 Given that lim x→∞( (2 + x^2)/(1 + x) – Ax – B ) = 3. What is value of A?

A. -1

B. 1

C. 2

D. 3

Q. 94 Given that lim x→∞( (2 + x^2)/(1 + x) – Ax – B ) = 3. What is the value of B?

A. -1

B. 3

C. -4

D. -3

Q. 95 What is the solution of the differential equation ydx – xdy / y^2 = 0? ( where c is an arbitrary constant )

A. xy = c

B. y = cx

C. x + y = c

D. x – y = c

Q. 96 What is the solution of the differential equation sin(dy/dx) – a = 0 ? ( where c is an arbitrary constant )

A. y = x sin^(-1) a + c

B. x = y sin^(-1) a + c

C. y = x + x sin^(-1) a + c

D. y = sin^(-1) a + c

Q. 97 What is the solution of the differential equation dx/dy + x/y – y^2 = 0? ( where c is an arbitrary constant )

A. xy = x^4 + c

B. xy = y^4 + c

C. 4 xy = y^4 + c

D. 3xy = y^3 + c

Q. 98 What is ∫( (x e^x)/(x + 1)^2 )dx equal to? ( where c is the constant of integration. )

A. (x + 1)^2 e^x + c

B. (x + 1) e^x + c

C. e^x/(x + 1) + c

D. e^x/(x + 1)^2 + c

Q. 99 The adjacent sides AB and Ac of a triangle ABC are represented by the vectors -2 i^ + 3j^ + 2k^ and -4i^ + 5j^ +2k^ respectively. The area of the triangle ABC is

A. 6 square units

B. 5 square units

C. 4 square units

D. 3 square units

Q. 100 A force F ⃗ = 3i^ + 4 j^ – 3k^ is applied at the point P, whose position vector is r ⃗ = 2i^ – 2j^ – 3k^. What is the magnitude of the moment of the force about the origin?

A. 23 units

B. 19 units

C. 18 units

D. 21 units

Q. 101 Given that the vectors α ⃗ and β ⃗ are non-collinear. The values of x and y for which u ⃗ – v ⃗ = w ⃗ holds true if u ⃗ = 2xα ⃗ + yβ ⃗, v ⃗ = 2yα ⃗ + 3xβ ⃗ and w ⃗ = 2α ⃗ – 5β ⃗, are

A. x = 2, y = 1

B. x = 1, y = 2

C. x = -2, y = 1

D. x = -2, y = -1

Q. 102 If |a ⃗| = 7, |b ⃗| = 11 and | a ⃗ + b ⃗ | = 10√3, then | a ⃗ + b ⃗ | is equal to

A. 40

B. 10

C. 4√10

D. 2√10

Q. 103 Let α, β, γ be distinct real numbers. The points with position vectors αi^ + βj^ + γk^, βi^ + γj^ + αk^ and γi^ + αj^ + βk^

A. are collinear

B. form an equilateral triangle

C. form a scalene triangle

D. form a right-angled triangle

Q. 104 If a ⃗ + b ⃗ + c ⃗ = 0 ⃗, then which of the following is/are correct? 1. a ⃗,b ⃗,c ⃗ are coplanar 2. a ⃗ × b ⃗ = b ⃗ × c ⃗ = c ⃗ × a ⃗. 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. 105 If |a ⃗ + b ⃗ | = |a ⃗ – b ⃗ |, then which one of the following is correct?

A. a ⃗ = λb ⃗ for some scalar λ

B. a ⃗ is parallel to b ⃗

C. a ⃗ is perpendicular to b ⃗

D. a ⃗ = b ⃗ = 0 ⃗

Q. 106 The mean and the variance of 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectively

A. 8 and 20

B. 8 and 4

C. 8 and 8

D. 80 and 40

Q. 107 Which one of the following measure of central tendency is used in construction of index numbers?

A. Harmonic mean

B. Geometric mean

C. Median

D. Mode

Q. 108 The correlation coefficient between two variables X and Y is found to be 0.6. All the observations on X and Y are transformed using the transformations U = 2 – 3X and V = 4Y + 1. The correlation coefficient between the transformed variables U and V will be

A. -0.5

B. +0.5

C. -0.6

D. +0.6

Q. 109 Which of the following statements is/are correct in respect of regression coefficients?

1.) It measures the degree of linear relationship between two variables.

2.) It gives the value by which one variable changes for a unit change in the other variable. 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. 110 A set of annual numerical data, comparable over the years, is given for the last 12 years. Consider the following statements: 1.The data is best represented by a broken line graph, each corner ( turning point ) representing the data of one year. 2. Such a graph depicts the chronological change and also enables one to make a short-term forecast/ 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. 111 Two men hit a target with probabilities 1/2 and 1/3 respectively. What is the probability that exactly one of them hits the target?

