## BITSAT Examination Previous Year Question Paper 2017 With Answer Key

Part I

BITSAT Physics Exam Paper-2017

1. It temperature of a black body increases from 300 K to 900 K, then the rate of energy radiation increases by

(a)   81

(b)   3

(c)   9

(d)   2

2. A whistle of frequency 500 Hz tied to the end of a string of length 1.2 m revolves at 400 rev/min. A listener standing some distance away in the plane of rotation of whistle hears frequencies in the range.

(Speed of sound = 340 m/s)

(a)   436 to 574

(b)   426 to 586

(c)   426 to 574

(d)   436 to 586

3. The focal length of a thin convex lens for red and blue rays are 100 cm and 96.8 cm respectively. Then, the dispersive power of the material of the lens is

(a)   0.968

(b)   0.98

(c)   0.325

(d)   0.325

4. Two metal plates having a potential difference of 800 V are 2 cm apart. It is found that a particle of mass 1.96 × 1015 kg remains suspended in the region between the plates. The charge on the particle must be (e = elementary charge).

(a)   2e

(b)   3e

(c)   6e

(d)   8e

5. At what angle θ to the horizontal should an object is projected so that the maximum height reached is equal to the horizontal range?

(a)   tan1 (1)

(b)   tan1 (4)

(c)   tan1 (2/3)

(d)   tan1 (3)

6. A body of mass 1 kg is executing simple harmonic motion. Its displacement y (cm) at t seconds is given by

Its maximum kinetic energy is

(a)   6 J

(b)   18 J

(c)   24 J

(d)   36 J

7. A positive charge q is projected in magnetic field of width  with velocity v. Then, the time taken by charged particle to emerge from the magnetic field is

(a)

(b)

(c)

(d)

8. In Young’s double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths λ1 = 12000 Å and λ2 = 10000 Å. At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

(a)   8 mm

(b)   6 mm

(c)   4 mm

(d)   3 mm

9. Two blocks A and B are placed one over the other on a smooth horizontal surface. The maximum horizontal force that can be applied on lower block B, so that A and B move without separation is 49 N.

The coefficient of friction between A and B is

(a)   0.2

(b)   0.3

(c)   0.5

(d)   0.8

10. An aeroplane is flying in a horizontal direction with a velocity u and at a height of 2000 m. When it is vertically below a point A on the ground food packet is released from it. The packet strikes the ground at point B.

If AB = 3 km and g = 10 m/s2, then the value of u is

(a)   54 km/h

(b)   540 km/h

(c)   150 km/h

(d)   300 km/h

11. A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1 mm/s. The induced emf when the radius is 2 cm, is

(a)   2 πμV

(b)   πμV

(c)

(d)   2 μV

12. A mild steel wire of length 2L and cross-sectional area A is stretched, well with in the elastic limit, horizontally between two pillars as shown in figure. A mass m is suspended from the mid-point of the wire strain in the wire is

(a)   x2/2L2

(b)   x/L

(c)   x2/L

(d)   x2/2L

13. The resistance of a wire at 20℃ is 20 Ω and 500℃ is 60 Ω. At which temperature, its resistance will be 25 Ω?

(a)   50℃

(b)   60℃

(c)   70℃

(d)   80℃

14. The de-Broglie wavelength of a proton (charge = 1.6 × 1019 C, m = 1.6 × 1027 kg) accelerated through a potential difference of 1 kV is

(a)   600 Å

(b)   0.9 × 1012 m

(c)   7 Å

(d)   0.9 nm

15. An ice-berg of density 900 kgm3 is floating in water of density 1000 kgm3. The percentage of volume of ice-berg outside the water is

(a)   20%

(b)   35%

(c)   10%

(d)   11%

16. The total energy of an electron in the first excited state of hydrogen is about −4 eV. Its kinetic energy in this state is

(a)   −3.4 eV

(b)   −6.8 eV

(c)   6.8 eV

(d)   3.4 eV

17. A common emitter amplifier has a voltage gain of 50, an input impedance of 100 Ω and an output impedance of 200 Ω. The power gain of the amplifier is

