**BITSAT SOLVED PAPER-2019**

**PART-I : PHYSICS**

1. Which one of the following graphs represents the variation of electric field with distance r from the centre of a charged spherical conductor of radius R?

(a)

(b)

(c)

(d)

2. If are the electric and magnetic field vectors of e.m. waves then the direction of propagation of e.m. wave is along the direction of

(a)

(b)

(c)

(d) None of these

3. The young’s modulus of a wire of length L and radius r Y N/m^{2}. If the length and radius are reduced to L/2 and r/2, then its young’s modulus will be

(a) Y/2

(b) Y

(c) 2Y

(d) 4Y

4. Twelve resistors each of resistance 16 Ω are connected in the circuit as shown. The net resistance between A and B is

(a) 1 Ω

(b) 2 Ω

(c) 3 Ω

(d) 4 Ω

5. The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become

(a) 10 hours

(b) 80 hours

(c) 40 hours

(d) 20 hours

6. Two rains are moving towards each other with speeds of 20 m/s and 15 m/s relative to the ground. The first train sounds a whistle of frequency 600 Hz. The frequency of the whistle heard by a passenger in the second train before the train meets, is (the speed of sound in air is 340 m/s)

(a) 600 Hz

(b) 585 Hz

(c) 645 Hz

(d) 666 Hz

7. You are asked to design a having mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be:

(a) 60 cm

(b) −24 cm

(c) −60 cm

(d) 24 cm

8. A block is kept on a frictionless inclined surface with angle of inclination ‘α’. The incline is given an acceleration ‘a’ to keep the block stationary. Then ‘a’ is equal to

(a) g cosec α

(b) g/tan α

(c) g tan α

(d) g

9. With the increase in temperature, the angle of contact

(a) decreases

(b) increases

(c) remains constant

(d) sometimes increases and sometimes

10. Forward biasing is that in which applied voltage

(a) increases potential barrier

(b) cancels the potential barrier

(c) is equal to 1.5 volt

(d) None of these

11. Number of significant figures in expression is

(a) 2

(b) 4

(c) 3

(d) 5

12. The ratio of the specific heats in terms of degrees of freedom (n) given by

(a) (1 + n/3)

(b) (1 + 2/n)

(c) (1 + n/2)

(d) (1 + 1/n)

13. A stone is thrown with a velocity u making an angle θ with the horizontal. The horizontal distance covered by its fall to ground is maximum when the angle θ is equal to

(a) 0°

(b) 30°

(c) 45°

(d) 90°

14. A ball of mass 150 g, moving with an acceleration 20 m/s^{2}, is his by a force, which acts on it for 0.1 sec. The impulsive force is

(a) 0.5 N

(b) 0.1 N

(c) 0.3 N

(d) 1.2 N

15. A man drags a block through 10 m on rough surface (μ = 0.5). A force of √3 kN acting at 30° to the horizontal. The work done by applied force is

(a) zero

(b) 7.5 kJ

(c) 5 kJ

(d) 10 kJ

16. A force of acts on a body for 4 second, produces a displacement of The power used is

(a) 9.5 W

(b) 7.5 W

(c) 6.5 W

(d) 4.5 W

17. The Earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the Earth. The escape velocity of a body from this platform is fv, where v is its escape velocity from the surface of the Earth. The value of f is

(a) 1/3

(b) 1/2

(c) √2

(d) 1/√2

18. Kepler’s second law regarding constancy of areal velocity of a planet is a consequence of the law of conservation of

(a) Energy

(b) Angular momentum

(c) Linear momentum

(d) None of these

19. Water is flowing through a horizontal tube having cross-sectional areas of its two ends being A and A’ such that ratio A/A’ is 5. If the pressure difference of water between the two ends is 3 × 10^{5} N m^{−}^{2}, the velocity of water with which it enters the tube will be (neglect gravity effects)

(a) 5ms^{−}^{1}

(b) 10 ms^{−}^{1}

(c) 25 ms^{−}^{1}

(d) 50√10 ms^{−}^{1}

20. A thermodynamic system is taken from state A to B along ACB and is brought back to A along BDA as shown in the PV diagram. The net work done during the complete cy cle is given by the area