A. 1/2

B. 1/3

C. 1/6

D. 2/3

Q. 112 Two similar boxes B(i) where ( i= 1, 2) contain ( i + 1) red and ( 5 – i -1) black balls. One box is chosen at random and two balls are drawn randomly. What is the probability that both the balls are of different colours?

A. 1/2

B. 3/10

C. 2/5

D. 3/5

Q. 113 In an examination. The probability of a candidate solving a question is 1/2. Out of given 5 question in the examination, that is the probability that the candidate was able to solve at least 2 questions?

A. 1/64

B. 3/16

C. 1/2

D. 13/16

Q. 114 If A ⊆B, then which one of the following is not correct?

A. P( A ∩ B’ ) = 0

B. P( A | B ) = P(A)/P(B)

C. P( B | A ) = P(B)/P(A)

D. P( A | (A ∪ B) ) = P(A)/P(B)

Q. 115 The mean and the variance in a binomial distribution are found to be 2 and 1 respectively. The probability P( X = 0) is

A. 1/2

B. 1/4

C. 1/8

D. 1/16

Q. 116 The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is

A. 28

B. 30

C. 35

D. 38

Q. 117 If A and B are two events such that P(A∪B) = 3/4, P(A∩B) = 1/4 and P(A’) = 2/3, then what is P(B) equal to?

A. 1/3

B. 2/3

C. 1/8

D. 2/9

Q. 118 The ‘less than’ ogive curve and the ‘more than’ ogive curve intersect at

A. median

B. mode

C. arithmetic mean

D. None of the above

Q. 119 In throwing of two dice, the number of exhaustive events that ‘5’ will never appear on any one of the dice is

A. 5

B. 18

C. 25

D. 36

Q. 120 Two cards are drawn successively without replacement from a well-shuffled pack of 52 cards. The probability of drawing two aces is

A. 1/26

B. 1/221

C. 4/223

D. 1/13

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

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

NDA/NA(II) Exam 2015 General Ability Test

Questions: 1 – 10

Look at the quoted part in each sentence. Select the most appropriate option from the three possible substitution for the quoted part. If none of the substitutions improves the sentence, select the ‘No improvement’.

Q. 1 “Had she been hungry”, she would have devoured the whole lot of it

A. Unless she had been hungry

B. However she had been hungry

C. As if she had been hungry

D. No improvement

Q. 2 “Until you don’t finish”the work, you won’t be given leave.

A. Until you must finish

B. Until finishing

C. Until you finish

D. No improvement

Q. 3 The names of the defaulters have been “cut off” the register.

A. cut out

B. struck out

C. struck off

D. No improvement

Q. 4 This is a matter “I’d rather not talk about”.

A. of which I’d rather not talk about

B. I rather not talk about

C. than I’d rather not talk about

D. No improvement

Q. 5 Only when you left “I did sleep”.

A. I slept

B. did I sleep

C. had I sleep

D. No improvement

Q. 6 I will be happy if you “will buy” me apples.

A. buy

B. bought

C. will be buying

D. No improvement

Q. 7 After I “saved” some money, I shall go abroad.

A. shall save

B. should have saved

C. have saved

D. No improvement

Q. 8 Can you “arrange the car” to be ready this evening?

A. arrange with the car

B. arrange for the car

C. arrange that the car

D. No improvement

Q. 9 Hardly “had he reached” home when the telephone rang.

A. he had reached

B. did he reach

C. he reached

D. No improvement

Q. 10 He is likely to win the elections “by the sweeping majority”.

A. with the sweeping majority

B. in a sweeping majority

C. by a sweeping majority

D. No improvement

Questions: 11 – 16

Each of the following items 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). Select the correct sequence.

Q. 11 His uncle

P. for success in life.

Q. always advised his son,

R. who was a self-made man

S. to depend on his own efforts

The proper sequence should be:

A. SQPR

B. RQSP

C. PRSQ

D. QPSR

Q. 12 The doctor

P. did not like the behavior of the patients

Q. who was very competent in his profession

R. when they talked at length

S. about their problems

The proper sequence should be:

A. RPSQ

B. SRPQ

C. QPRS

D. PRQS

Q. 13 P. from leadership in culture

Q. in military situations and in face-to-face small groups

R. leadership has wide range of expressions

S. to leadership in politics

The proper sequence should be:

A. RSQP

B. PQRS

C. RPSQ

D. SQRP

Q. 14 He sat

P. glancing occasionally

Q. peering through the window

R. at the figure of the old woman

S. until he was chilled with the cold.

The proper sequence should be:

A. PSRQ

B. QRPS

C. SPRQ

D. PRSQ

Q. 15 After the earthquake tremors, the TV showed a haggard man

P. shaking his fist at the sky

Q. clambering over the ruins

R. and collapsing with a howl of revolt

S. of his house and factory

The proper sequence should be:

A. SRQP

B. QSPR

C. PQRS

D. RPSQ

Q. 16 Everyone

P. acknowledges

Q. when he considers the case calmly

R. who knows you

S. that you have been wronged

The proper sequence should be:

A. RSQP

B. RPQS

C. PQRS

D. QRPS

Questions: 17 – 21

Each sentence has a quoted part followed by four words. Select the word that is nearest in meaning to the quotes word.