(a)   500

(b)   1000

(c)   1250

(d)   50

18. The horizontal range and maximum height attained by a projectile are R and H respectively. If a constant horizontal acceleration a = g/4 is imparted to the projectile due to wind, then its horizontal range and maximum height will be

(a)   (R + H), H/2

(b)   (R + H/2), 2H

(c)   (R + 2H), H

(d)   (R + H), H

19. A balloon is filled at 27℃ and 1 atm pressure by 500 m3 At −3℃ and 0.5 atm pressure, the volume of He will be

(a)   700 m3

(b)   900 m3

(c)   1000 m3

(d)   500 m3

20. The ratio of intensity at the centre of a bright fringe to the intensity at a point distance one-fourth of the distance between two successive bright fringes will be

(a)   4

(b)   3

(c)   2

(d)   1

21. A rectangular block of mass m and area of cross-section A floats in a liquid of density ρ. If it is given a vertical displacement from equilibrium, it undergoes oscillation with a time period T. Then

(a)   T ∝ √ρ

(b)   T ∝ 1/√A

(c)   T ∝ 1/√ρ

(d)   T ∝ 1/√m

22. Three charges are placed at the three vertices of an equilateral triangle of side ‘a’ as shown in the figure. The force experienced by the charge placed at the vertex A in a direction normal to BC is

(a)

(b)

(c)

(d)

23. A load of mass m falls from a height on the scale pan hung from a spring as shown. If the spring constant is k and the mass of the scale pan is zero and the mass m does not bounce relative to the pan, then the amplitude of vibration is

(a)

(b)

(c)

(d)

24. The activity of a radioactive sample is measured as N­0 counts per minute at t = 0 and N0/e counts per minute at t = 5 min. The time (in minutes) at which the activity reduces to half its value is

(a)   loge 2/5

(b)   5/loge 2

(c)   5 log10 2

(d)   5 loge 2

25. A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces parallel to each other. If lenses are made of different materials of refractive indices μ1 and μ2 R is the radius of curvature of the curved surface of the lenses, then the focal length of combination is

(a)

(b)

(c)

(d)

26. In the given circuit diagram,

E = 5V, r = 1Ω

E= 5 V, r = 1Ω, R2 = 4Ω, R1 = R3 = 1Ω and C = 3μF

Then, what will be the numerical value of charge on each plates of the capacitor.

(a)   24 μC

(b)   12 μC

(c)   6 μC

(d)   3 μC

27. A block A of mass 100 kg rests on another block B of mass 200 kg and is tied to a wall as shown in the figure. The coefficient of friction between A and B is 0.2 and that between B and ground is 0.3. The minimum force required to move the block B is (g = 10 ms2)

(a)   900 N

(b)   200 N

(c)   1100 N

(d)   700 N

28. A uniform rod of length l and mass m is free to rotate in a vertical plane about A. The rod initially in horizontal position is released. The initial angular acceleration of the rod is (Moment of inertia of rod about A is ml2/3)

(a)   3g/2l

(b)   2l/3g

(c)   3g/2l2

(d)

29. Monochromatic radiation of wavelength λ is incident on a hydrogen sample in ground state. Hydrogen atom absorbs a friction of light and subsequently emits radiations of six different wavelengths. The wavelength λ is

(a)   97.5 nm

(b)   121.6 nm

(c)   110.3 nm

(d)   45.2 nm

30. A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that B is in plane of the coil. If due to a current i in the triangle, a torque τ rests on it, the side l of the triangle is

(a)

(b)

(c)

(d)

31. Work done in increasing the size of a soap bubble from radius of (3 to 5) cm is nearly (surface tension of soap solution = 0.03 Nm1)

(a)   0.2 π mJ

(b)   2π mJ

(c)   0.4 mJ

(d)   4π mJ

32. The velocity of a projectile at the initial point A is Its velocity (in m/s) at point B is

(a)

(b)

(c)

(d)