(a) P_{1}ACBP_{2}P_{1}

(b) ACBB’A’A

(c) ACBDA

(d) ADBB’A’A

21. A boat crosses a river from port A to port B, which are just on the opposite side. The speed of the water is V_{w} and that of boat is V_{B} relative to still water. Assume V_{w} = 2V_{w}. What is the time taken by the boat, if it has to cross the river directly on the AB line (D = width of the river]

(a)

(b)

(c)

(d)

22. Two springs, of force constants k_{1} and k_{2} are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both k_{1} and k_{2} are made four times their original values, the frequency of oscillation becomes

(a) 2f

(b) f/2

(c) f/4

(d) 4f

23. When a potential difference V is applied across a conductor at a temperature T, the drift velocity of electrons is proportional to

(a) √V

(b) V

(c) √T

(d) T

24. The amplitude of a damped oscillator becomes (1/3rd) in 2 seconds. If its amplitude after 6 seconds is 1/n times the original amplitude, the value of n is

(a) 3^{2}

(b) 3^{3}

(c) ∛3

(d) 2^{3}

25. The angular speed of the electron in the nth orbit of Bohr hydrogen atom is

(a) directly proportional to n

(b) inversely proportional to √n

(c) inversely proportional to n^{2}

(d) inversely proportional to n^{3}

26. In the given figure, the charge on 3 μF capacitor is

(a) 10 μC

(b) 15 μC

(c) 30 μC

(d) 5 μC

27. Two bodies A and B are placed in an evacuated vessel maintained at a temperature of 27° The temperature of A is 327°C and that of B is 227°C. The ratio of heat loss from A and B is about

(a) 2 : 1

(b) 1 : 2

(c) 4 : 1

(d) 1 : 4

28. If a rigid body is rotating about an axis with a constant velocity, then

(a) Velocity, Angular velocity of all particles will be same

(b) Velocity, Angular velocity of all particles will be different

(c) Velocity of all particles will be different but angular velocity will be same.

(d) Angular velocity of all particles will be different but velocity will be same.

29. The fundamental frequency of an open organ pipe is 300 Hz. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330 m/s, then the length of closed organ pipe is

(a) 41 cm

(b) 30 cm

(c) 45 cm

(d) 35 cm

30. In Young’s experiment, the distance between the slits is reduced to half and the distance between the slit and screen is doubled, then the fringe width

(a) will not change

(b) will become half

(c) will be doubled

(d) will become four times

31. If a rolling body’s angular momentum changes by 20 SI units in 3 seconds, by a constant torque. Then find the torque on the b ody

(a) 20/3 SI units

(b) 100/3 SI units

(c) 20 SI units

(d) 5 SI units

32. Charge Q is distributed to two different metallic spheres having radii x and 2x such that both spheres have equal surface charge density, then charge on large sphere is

(a) 4Q/5

(b) Q/5

(c) 3Q/5

(d) 5Q/4

33. In an LR circuit f = 50 Hz, L = 2 H, E = 5 volts, R = 1 Ω then energy stored in inductor is

(a) 50 J

(b) 25 J

(c) 100 J

(d) None of these

34. A straight wire of length 0.5 metre and carrying a current of 1.2 ampere is placed in uniform magnetic field induction 2 tesla. The magnetic field is perpendicular to the length of the wire. The force on the wire is

(a) 2.4 N

(b) 1.2 N

(c) 3.0 N

(d) 2.0 N

35. A man drives a car from station B towards station A at speed 60 km/h. A car leaves station A for station B every 10 min. The distance between A and B is 60 km. The car travels at the speed of 60 km/h. A man drives a car from B towards A at speed of 60 km/h. If he starts at the moment when first car leaves the station B, then how many cars would be meet on the route?