Q. 17 Many of his acquaintances avoid him because he is so “garrulous”.

A. unreasonable

B. talkative

C. quarrelsome

D. proud

Q. 18 He bore the pain with great “fortitude”.

A. resignation

B. defiance

C. indifference

D. forbearance

Q. 19 He gave his “tacit” approval to the proposition.

A. full

B. loud

C. clean

D. implied

Q. 20 In spite of hard work, the farmers could only get a “meagre” yield.

A. satisfactory

B. scanty

C. plenty

D. normal

Q. 21 He was “exhilarated” at the outcome of the election results.

A. satisfied

B. surprised

C. disappointed

D. overjoyed

Questions: 22 – 26

Each sentence has a quoted word followed by four word. Select the word that is opposite in meaning to the quoted word.

Q. 22 He “concealed” his thoughts very cleverly.

A. emphasized

B. expressed

C. affirmed

D. revealed

Q. 23 The proposal was “denounced” by one and all.

A. renounced

B. recommended

C. announced

D. commended

Q. 24 She was “skeptical” about the safety of the new drug.

A. doubtful

B. certain

C. hopeful

D. sanguine

Q. 25 The answers to the question were “coherent”.

A. relaxed

B. loose

C. consistent

D. disconnected

Q. 26 It was no “altruistic” motive that prompted him to help her.

A. selfish

B. inhuman

C. brutal

D. wicked

Questions: 27 – 41

Each of the following sentences in this section has a blank space and four words or group or words given after the sentence. Select the most appropriate word or groups of words.

Q. 27 Man has won his dominant position on this planet by his ____________ of technology

A. command

B. emphasis

C. belief

D. stress

Q. 28 The day was extremely hot and, in no time, my back was drenched with _____.

A. prickly heat

B. perspiration

C. sores

D. fatigue

Q. 29 The Government is encouraging village uplifting __________ in the country.

A. programmes

B. designs

C. talks

D. propaganda

Q. 30 Satish was endowed ____________ a natural talent for music.

A. in

B. by

C. for

D. with

Q. 31 Mr. Ghosh is very happy ______________ his son’s excellent result.

A. for seeing

B. to see

C. by seeing

D. see

Q. 32 Sunlight filtering __________ the stained glass window created a mosaic of colours on the floor.

A. in

B. through

C. at

D. into

Q. 33 Are you feeling doubtful _____________ your decision?

A. about

B. upon

C. at

D. for

Q. 34 I want to study Geology now for I _________ Zoology for the last three years.

A. am studying

B. have been studying

C. had studied

D. had been studying

Q. 35 Increase in storage facilities has made it possible to store goods at places _____

to people all over the country.

A. safe

B. easy

C. proper

D. convenient

Q. 36 To say that we were surprised at the cleverness of the child is an understatement; we were really ___________.

A. annoyed

B. astounded

C. flattered

D. confused

Q. 37 In spite of the old woman’s repeated entreaties, he remained ____________.

A. ashamed

B. docile

C. indifferent

D. lethargic

Q. 38 There was __________ competition for electoral seats.

A. diligent

B. rapid

C. cut-throat

D. sparse

Q. 39 The cricket team _______________ mainly of State players.

A. composed

B. consist

C. made with

D. comprises

Q. 40 His love for money is the only __________ that drives him to work so hard.

A. programme

B. plan

C. reason

D. greed

Q. 41 According to ________ sources, the Chief Minister did not consult his Cabinet Members on this issue.

A. intelligent

B. simple

C. reliable

D. fundamental

Questions: 42 – 50

Each sentence has been divided into 3 parts – (a), (b) and (c). There is an error in any of the three part. Select the correct part. If there is no error, select “no error” .

Q. 42 (a) I am told / (b) John is ill / (c) since Monday. / (d) No error.

A. (a)

B. (b)

C. (c)

D. (d)

Q. 43 (a) I shall leave school / (b) as soon as / (c) I shall find a job. / (d) No error.

A. (a)

B. (b)

C. (c)

D. (d)

Q. 44 (a) He is a rich man / (b) he is owning / (c) a number of buildings in Bombay. / (d) No error.

A. (a)

B. (b)

C. (c)

D. (d)

Q. 45 (a) We were able to make it / (b) in spite of / (c) a bad weather. / (d) No error.

A. (a)

B. (b)

C. (c)

D. (d)

Q. 46 (a) Neither of the two letters of credit / (b) were useful / (c) when he needed it. / (d) No error.

A. (a)

B. (b)

C. (c)

D. (d)

Q. 47 (a) Little he realized / (b) that he wouldn’t live / (c) to see his grandson married. (d) No error.

A. (a)

B. (b)

C. (c)

D. (d)

Q. 48 (a) A difficult syllabus / (b) is supposed to hurt / (c) juvenile mind. / (d) No error.

A. (a)

B. (b)

C. (c)

D. (d)

Q. 49 (a) The voice of sanity and patriotism / (b) are important to dispel / (c) the prevailing confusion. / (d) No error.