33. In the circuit shown, the heat produced in 5Ω resistor is 10 cal s1. The heat produced per sec in 4Ω resistor will be

(a)   1 cal

(b)   2 cal

(c)   3 cal

(d)   4 cal

34. An α-particle after passing through potential difference of V volt collides with a nucleus. If the atomic number of the nucleus is Z, then distance of closest approach is

(a)

(b)

(c)

(d)

35. Two simple pendulums of lengths 5 m and 20 m respectively are given small displacement are given small displacement in one direction at the same time they will again be in the same sense when the pendulum of shorter length has completed n oscillations. Then, n is

(a)   5

(b)   1

(c)   2

(d)   3

36. A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between the plates is d. The space between the plates is now filled with two dielectrics constant K1 = 3 and thickness d/3 while the other one has dielectric constant K2 = 6 and thickness 2d/3. Capacitance of the capacitor is now

(a)   1.8 pF

(b)   45 pF

(c)   40.5 pF

(d)   20.25 pF

37. A particle moving along X-axis has acceleration f, at time t given by  where f0 and T are constants. The particle at t = 0 and the instant when f = 0, the particle’s velocity vX is

(a)   f0T

(b)

(c)   f0T2

(d)

38. A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time period of a sky satellite orbiting a few 100 km above the earth’s surface (R = 64000 km) will approximately be

(a)

(b)   1 h

(c)   2 h

(d)   4 h

39. A transverse wave propagating on a stretched string of linear density 3 × 104 kgm1 is represented by the equation

y = 0.2 sin(1.5x + 60t)

where, x in metres and t is in seconds. The tension in the string (in Newton) is

(a)   0.24

(b)   0.48

(c)   1.20

(d)   1.80

40. What is the magnetic field at the centre of arc in the figure below?

(a)

(b)

(c)

(d)

Part II

BITSAT Chemistry Exam Paper-2017

41. 4g of copper was dissolved in conc. HNO3. The copper nitrate thus obtained gave 5g of its oxide on strong heating the equivalent weight of copper is

(a)   23

(b)   32

(c)   12

(d)   20

42. Choose the incorrect statement.

(a)   Sodium borohydride reacts very slowly with cold water

(b)   Sodium borohydride reacts violently with cold water to give H2(g)

(c)   Solubility of sodium borohydride in water at 25℃ is 10.05 g/ml

(d)   Melting point of sodium borohydride is 500℃

43. The orbital angular momentum of an electron is 2 S orbital is

(a)   h/4π

(b)   zero

(c)   h/2π

(d)   √2 ∙ h/2π

44. Which of the following are isoelectronic species?

(a)   I, II and III

(b)   II, III and IV

(c)   I, II and IV

(d)   II and I

45. Two elements A and B have electronegativities 1.2 and 3.0 respectively. The nature of bond between A and B would be

(a)   ionic

(b)   covalent

(c)   co-ordinate

(d)   metallic

46. In the compound,

The most acidic hydrogen atom is

(a)   Only I

(b)   Only II

(c)   Only III

(d)   All are equally acidic

47. Reductive ozonolysis of (CH3)2 C = C(CH3)2 followed by hydrolysis gives

(a)   only one type of ketone

(b)   only one type of aldehyde

(c)   two types of ketone

(d)   two types of aldehyde

48. Which of the following reactions does not involved absorption energy?

I. O (g) + e → O (g)

II. S(g) + e → S (g)

III. O(g) + e → O2 (g)

IV. Cl(g) + e → Cl (g)

(a)   Only II

(b)   I and III

(c)   I, II and III

(d)   I, II and IV

49. The most reactive amine towards reactions with dil. HCl is

(a)   CH3 – NH2

(b)

(c)   (CH3)3N

(d)

50. Blocks of magnesium are fixed to the bottom of a ship to

(a)   block hole in the ship

(b)   acidity of sea water

(c)   make the ship lighter

(d)   prevent the action of water and salt

51. On electrolysis of water, a total of 1 mole of gasses is evolved. The amount of water decomposed is

(a)   1 mol

(b)   2 mol

(c)