(a) 4

(b) 7

(c) 9

(d) 12

36. In rotatory motion, linear velocities of all the particles of the body are

(a) same

(b) different

(c) zero

(d) cannot say

37. If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

(a) aT/x

(b) aT + 2πv

(c) aT/v

(d) a^{2}T^{2} + 4π^{2}v^{2}

38. A conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires AB and CD are

(a) B to A and D to C

(b) A to B and C to D

(c) A to B and D to C

(d) B to A and C to D

39. Find the acceleration of block A and B. Assume pulley is massless.

(a)

(b)

(c)

(d)

40. The nuclei of which one of the following pairs of nuclei are isotones?

(a) _{34}Se^{74}, _{31}Ga^{71}

(b) _{38}Sr^{84}, _{38}Sr^{86}

(c) _{42}Mo^{92}, _{40}Zr^{92}

(d) _{20}Ca^{40}, _{16}S^{32}

**PART-II : CHEMISTRY**

41. Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows Arrhenius equation is

(a)

(b)

(c)

(d)

42. 3.6 g of oxygen is adsorbed on 1.2 g of metal powder. What volume of oxygen adsorbed per gram of the adsorbent at 1 atm and 273 K?

(a) 0.19 L g^{−}^{1}

(b) 1 L g^{−}^{1}

(c) 2.1 L g^{−}^{1}

(d) None of these

43. In the purification of impure nickel by Mond’s process, metal is purified by:

(a) Electrolytic reduction

(b) Vapour phase thermal decomposition

(c) Thermite reduction

(d) Carbon reduction

44. When chlorine water is added to an aqueous solution of sodium iodide in the presence of chloroform, a violet colouration is obtained. ON adding more the chlorine water and vigorous shaking, the violet colour disappears. This shows the conversion of ….. into ….

(a) I_{2}, HIO_{3}

(b) I_{2}, HI

(c) HI, HIO_{3}

(d) I_{2}, HOI

45. In the clathrates of xenon with water, the nature of bonding between xenon and water molecule is

(a) covalent

(b) hydrogen bonding

(c) coordinate

(d) dipole-include dipole

46. The electronic configurations of Eu(Atomic No. 63), Gd(Atomic No. 64) and Tb(Atomic No. 65) are

(a) [Xe]4f^{7}6s^{2}, [Xe]4f^{8} 6s^{2} and [Xe]4f^{8}5d^{1}6s^{2}

(b) [Xe]4f^{7}5d^{1}6s^{2}, [Xe]4f^{7} 5d^{1} 6s^{2} and [Xe]4f^{9}6s^{2}

(c) [Xe]4f^{6}5d^{1}6s^{2}, [Xe]4f^{7}5d^{1}6s^{2} and [Xe]4f^{8}5d^{1}6s^{2}

(d) [Xe]4f^{7}6s^{2}, [Xe]4f^{7}5d^{1} 6s^{2} and [Xe]4f^{9}6s^{2}

47. Which of the following carbonyls will have the strongest C – O bond?

(a) [Mn(CO)_{6}]^{+}

(b) [Cr(CO)_{6}]

(c) [V(CO_{6}]^{−}

(d) [Fe(CO)_{5}]

48. How many chiral compounds are possible on monochlorination of 2-methyl butane?

(a) 8

(b) 2

(c) 4

(d) 6

49. How many chiral compounds are possible in the reaction of excess of CH_{3}MgBr with C_{6}H_{5}COOC_{2}H_{5} to make 2-phenyl-2-propanol?

(a) A and B

(b) A, B and C

(c) A and C

(d) B and C

50.

(a)

(b)

(c)

(d)

51. Which of the following is the strongest base?

(a)

(b)

(c)

(d)

52. Which of the following does not reduce Benedict’s solution?

(a) Glucose

(b) Fructose

(c) Sucrose

(d) Aldehyde

53. General formula of solid in zinc blende structure is

(a) AB_{2}

(b) AB_{3}

(c) AB

(d) A_{2}B

54. Glycine in alkaline solution exists as ______ and migrates to

(a) Cation, cathode

(b) Neutral , anode

(c) Zwitter ion, cathode

(d) anion, anode

55. Product on reaction of ethanamide with phosphorus pentoxide is

(a) ethanamine

(b) acetonitrile

(c) ethanol

(d) ethane isonitrile

56. K_{a} of HX is 10^{−}^{5}, then find concentration of H_{3}O^{+} when equal volumes of 0.25M HX and 0.05 M NaOH are mixed.