A. (a)

B. (b)

C. (c)

D. (d)

Q. 50 (a) You were going to explain / (b) your late arrival, / (c) isn’t it? / (d) No error.

A. (a)

B. (b)

C. (c)

D. (d)

Q. 51 A brass ball is tied to a thin wire and swung so as to move uniformly in a horizontal circle.

Which of the following statements in this regard is/are true?

1. The ball moves with constant velocity.

2. The ball moves with constant speed.

3. The ball moves with constant acceleration.

4. The magnitude of the acceleration of the ball is constant.

Select the correct answer using the code given below:

A. 1 only

B. 1 and 3

C. 1, 2 and 4

D. 2 and 4 only

Q. 52 Two long wires each carrying a d.c. current in the same direction are placed close to each other. Which one of the following statements is correct?

A. The wires will attract each other.

B. The wires will repel each other.

C. There will be no force between the wires.

D. There will be a force between the wires only at the moment when the current is switched ON or OFF.

Q. 53 The first Indian Satellite, Aryabhatt, was launched in the year:

A. 1972

B. 1975

C. 1976

D. 1979

Q. 54 Which one of the following sea routes is the shortest from point to point?

A. Kolkata to Yangoon

B. Kolkata to Chennai

C. Chennai to Port Blair

D. Mumbai to Colombo

Q. 55 Which one of the following is not a Green House Gas?

A. Water vapours

B. Methane

C. Ozone

D. Carbon Monoxide

Q. 56 Muscle fatigue is due to the accumulation of:

A. Cholesterol

B. Lactic acid

C. Lipoic acid

D. Triglycerides

Q. 57 The absolute zero, i.e., temperature below which is not achievable, is about:

A. 0°C

B. -273 K

C. -273° C

D. -300° C

Q. 58 Lightning conductors are used to protect building from lightning strikes. Which of the following statements is /are are true about lightning conductors?

1. Lightning conductors create an electric field at its top so that lightning strikes it

preferentially.

2. Lightning conductors reduce the effect of the strike by uniformly distributing the charge (current) over the surface of the building.

3. Lightning conductors take all charge (current) to deep down in the earth.

4. Lightning conductors must be installed at a place taller than the building.

Select the correct answer using the code given below:

A. 1 and 2

B. 3 and 4 only

C. 1, 3 and 4

D. 4 only

Q. 59 Match List I with List II (given in figure and select the correct answer using the code given below:

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

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

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

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

Q. 60 Which one of the following is not a sea port?

A. Paradeep

B. Haldia

C. Diamond Harbour

D. Dhamra

Q. 61 Consider the following reaction:

CH₄(g) + H₂O(g) →(1270 K) CO(g) + 3H₂(g)

In this reaction given above, the mixture of CO and H₂ is:

A. natural gas

B. water gas

C. producer gas

D. industrial gas

Q. 62 Living things are grouped into subgroups like plant kingdom/ animal kingdom. Which one of the following is not correct for animal kingdom?

A. Cannot make their own food

B. Body contains cellulose

C. Do not have chlorophyll

D. Migrate from one place to another

Q. 63 The silvering in thermos flasks is done to avoid heat transfer by:

A. Convection

B. Conduction

C. Radiation

D. Both convection and conduction

Q. 64 The Manas National Park is situated in the State of:

A. Madhya Pradesh

B. Jharkhand

C. Assam

D. West Bengal

Q. 65 Addition of gypsum to cement:

A. reduces setting time of cement

B. produces very light colour cement

C. increases setting time of cement

D. shining surface is formed

Q. 66 In case of a compound microscope which of the following statements is/are correct?

1. The focal length of the eye piece is larger than the focal length of the objective.

2. The focal length of the eye piece is smaller than the focal length of the objective.

3. The image produced in a normal optical microscope is real.

4. The image produced in a normal optical microscope is virtual.

Select the correct answer using the code given below:

A. 1 only

B. 1 and 4

C. 2 and 3

D. 2 and 4

Q. 67 Which one of the following statements is not correct?

A. The radius of curvature of a concave mirror is twice its focal length

B. Power of a convex lens is negative and that of a concave lens is positive

C. The radius of curvature of a plane mirror is infinity

D. When a ray of light passes from an optically denser medium to an optically rarer medium, the angle of refraction is greater than the corresponding angle of incidence

Q. 68 Identify the place that is not an oil field:

A. Naharkatiya

B. Kalol

C. Ledo

D. Ankleshwar

Q. 69 Ammonia (NH₃) obtained from different sources always has same proportion of Nitrogen and Hydrogen . It proves the validity of law of:

A. Reciprocal proportion

B. Constant proportion

C. Multiple proportion

D. None of the above

Q. 70 Which one of the following statements is not correct?

A. If the velocity and acceleration have opposite sign, the object is slowing down

B. If the velocity is zero at as instant, the acceleration should also be zero at that instant

C. If the velocity is zero for a time interval; the acceleration is zero at any instant within the time interval

D. If the position and velocity have opposite sign, the object is moving towards the origin

Q. 71 The IST meridian 821/2°E passes through a number of States in India. Which one of the following sets of States is correct in this respect?