(d)

52. How many moles of Fe2+ ions are formed when excess of iron react with 500 mL O. 4NHCl, under inert atmosphere?

(assume no change in volume)

(a)   0.4

(b)   0.1

(c)   0.2

(d)   0.8

53. Sodium sulphate is soluble in water but barium sulphate is insoluble because

(a)   hydration energy of Na2SO4 is more than of its lattice energy

(b)   lattice energy of BaSO4 is more than its hydration energy

(c)   Both (a) and (b)

(d)   None of the above

54. In the reaction,   end product (P) is

(a)   CH3CH2 ∙ NO2

(b)   CH3CH2CH2NO2

(c)   CH3CH2NH2

(d)   CH3 ∙ CH2 ∙ CH2NH2

55. Which of the following reactions is an example of calcinations process?

(a)   2Ag + 2HCl + [O] → 2AgCl + H2O

(b)   2Zn + O2 → 2ZnO

(c)   2ZnS + O2 → 2ZnO + 2SO2

(d)

56. For an endothermic reaction, where ∆H represent the enthalpy of reaction in kJ/mol, the minimum value for energy of activation (for forward reaction) will be

(a)   less than ∆H

(b)   zero

(c)   more than ∆H

(d)   equal to ∆H

57. Which of the following metals is leached by cyanide process

(a)   Ag

(b)   Na

(c)   Al

(d)   Cu

58. Which of the following is a diamagnetic complex

(a)   [Co(NH)6­]3+

(b)   [NiCl4]2

(c)   [CuCl4]2

(d)   [Fe(H2­O)6]3+

59. Neoprene is a

(a)   monomer of rubber

(b)   synthetic rubber

(c)   a natural rubber

(d)   vulcanized rubber

60. Among the following, which have highest melting point?

(a)   Ionic solids

(b)   Pseudo solids

(c)   Molecular solids

(d)   Amorphous solids

61. The night-blindness is developed due to deficiency of vitamin

(a)   B6

(b)   C

(c)   B12

(d)   A

62. The transfer RNA anticodon for the messenger RNA codon G – C – A is

(a)   C – G – U

(b)   C – C – U

(c)   U – C – C

(d)   G – U – C

63. 765 g of an acid gives 0.535 g of CO2 and 0.138 g of H2O. Then, the ratio of percentage of carbon and hydrogen is

(a)   19 : 2

(b)   18 : 11

(c)   20 : 17

(d)   1 : 7

64. Maximum pKb value is of

(a)

(b)   (CH3CH2)2NH

(c)   (CH3)2NH

(d)

65. Which of the following is an incorrect set of quantum members?

(a)   n = 2, l = 0, m = 0

(b)   n = 1, l = 0, m = 0

(c)   n = 3, l = 3, m = 0

(d)   n = 2, l = 1, m = 0

66. The most acidic oxide for nitrogen is

(a)   NO2

(b)   N2O

(c)   NO

(d)   N2O5

67. Which of the following show maximum bond-order?

(a)   O2

(b)   O2

(c)   O2+

(d)   O22

68. Which of the following shown an increase in entropy?

I. Boiling of water

II. Melting of ice

III. Freezing of water

IV. Formation of hydrogen gas from water

(a)   (I) and (II)

(b)   Only (III)

(c)   (I), (II) and (IV)

(d)   (III) and (IV)

69. BF3 is an acid, according to

(a)   Lewis

(b)   Arrhenius

(c)   Bronsted and Lowery

(d)   All of the above

70. For the reaction

N2O4(g) → 2NO2(g)

(a)   ∆H > ∆E

(b)   ∆H < ∆E

(c)   ∆H = ∆E

(d)   ∆H = 0

71. Which of the following elements mostly form covalent compounds?

(a)   Cs

(b)   Rb

(c)   K

(d)   Li

72. When aqueous solutions of borax is acidified with HCl, we get

(a)   B2H6

(b)   H3­BO3

(c)   B2O3

(d)   All of these

73. Which of the following compound does not follow Huckel’s rule?

(a)