(a) 4 × 10^{−}^{5} M

(b) 6 × 10^{−}^{5} M

(c) 8 × 10^{−}^{3} M

(d) 2 × 10^{−}^{5} M

57. Net cell reaction of Pt|H_{2}(640 mm)|HCl|H_{2}(510 mm)|Pt.

(a) 0.89V

(b) 0.93V

(c) 2.91 × 10^{−}^{3} V

(d) 2.5 × 10^{−}^{2} V

58. Which of the following has zero net dipole moment?

(a) XeF_{4}

(b) BrF_{3}

(c) ClF_{3}

(d) SF_{4}

59. Which of the following element has the highest ionization enthalpy?

(a) Boron

(b) Aluminium

(c) Germanium

(d) Thallium

60. Out of the elements with atomic number 7, 8, 9, 13 which has the smallest size and highest ionization enthalpy?

(a) 7

(b) 8

(c) 9

(d) 13

61. Which one is classified as a condensation polymer?

(a) Dacron

(b) Neoprene

(c) Teflon

(d) Acrylonitrile

62. Which of the following compounds is not an antacid?

(a) Phenelzine

(b) Ranitidie

(c) Aluminium hydroxide

(d) Cimetidine

63. Mole fraction of the solute in a 1.00 molal aqueous solution is

(a) 0.1770

(b) 0.0177

(c) 0.0344

(d) 1.7700

64. The IUPAC name of the following compound is

(a) trans-2-chloro-3-iodo-2-pentene

(b) cis-3-iodo-4-chloro-3-penten

(c) trans-3-iodo-4-chloro-3-pentene

(d) cis-2-chloro-3-iodo-2-pentene

65. Most stable carbocation among the following is

(a)

(b)

(c)

(d)

66. Which is correct for the following changes?

(a) X is Lindlar Catalyst, B is cis-2-butene

(b) A is 2-butyne, X is Na-liq. NH_{3}

(c) B is trans-2-butene, X is Na-liq. NH_{3}

(d) A is 2-butene, X is SeO_{2}

67. The stability of +1 oxidation state among Al, Ga, ln and Tl increases in the sequence :

(a) Ga < In < Al < Tl

(b) Al < Ga < ln < Tl

(c) Tl < In < Ga < Al

(d) In < Tl < Ga < Al

68. Which of the following alkaline earth metal hydroxide is amphoteric in character?

(a) Be(OH)_{2}

(b) Ca(OH)_{2}

(c) Sr(OH)_{2}

(d) Ba(OH)_{2}

69. Which reaction show oxidizing nature of H_{2}O_{2}?

(a) H_{2}O_{2} + 2KI → 2KOH + I_{2}

(b) Cl_{2} + H_{2}O_{2} → 2HCl + O_{2}

(c) H_{2}O_{2} + Ag_{2}O → 2Ag + H_{2}O + O_{2}

(d) NaClO + H_{2}O_{2} → NaCl + H_{2}O + O_{2}

70. aK_{2}Cr_{2}O_{7} + bKCl + cH_{2}SO_{4} → xCrO_{2}Cl_{2} + yKHSO_{4 }+ zH_{2}O

The above equation balances when

(a) a = 2, b = 4, c = 6 and x = 2, y = 6, z = 3

(b) a = 4, b = 2, c = 6 and x = 6, y = 2, z = 3

(c) a = 6, b = 4, c = 2 and x = 6, y = 3, z = 2

(d) a = 1, b = 4, c = 6 and x = 2, y = 6, z = 3

71. For the reactions

A ⇌ B; K_{c} = 2

B ⇌ C; K_{c} = 4

C ⇌ D; K_{c} = 6

K_{c} for the reaction A ⇌ D is

(a) 2 × 4 × 6

(b)