A. Uttarakhand, Uttar Pradesh, Chattisgarh and Andhra Pradesh

B. Uttar Pradesh, Jharkhand, Chattisgarh and Odisha

C. Uttarakhand, Uttar Pradesh, Madhya Pradesh and Chattisgarh

D. Uttar Pradesh, Odisha, Chattisgarh and Andhra Pradesh

Q. 72 Boric acid is ab acid because its molecule:

A. accepts OH⁻ from water releasing proton

B. combine with proton from water molecules

C. contains replaceable H^+ ion

D. gives up a proton

Q. 73 Who among the following discovered the antibiotic producing fungus from Penicillium genus?

A. Louis Pasteur

B. Sir Alexander Fleming

C. Stanley Prusiner

D. Robert Hooke

Q. 74 Three equal resistances when combined in series are equivalent to 90 ohm. Their equivalent resistance when combined in parallel will be:

A. 10 ohm

B. 30 ohm

C. 270 ohm

D. 810 ojm

Q. 75 The following figure represents the velocity-time graph of a moving car on a road. Which segment of the graph represents the retardation?

A. AB

B. BC

C. CD

D. None

Q. 76 Which one among the following places is not an iron-ore mining area?

A. Badampahar

B. Zawar

C. Bailadila

D. Anantpur

Q. 77 Match List I with List II (given in figure (1)) and select the correct answer using the code given below:

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

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

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

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

Q. 78 The main constituent of Vinegar is:

A. Acetic acid

B. Ascorbic acid

C. Citric acid

D. Tartaric acid

Q. 79 White Phosphorous glows in the dark due to:

A. amorphous character

B. slow oxidation

C. high ignition temperature

D. good conducting property of electricity

Q. 80 Which one of the following is not an example of eukaryotes organism?

A. Yeast

B. Bacteria

C. Plant

D. Human being

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

A. The Kelvin scale of temperature is called the Absolute scale

B. Visible light radiation has wavelength range of 400 – 700 nm

C. The capacity to do work is called power

D. The wavelength of Gamma rays is less than that of X-rays

Q. 82 A man is sitting in a train which is moving with a velocity of 60 km/hour. His speed with respect to the train is:

A. 10/3 m/s

B. 60 m/s

C. infinite

D. zero

Q. 83 Match List I with List II in figure and select the correct answer using the code given below:

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

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

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

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

Q. 84 The term ‘Regur’ is used to mean:

A. Laterite soil

B. Deltaic soil

C. Red soil

D. Black cotton soil

Q. 85 Graphite is a much better conductor of heat and electricity than diamond. This is due to the fact that each carbon atom is graphite:

A. undergoes sp² hybridisation and forms three sigma bonds with three neighbouring

carbon atoms

B. undergoes sp³ hybridisation

C. is tetrahedrally bonded

D. is free from van der Waals force

Q. 86 Which one of the following vitamins is synthesized in our own skin?

A. Vitamin A

B. Vitamin B

C. Vitamin C

D. Vitamin D

Q. 87 Which one of the following is the SI unit of the thermal conductivity of a material?

A. Wm⁻¹K⁻¹

B. Wm/K

C. Wm⁻¹/K⁻¹

D. Js⁻¹m⁻¹K

Q. 88 Which one of the following statements is not correct?

A. Conduction can occur easily in solids less easily in liquids but hardly at all in gases

B. Heat energy is carried by moving particles in a convection current

C. Heat energy is carried by electromagnetic waves in radiation

D. The temperature at which a solid changes into a liquid is called the boiling point

Q. 89 Which one of the following combinations of stalactites and stalagmites occurrences is correct?

A. Stalactites hang as icicles of different diameters and stalagmites hang from the floor of the caves

B. Stalactites hang as icicles of different diameters and stalagmites rise up from the floor of the caves

C. Stalactites rise up from the floor of the caves and stalagmites hang as icicles of

different diameters

D. Stalactites hang as icicles of different diameters and stalagmites also hang as icicles of different diameters

Q. 90 Which one of the following is the correct sequence about various levels of organisation of Biosphere?

A. Ecosystem – Biosphere – Community – Population

B. Population – Organism – Ecosystem – Biosphere

C. Organism – Community – Population – Biosphere

D. Organism – Population – Ecosystem – Biosphere

Q. 91 Which of the following are the properties of an electron?

1. Electron is a constituent of cathode ray.

2. Electron is a negatively charged particle.

3. The mass of the electron is equal to the mass of the proton.

4. Electron is deflected by the electric field but not by magnetic field.

Select the correct answer using the code given below:

A. 1 and 2 only

B. 1, 2 and 3

C. 3 and 4

D. 1 and 4

Q. 92 Carbon and energy requirements of autotrophic organisms are fulfilled by:

A. Photosynthesis

B. Gluconeogenesis

C. Glycogenesis

D. External sources

Q. 93 The resistance of a wire of length l and area of cross-section α is x ohm. If the wire is stretched to double its length, its resistance would become:

A. 2 x ohm

B. 0.5 x ohm

C. 4 x ohm

D. 6 x ohm

Q. 94 Which one of the following describes the Lithosphere?

A. Upper and lower mantle

B. Crust and upper mantle

C. Crust and core

D. Mantle and core

Q. 95 Which of the following statements regarding heavy water are correct?

1. It is extensively used as a moderator in nuclear reactors

2. It cannot be used in exchange reaction to study reaction mechanism

3. Viscosity of heavy water is relatively smaller than that of ordinary water

4. The dielectric constant of heavy water is smaller than that of ordinary water

Select the correct answer using the code given below:

A. 1 and 2

B. 2 and 3

C. 3 and 4

D. 1 and 4

Q. 96 Conservation of momentum in a collision between particles can be understood on the basis of:

A. Newton’s first law of motion

B. Newton’s second law of motion only

C. Both Newton’s second law of motion and Newton’s third law of motion

D. Conservation of energy

Q. 97 Which one of the following statements is not correct?

A. Temperatures decrease from the equator to poles

B. Temperatures in equatorial regions change substantially from January to July

C. Large land masses located in the subarctic and arctic zones develop centres of

extremely low temperatures in winter

D. Highlands are always colder than surrounding low lands

Q. 98 To weld metals together, high temperature is required. Such a high temperature is obtained by burning:

A. Acetylene in oxygen

B. LPG in oxygen

C. Methane in oxygen

D. Acetylene in nitrogen

Q. 99 Two forces, one of 3 newton and another of 4 newton are applied on a standard 1 kg body, placed on a horizontal and frictionless surface, simultaneously along the x-axis and the yaxis, respectively, as shown in figure. The magnitude of the resultant acceleration

A. 7 m/s²

B. 1 m/s²

C. 5 m/s²

D. √7 m/s²

Q. 100 Magnetic meridian is an imaginary:

A. line along north-south

B. point

C. vertical plane

D. horizontal plane

Q. 101 An up fold in rock is:

A. graben

B. horse

C. anticline

D. syncline

Q. 102 Which one of the following gases is found in highest quantity in Exosphere?

A. Hydrogen

B. Helium

C. Nitrogen

D. Oxygen

Q. 103 In blood, platelets are required for:

A. transporting oxygen

B. transporting carbon dioxide

C. initiating blood clotting

D. initiating degradation of urea

Q. 104 In SI unit of ‘Newton’ (N) is given by (where m stands for metre and s stands for seconds):

A. 1 N = 1kg/ms²

B. 1 N = 1kgm/s²

C. 1 N = 1kgs²/m

D. 1 N = 1kgms²

Q. 105 The acceleration due to gravity ‘g’ for objects on or near the surface of earth is related to the universal gravitational constant ‘G’ as (‘M’ is the mass of the earth and ‘R’ is its radius):

A. G = g(M/R²)

B. g = G(M/R²)

C. M = gG/R²

D. R = gG/M²

Q. 106 Match List I with List II (given in figure) and select the correct answer using the code given below:

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

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

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

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

Q. 107 Match List I with List II (given in figure) and select the correct answer using the code given below:

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

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

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

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

Q. 108 Which one of the following is not a site of action in human body for the malarial parasite plasmodium?

A. Liver

B. Kidney

C. Red blood cell

D. Brain

Q. 109 The loudness of sound is related to:

A. its frequency

B. its amplitude

C. its speed

D. its pitch

Q. 110 X-ray are electromagnetic radiation whose wavelengths are of the order of:

A. 1 metre

B. 10⁻¹ metre

C. 10⁻⁵ metre

D. 10⁻¹⁰ metre

Q. 111 Which one of the following pairs of properties of typical air masses (given in figure ) is correct?

A. (a)

B. (b)

C. (c)

D. (d)

Q. 112 The symbol of the element ‘Tungsten’ is

A. Ta

B. W

C. Tl

D. Tc

Q. 113 In Egypt, ancient mummies can be found to have their arteries intact due to well preserved:

A. mineralised blood

B. fibroblasts fibre

C. elastic fibre

D. brown fat

Q. 114 Which one of the following statements is correct?

A. The image formed by a concave mirror for an object lying at infinity is at the principal focus, highly diminished, real and inverted.