(b)

(c)

(d)

74. A graph is ploted between log K virsus 1/T for calculation of activation energy (Ea). The correct plot is

(a)

(b)

(c)

(d)

75. The hybridization of Fe is K3Fe(CN)6 is

(a)   sp3

(b)   dsp3

(c)   sp3d2

(d)   d2sp3

76. Which of the following shows maximum magnetic moment?

(a)   Mg2+

(b)   Ti3+

(c)   V3+

(d)   Fe2+

77. Consider the following radioactive decays

In which case group of parent and daughter elements remains unchanged.

(a)   In (I)

(b)   In (II)

(c)   Both in (I) and (II)

(d)   None of the above

78.

The reactions (s) ‘X’ and ‘Y’ respectively are

(a)   Fries rearrangement and Kolble

(b)   Cumene and Reimer-Tiemann

(c)   Dow and Reimer-Tiemann

(d)   Dow and Sandmeyer.

79. Which of the following has largest number of moles?

(a)   8g of oxygen atoms

(b)   16 g of oxygen gas

(c)   14 g of nitrogen gas (N2)

(d)   All have same number of moles

80. One moles each of four ideal gasses are kept as follows.

I. 5 L of gas (A) at 2 atm pressure

II. 2.5 L of gas (B) at 2 atm pressure

III. 1.25L of gas (C) at 2 atm pressure

IV. 2.5 L of gas (D) at 2.5 atm pressure

Which of the above gases is kept at highest temperature.

(a)   Gas (A)

(b)   Gas (B)

(c)   Gas (C)

(d)   Gas (D)

Part III

BITSAT English & Reasoning Exam Paper-2017

a. English Proficiency

Directions (Q. Nos. 81-83) In the following questions the sentences may or may not be grammatically correct. Find out which part of a sentence has an error and mark that part. If there is no error mark part ‘d’ as your answer.

81. Along the northern frontier of India / is seen / the Himalayas mighty in their /No error

(a)   Along the northern frontier of India

(b)   is seen

(c)   the Himalayas mighty in their splendor

(d)   No error

82. The father with the son were / mysteriously missing / from the house. /No error

(a)   The father with the son were

(b)   mysteriously missing

(c)   from the house

(d)   No error

83. It is not advisable / to take heavy luggages / while on journey these days./ No error

(b)   to take heavy luggages

(c)   while on journey these days

(d)   No error

Directions (Q. Nos. 84-85) Fill in the blanks with suitable preposition from the alternatives given under each sentence.

84. The problem of communal harmony cannot be glossed …………. by the government.

(a)   at

(b)   on

(c)   over

(d)   for

85. She could not muster …………. courage to stand against the maltreatment.

(a)   to

(b)   up

(d)   on

Directions (Q. Nos. 86-88) The following sentences consist of a word or a phrase which is written in italicized letters. Each sentence is followed  by four words or phrases. Select the word or the phrase which is closest to the opposite in meaning of the italicized word or phrase.

86. Philosophers say that the world is an

(a)   a fact

(b)   a reality

(c)   an actuality

(d)   truth

87. She used to disparage her neighbours every now and then.

(b)   praise

(c)   belittle

(d)   denigrate

88. The momentum of the movement slackened in course of time

(a)   stopped

(b)   quickened

(c)   multiplied

(d)   recovered

Directions (Q. Nos. 89-90) In the following sentences, a word or a phrase is written in italicized letters. For each italicized part four words/phrases are listed below each sentence. Choose the word nearest in meaning to the italicized word/phrase.

89. The opposition criticized the ruling party for the deteriorating law and order situation in the state.

(a)   disrupting

(b)   worsening

(c)   crumbling

(d)   eroding

90. The two opposing parties have reached stalemate.

(a)   dilemma

(c)   exhaustion

(d)   settlement

Directions (Q. Nos. 91-95) Read the passage given below and answer the questions that follow.