(c) 2 + 4 + 6

(d)

72. Which of the following will always lead to a non-spontaneous change?

(a) ∆H and ∆S both +ve

(b) ∆H is –ve ∆S both +ve

(c) ∆H and ∆S both -ve

(d) ∆H is +ve ∆S both -ve

73. The densities of two gasses are in the ratio of 1 : 16. The ratio of their rates of diffusion is

(a) 16 : 1

(b) 4 : 1

(c) 1 : 4

(d) 1 : 16

74. In the reaction, 2PCl_{5} ⇌ PCl_{4}^{+} + PCl_{6}^{−}, the change in hybridization is from

(a) sp^{3}d to sp^{3} and sp^{3}d^{2}

(b) sp^{3}d to sp^{2} and sp^{3}

(c) sp^{3}d to sp^{3}d^{2} and sp^{3}d^{3}

(d) sp^{3}d^{2} to sp^{3} and sp^{3}d

75. The group having isoelectronic species is:

(a) O^{2−}, F^{−}, Na^{+}, Mg^{2+}

(b) O^{−}, F^{−}, Na, Mg^{+}

(c) O^{2−}, F^{−}, Na, Mg^{2+}

(d) O^{−}, F^{−}, Na^{+}, Mg^{2+}

76. 100 mL O_{2} and H_{2} kept at same temperature and pressure. What is true about their number of molecules

(a)

(b)

(c)

(d)

77. If m_{A} gram of a metal A displaces m_{B} gram of another metal B from its salt solution and if the equivalent mass are E_{A} and E_{B} respectively then equivalent mass of A can be expressed as:

(a)

(b)

(c)

(d)

78. Which one of the following set of quantum numbers is not possible for 4p electron?

(a) n = 4, l = 1, m = −1, m_{s} = +1/2

(b) n = 4, l = 1, m = 0, m_{s} = +1/2

(c) n = 4, l = 1, m = 2, m_{s} = +1/2

(d) n = 4, l = 1, m = −1, m_{s} = −1/2

79. Which of the following radial distribution graphs correspond to l = 2 for the H atom?

(a)

(b)

(c)

(d)

80. Which of the following is paramagnetic?

(a) B_{2}

(b) C_{2}

(c) N_{2}

(d) F_{2}

**PART-III(A): ENGLISH PROFICIENCY**

**DIRECTIONS (Qs. 81-83): **In the following questions below, out of the four alternatives, choose the one which best expresses the meaning of the given word.

81. Garrulous

(a) Talkative

(b) Sedative

(c) Cocative

(d) Positive

82. Tinsel

(a) Tinkle

(b) Decoration

(c) Tin

(d) Colourful

83. Labyrinth

(a) Meandering

(b) Rotating

(c) Pacing

(d) Wriggling

**DIRECTIONS(Qs .84-86) : **In the following questions, choose the word opposite in meaning to the given word.

84. Knack:

(a) Talent

(b) Dullness

(c) Dexterity

(d) Balance

85. Pernicious:

(a) Prolonged

(b) Ruinous

(c) Ruthless

(d) Beneficial

86. Opulence :

(a) Luxury

(b) Transparency

(c) Wealth

(d) Poverty

**DIRECTIONS (Qs. 87-90) : **Read the passage carefully and choose the best answer to each question out of the four alternatives and mark it by blackening the appropriate circle [•].

** **Like watering a plant, we grow our friendships [and all our relationship) by running them, Friendships need the same attention as other relationships. If they are to continue. These relationships can be delightfully non-judgemental, supportive, understanding and fun.

Sometimes a friendship can bring out the positive side that you never show in any other relationship. This may be because the pressure of playing a ‘role’ (daughter, partner or child) is removed. With friend you are to be yourself and free to change. Of course, you are free to do this in all other relationships as well, but in friendships you get to have lats of rehearsals and discussion about changes as you experience them. It is an unconditional experience where you receive as much as you give. You can explain yourself to a friend openly without the fear of hurting a family member. How do friendships grow? The answer is simple. By revealing yourself; being attentive: remembering what is most showing empathy; seeing the world through the eyes of your friend, you will understand the value of friendship. All this means learning to accept a person from a completely different family to your own or perhaps someone from a completely different cultural background. This is the way we learn tolerance. In turn we gain tolerance and acceptance for our own differences.