B. A ray of light parallel to the principal axis after reflection from a concave mirror

appears to diverge from the principal focus of the mirror.

C. The focal length of a spherical mirror is double of its radius of curvature

D. A ray of light traveling from a rarer medium to a denser medium bends away from the normal.

Q. 115 Which one of the following statements is correct?

A. Rutherford’s alpha-particle scattering experiment led to the discovery of electron

B. J J Thomson suggested that the nucleus of an atom contains protons

C. The atomic number of an element is the same as the number of protons in the nucleus of its atom

D. The mass number of an atom is equal to the number of electrons in its shells

Q. 116 Which one of the following statements is not correct?

A. Application of lime makes the soil acidic

B. High acidity in soil is typical of humid climate

C. Increasing soil acidity results in decline soil fertility

D. Arid climate is characterised by alkaline soil

Q. 117 The alkali metals have relatively low melting point. Which one of the following alkali metals is expected to have the highest melting point?

A. Li

B. Na

C. K

D. Rb

Q. 118 Which one of the following is useful in paper manufacturing industry?

A. Fibrous plants

B. Orchids

C. Non-flowering plants

D. Plants growing in high altitude

Q. 119 Which of the following statements is not correct?

A. In steady flow of a liquid, the velocity of liquid particles reaching at a particular point is the same at all points

B. Steady flow is also called streamlined flow

C. In steady flow, each particle may not follow the same path as taken by a previous

particle passing through that point

D. Two streamlines cannot intersect each other

Q. 120 According to the Geo-Scientists, the shape of the earth is:

1. round

2. spherical

3. close to that of a sphere

4. an oblate ellipsoid

Select the correct answer using the code given below:

A. 2, 3 and 4

B. 1, 2 and 3

C. 1 and 2 only

D. 3 and 4 only

Q. 121 The word ‘Secular’ was inserted into the Constitution of India by

A. 44th Amendment Act

B. 52ndAmendment Act

C. 42nd Amendment Act

D. 34th Amendment Act

Q. 122 Which one of the following is not correct in the context of balance of payments of India during 2013-2014?

A. India’s exports were less than its imports

B. Trade balance was negative

C. Net invisibles were positive

D. Capital account balance was negative

Q. 123 Which one of the following continents accounts for the maximum share in exports from India?

A. Asia

B. Europe

C. Africa

D. North America

Q. 124 The two provisions of the Constitution of India that most clearly express the power of judicial review are:

A. Article 21 and Article 446

B. Article 32 and Article 226

C. Article 44 and Article 152

D. Article 17 and Article 143

Q. 125 Which one of the following statements about Subsidiary Alliance devised by Lord Wellesley in the year 1798 is not correct?

A. The territories entering into a subsidiary alliance with the British were responsible for their own internal and external protection

B. In the territory of the ally, a British armed contingent would be stationed

C. The ally would have to provide the resources for maintaining the British contingent in the territory

D. The permission of the British was needed for the ally to enter into agreements with other rulers

Q. 126 Who among the following was associated with the Mughal Court as a Physician to Prince Dara Shukoh?

A. Hakim Afzal Khan

B. Ibn Battuta

C. Francois Bernier

D. Duarte Barbosa

Q. 127 During the Eleventh Five Year Plan (FYP), agriculture sector in India witnessed a growth rate of 3.3 per cent per annum which is higher than 2.4 per cent per annum in the previous FYP. This is largely due to better performance of:

A. Crops and Livestock

B. Oilseeds and Fibres

C. Fishing and Oilseeds

D. Fibres and Fishing

Q. 128 An emergency under Article 352 of the Constitution of India can be declared only during:

A. War, external aggression or internal disturbance.

B. War, external aggression or armed rebellion.

C. Failure of Constitutional Machinery in the State.

D. Financial instability in the country.

Q. 129 Which of the following statements about the Livestock sector in India is/are correct?

1. Livestock contributed about 25 percent of gross value added in agriculture.

2. It provides self employment to a large segment of population.

3. Rapid growth of livestock sector can be egalitarian and inclusive.

Select the correct answer using the code given below:

A. 3 only

B. 1 and 2 only

C. 2 and 3 only

D. 1, 2 and 3

Q. 130 Which one of the following statements about Khilafat Movement is not correct?

A. The Khilafat Movement demanded that the Khalifa must retain control over Muslim holy places

B. The radical trend in the Khilafat Movement was represented by younger leaders like Muhammad Ali, Shaukat Ali and Maulana Azad.