A pioneering scheme has been started recently in Southampton of England’s south coast to educate tourists who have been convicted of drunken driving.

The penalty for drunken driving might be the loss of the driving licence and a heavy fine. But under the new scheme, convicted drivers do not pay the fine. Instead they have to attend eight training sessions; one a week organized by the local authority probation service.

Designed to demonstrate the damage alcohol can do, the scheme was devised by senior probation officer John Cook. He said that about a quarter of the people who came to him had a drinking problem, and had not realized how much they were drinking. One way of getting the message across was to make the drivers pour out their usual ration of alcohol and then measure it. Almost everyone poured not a single measure, but a double atleast, an example of how easy it is to have more than just one drink and to encourage other people to do the same. The instructors on the course are giving clinical evidence of the effects of alcohol on the body and brain. The sober truth is that drinking badly affects driving skills, although the drinker might like to believe otherwise.

91. The Southampton scheme requires convicted drivers

(a)   to pay a heavy fine

(b)   to attend eight driving sessions-one a week

(c)   to undergo a probation service

(d)   to surrender their driving licence

92. John Cook devised the scheme

(a)   as a demonstration technique for driving

(b)   to deny the harmful effects of alcohol

(c)   to show that Southampton was concerned about drivers

(d)   to prove that alcohol does influence driving

93. The problem with a quarter of the people who went to John Cook was that they

(a)   did not want to stop drinking

(b)   were unaware of the fact that they could get drunk

(d)   did not know how much they were drinking

94. Most driver start off with atleast

(a)   a double measure

(b)   a single measure

(c)   a little less than a single measure

(d)   two doubles

95. The truth is that alcohol

(a)   does not affect the body but only the brain

(b)   affects only the brain

(c)   affects the body and the  brain

(d)   has no effects on the body or the brain

b. Logical Reasoning

96. ‘Shoes’ is related t ‘Leather’, in the same way as

(a)   Plastic

(b)   Polythene

(c)   Latex

(d)   Chappal

97. Find the odd one from the following options

(a)   81 : 243

(b)   25 : 75

(c)   64 : 192

(d)   16 : 64

98. Complete the series by replacing ‘?’ mark.

4, 11, 30, 67, 128, ?

(a)   219

(b)   228

(c)   237

(d)   240

99. Lakshmi is elder than Meenu. Leela is elder. than Meenu but younger than Lakshmi. Latha is younger than both Meenu and Hari but Hari is younger than Meenu. Who is the youngest?

(a)   Lakshmi

(b)   Meenu

(c)   Leela

(d)   Latha

100. In the following question a part of problem figure is missing. Find out from the given answer figures a, b, c and d that can replace the question mark (?) to complete the figure.

101. In the following question, five figures are given. Out of them find three figures that can be joined to form a square.

(a)   ACD

(b)   BCD

(c)   BDE

(d)   CDE

102. The three problem figures marked X, Y and Z show the manner in which a piece of paper is folded step by step and then cut. From the answer figures a, b, c and d select the one showing the unfolded pattern of the paper after the cut.

103. Choose the answer figure which completes the problem figure matrix.

104. In the following question, one or more dots are place in the figure marked as (A). This figure is followed by four alternatives marked as a, b, c and d. One out of these four options contains region (s) common to circle, square and triangles, similar to that marked by the dot in figures (A). Find that figure

105. How many different triangles are there in the figures shown below?

(a)   28

(b)   24

(c)   20

(d)   16

Part IV

BITSAT Mathematics Exam Paper-2017

106. The coefficient of x5 ­in the expansion of (1 + x)21 + (1 + x)22 + … + (1 + x)30 is

(a)   51C5

(b)   9C5

(c)   31C621C6

(d)   30C5 + 20C5

107. If z = a + ib satisfies arg(z – 1) = arg (z + 3i),, then (a – 1) : b=

(a)   2 : 1

(b)   1 : 3

(c)   −1 : 3

(d)   None of these

108. If p and pʹ denote the lengths of the perpendicular from a focus and the centre of an ellipse with semi-major axis of length a, respective, on a tangent to the ellipse and r denotes the focal distance of the point, then

(a)   ap = rpʹ

(b)   rp = apʹ

(c)   ap = rpʹ + 1

(d)   apʹ + rp = 1

109. The value of  is equal to

(a)   5(2n – 9)

(b)   10 n

(c)   9(n – 4)

(d)   None of these

110. The numbers 32 sin 2α – 1 , 14 and 34 – 2 sin 2α from first three terms of an A.P., its fifth term is

(a)   −25

(b)   −12

(c)   40

(d)   53

111. For the equation 3x2 + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal to

(a)   1/2

(b)   1

(c)   3

(d)   2/3

112. If a = log2 3, b = log2 5 and c = log7 2, then log140 63 in terms of a, b, c is

(a)

(b)

(c)

(d)

113. If cos (x – y), cos x and cos (x + y) are in HP, then cos x sec (y / 2) is equal to

(a)   ±√2

(b)   ±1/√2

(c)   ±2

(d)   None of these

114. Let A = {1, 2, 3, 4, 5} and R be a relation defined by

R = {(x, y) : x, y ∈ A, x + y = 5}. Then, R is

(a)   reflexive and symmetric but not transitive

(b)   an equivalence relation

(c)   symmetric but  neither reflexive nor transitive

(d)   neither reflexive nor symmetric but transitive

115. The number of times the digit 5 will be written when listing the integers from 1 to 1000, is

(a)   271

(b)   272

(c)   300

(d)   None of these

116. Let A and B be two sets such that A ∩ X = B ∩ X = ϕ and A ∪ X = B ∪ X for same set X. Then,

(a)   A = B

(b)   A = X

(c)   B = X

(d)   A ∪ B = X

117. Let A = [−1, 1] and f : A → A be defined as f(x) = x|x| for all x ∈ A, then f(x) is

(a)   many-one and into function

(b)   one-one and into function

(c)   many-one and into function

(d)   one-one and onto function

118. The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is

(a)

(b)

(c)

(d)

119. Two equal sides of an isosceles triangle are 7x – y + 3 = 0 and x + y – 3 = 0 and its third side passes through the point (1, −10). Find the equation of the third side

(a)   x – 3y = − 31

(b)   x – 3y = 31

(c)   x + 3y = 31

(d)   x + 3y = −31

120. If two distinct chords drawn from the point (p, q) on the circle x2 + y2 = px + qy (where pq ≠ 0) are bisected by the X-axis, then

(a)   p2 = q2

(b)   p2 = 8q2

(c)   p2 < 8q2

(d)   p2 < 8q2

121. The length of perpendicular drawn from the point (2, 3, 4) to line  is

(a)

(b)

(c)

(d)

122. The image of the point (1, 6, 3) in the line  is

(a)   (−1, 0, 7)

(b)   (−1, 0, −7)

(c)   (1, 0, 7)

(d)   (2, 0, 7)

123. The distances of the point (1, −5, 9) from the plane x + y + z = 5 measured along a straight line x = y = z is 2√3 k, then the value f k is

(a)   5

(b)   6

(c)   √3

(d)   4

124.  is equal to

(a)   ∞

(b)   0

(c)   does not exist

(d)   None of these

125. If

(a)   f(x) is differentiable at x = 0

(b)   f(x) is continuous at x = 0, 1

(c)   f(x) is differentiable at x = 1

(d)   None of the above

126. If a function f : R → R satisfy the equation f(x + y) = f(x) + f(y), ∀ x, y and the function f(x) is continuous at x = 0, then

(a)   f(x) is continuous for all positive real values of x

(b)   f(x) is continuous for all x

(c)   f(x) = 0 for all x

(d)   None of the above

127. The value of f(0), so that the function  is continuous at each point in its domain, is

(a)   1/3

(b)   −1/3

(c)   2/3

(d)   −2/3

128. Consider the greatest integer function, defined by f(x) = [x], 0 ≤x < 2. Then,

(a)   f is derivable at x = 1

(b)   f is not derivable at x = 1

(c)   f is derivable at x = 2

(d)   None of these

129. Let f(x) = −2x3 + 21x2 – 60x + 41, then

(a)   f(x) is decreasing in (−∞, 1)