C. Indian Muslim leaders used Khilafat as a symbol that could unite the Indian Muslim community

D. The Delhi conference of the Central Khilafat Committee in 1920 decided to launch a massive Non-Cooperation Movement

Q. 131 Which one of the following is not correct in the current Indian scenario?

A. Life expectancy is on the increase and is about 67 years as of now

B. Infant mortality rate is on the decline and has reached 47 per thousand

C. Maternal mortality rate (MMR) is on the rise due to lack of medical facilities

D. Percentage of women giving birth in health institutions is on the rise

Q. 132 The Fourth Schedule to the Constitution of India deals with:

A. provisions related to the administration of tribal areas

B. allocation of seats in the Council of States

C. the Union List, the State List and the Concurrent List

D. Recognised languages of the Union of India

Q. 133 The British officer who was a representative of the Governor General and who lived in a State was not under direct British rule was called:

A. Collector

B. Viceroy

C. Resident

D. Agent

Q. 134 Which of the following features of the Permanent Settlement of 1793 is/are correct?

1. The Permanent Settlement vested Land ownership rights in the peasants.

2. The Permanent Settlement vested land ownership rights in the Zamindars.

3. The Zamindars had to pay a fixed amount of rent by a particular date.

4. The Zamindars benefited hugely from the Permanent Settlement while the peasants

suffered.

Select the correct answer using the code given below:

A. 1 only

B. 2 and 3 only

C. 4

D. 1, 2 and 3

Q. 135 The Vijaynagara Empire received its death blow at the battle of:

A. Talikota in 1565

B. Panipat in 1661

C. Talikota in 1665

D. Raichur in 1510

Q. 136 The ‘basic Structure Doctrine’ was enunciated by the Supreme Court during the:

A. Golak Nath case

B. Maneka Gandhi case

C. Kesavananda Bharati case

D. S R Bommai case

Q. 137 Consider the following statements about the travellers who visited India:

1. Abdur Razzaq Samarqandi from Herat visited Delhi and Daulatabad.

2. Ibn Battuta provides detailed accounts of both Delhi and Daulatabad.

3. According to Francois Bernier there was no private property in land in Mughal India.

Which of the statements given above is/are correct?

A. 1 only

B. 1, 2 and 3

C. 1 and 3 only

D. 2 and 3 only

Q. 138 Which of the following statements about hill stations of colonial India is/are correct?

1. The architecture of hill stations sought to recreate the European style.

2. Hill stations were developed as sanitariums where soldiers were treated for illness.

3. Shimla became the official residence of the Commander in Chief of the Indian Army.

4. In 1864, Shimla had to be evacuated because of a Typhoid epidemic.

Select the correct answer using the code given below:

A. 1 only

B. 1, 2 and 3

C. 3 and 4

D. 2 and 3 only

Q. 139 Match List I with List II (figure 1) and select the correct answer using the code given below:

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

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

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

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

Q. 140 The Senia tradition is:

A. musical tradition that emerged from the colonial

B. dance drama written by Keshab Chandra Sen

C. textile tradition of eastern UP

D. musical tradition that invoked the name of Tansen, the celebrated musician of Akbar’s court

Q. 141 Who among the following founded the Rajamundri Social Reform Association in 1878 in support of widow remarriage?

A. Vishanshastra Pandit

B. Ishwar Chandra Vidyasagar

C. Pandita Ramabai

D. Veerasalingam Pantulu

Q. 142 The SAARC Secretariat is located at:

A. New Delhi

B. Colombo

C. Kathmandu

D. Karachi

Q. 143 The 19th Century Faraizi Movement in eastern Bengal developed under the leadership of:

A. Titu Rai

B. Haji Shariatullah

C. Shah Sayyid Ahmad

D. Dudu Miyan

Q. 144 The Indian States Committee was formed in 1928 under?

A. The Raja of Junagadh

B. Ian Copland

C. Sir Harcourt Butler

D. Motilal Nehru

Q. 145 The Panchayati Raj system under Part – IX of the Constitution of India does not apply to the States of:

A. Assam, Mizoram and Nagaland

B. Nagaland, Meghalaya and Tripura

C. Nagaland, Meghalaya and Mizoram

D. Sikkim, Tripura and Meghalaya

Q. 146 The First Five Year Plan (1951 – 1956) was drafted by:

A. P C Mahalanobis

B. KN Raj

C. K C Kumarappa

D. Jawaharlal Nehru

Q. 147 Who among the following is the author of the book, “Pakistan Paradox : Instability and Resilience”?

A. Christophe Jaffrelot

B. G Parthasarthy

C. Imran Khan

D. Mamnoon Hussain

Q. 148 Which one of the following was the theme of the ‘International Day of United Nations Peacekeepers’ for the year 2015?

A. Peacekeeping is a Global Partnership

B. UN 70 and UN Peacekeeping: Pat, Present and Future

C. Women in Peacekeeping

D. A Force for the Future

Q. 149 Indian athlete Vikas Gowda is associated with:

A. Wrestling

B. Sprint

C. Discus throw

D. Archery

Q. 150 The 19th Federation Cup National Senior Athletic Championships (2015) was held in:

A. Karnataka

B. Haryana

C. Uttar Pradesh

D. Kerala

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