(b)   f(x) is decreasing in (−∞, 2)

(c)   f(x) is increasing (−∞, 1)

(d)   f(x)is increasing in ((−∞, 2)

130. Rolle’s theorem is not applicable for the function f(x) = |x| in the interval [−1, 1] because

(a)   fʹ(1) does not exist

(b)   fʹ(1) does not exist

(c)   f(x) is discontinuous at x = 0

(d)   fʹ(0) does not exist

131. If the curve y = ax and y = bx intersect at angle α, then tan α is equal to

(a)

(b)

(c)

(d)

132. The expression  where [x] and {x} are integral and fractional part of x and n ∈ N, is equal to

(a)

(b)   1/n

(c)   n

(d)   n – 1

133. The maximum value of f(x) = x + sin 2x, x ∈ [0, 2π] is

(a)   π/2

(b)   2π

(c)   3π/4

(d)   3π/2

134. The area under the curve y = |cos x – sin x|, 0 ≤ x ≤ π/2 and above X-axis, is

(a)   2√2

(b)   2√2 – 2

(c)   2√2 + 2

(d)   0

135. The solution of is

(a)

(b)

(c)

(d)

136. The area enclosed by the curves y = x3 and y = √x is

(a)

(b)

(c)

(d)

137. If  where a is finite number, then

(a)   a = 2

(b)   a = 0

(c)   b= 1

(d)   b = −1

138. If the papers of 4 students can be checked by anyone of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers, is equal to

(a)   12/49

(b)   6/49

(c)   9/49

(d)   15/49

139. If equation (10x – 5)2 + (10y – 4)2 = λ2(3x + 4y – 1)2 represents a hyperbola, then

(a)   −2 < λ < 2

(b)   λ > 2

(c)   λ < −2 or λ > 2

(d)   0 < λ < 2

140. Let  be two non-collinear unit vectors. If  then |v| is equal to

(a)   |u|

(b)

(c)   2|v|

(d)

141. If the variance of the observations x1, x2 …………, xn is σ2, then the variance of αx1, αx2, ……, αxn, α ≠ 0 is

(a)   σ2

(b)   ασ2

(c)   α2σ2

(d)   σ22

142. Coefficient of variation of two distributions are 50 and 60 and their arithmetic means are 30 and 25, respectively. Difference of their standard deviation is

(a)   0

(b)   1

(c)   1.3

(d)   2.5

143. The maximum value of z = 9x + 13y subject to constraints 2x + 3y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0 is

(a)   130

(b)   81

(c)   79

(d)   99

144. A coin is tossed 7 times. Each time a man calls head. The probability that he wins the toss atleast 4 occasions is

(a)   1/4

(b)   5/8

(c)   1/2

(d)   1/6

145. If  and f(1) = 2 f(p + q) = f(p) ∙ f(q), ∀ p, q ∈ R, then  is equal to

(a)   0

(b)   1

(c)   2

(d)   3

146. The value of

(a)   e

(b)   2e

(c)   3e

(d)   None of these

147. If z1, z2 and z23 represent the vertices of an equilateral triangle such that |z1| = |z2| = |z3|, then

(a)   z1 + z2 = z3

(b)   z1 + z2 + z3 = 0

(c)   z1z2 = 1/z3

(d)   z1 – z2 = z3 – z2

148. If  then a + λ equal to

(a)   2

(b)   > 2

(c)   < 2

(d)   > 3

149. Line joining the points (0, 3) and (5, −2) is a tangent to the curve  then

(a)   a = 1 ± √3

(b)   a ∈ ϕ

(c)   a = −1 ± √3

(d)   a = −2 ± 2√3

150. The shortest distance between the parabolas y2 = 4x and y2 = 2x – 6 is

(a)   2

(b)   √5

(c)   3

(d)   None of these