87. In good friendships, we

(a) give and receive

(b) neither give nor receive

(c) only give

(d) only receive

88. Empathy means

(a) someone else’s misfortunes

(b) the ability to share and understand another feelings.

(c) skill and efficiency

(d) ability to do something

89. Through strong friendships, we gain

(a) only acceptance.

(b) only attention.

(c) acceptance and tolerance.

(d) only tolerance.

90. Friendships and relationships grow when they are

(a) compared

(b) divided

(c) favoured

(d) nurtured

**DIRECTIONS (Qs. 91-92) **In the following questions, sentences are given with blanks to be filled with an appropriate word(s). Four alternatives are suggested for each question. Choose the correct alternative out of the four as your answer.

91. There are not solitary, free-living creatures; every form of life is ______other forms.

(a) dependent on

(b) parallel to

(c) overshadowed by

(d) segregated from

92. I’ll take _____ now as I have another’s appointment some where else.

(a) departure

(b) your leave

(c) permission

(d) leave from work

**DIRECTIONS(Qs. 93-95) : **In the following questions, some parts of the sentences have errors and some are correct. Find out which part of a sentence has an error. The number of that part is the answer. If a sentence is free from error, then your answer is (d). i.e., No error.

93. When one hears of the incident (a)/about the plane crash(b)/ he feels very sorry. (c)/ No error (d)

94. I went there (a)/ with a view to survey (b)/ the entire procedure. (c)/No error (d)

95. It had laid(a)/in the closet(b)/ for a week before we found it. (c)/ No error(d)

**PART-III(B) : LOGICAL REASONING**

**DIRECTIONS (Qs. 96 & 97) : **In the following questions, which answer figure will complete the question figure?

96.

97.

98.

99. Select the related word from the given alternatives:

Medicine : Patient : Education :?

(a) Teacher

(b) School

(c) Student

(d) Tuition

100. Choose the correct alternative from the given ones that will complete the series.

A3E, F5J, K7O,_____

(a) Q11T

(b) Q9V

(c) P9T

(d) P11T

101. Which one of the following numbers lacks the common property in the series?

81, 36, 25, 9, 5, 16

(a) 5

(b) 9

(c) 36

(d) 25

102. In a certain code language, **“TIRED”** is written as **“56” **and **“BRAIN”** is written as **“44”**> How is **“LAZY”** written in that code language?

(a) 64

(b) 61

(c) 58

(d) 43

103. Select the missing number from the given response.

(a) 66

(b) 87

(c) 78

(d) 76

104. Which one of the following diagrams best depicts the relationship among Human Society – Youth Club, Political Party and Youths?

(a)

(b)

(c)

(d)

105. Among her children, Ganga’s favourites are Ram and Rekha. Rekha is the mother of Sharat, who is loved most by his uncle Mithun. The head of the family is Ram Lal, who is succeeded by his sons Gopoal and Mohan. Gopal and Ganga have been married for 35 years and have 3 children. What is the relation between Mithun and Mohan?

(a) Uncle

(b) Son

(c) Brother

(d) No relation

**PART-IV : MATHEMATICS**

106. If x cos α + y sin α = P is a tangent to the ellipse then

(a) a cos α + b sin α = P^{2}

(b) a sin α + b cos α = P^{2}

(c) a^{2} cos^{2} α + b^{2}sin^{2} α = P^{2}

(d) a^{2}sin^{2} α + b^{2}cos^{2} α = P^{2}

107. If a_{1}, a_{2}, a_{3} …….., a_{n} are in A.P. where a_{1} > 0 for all i, then

(a)

(b)

(c)

(d) none of these

108. In order to solve the differential equation the integrating factor is:

(a) x cos x

(b) x sec x

(c) x sin x

(d) x cosec x

109. Equation of two straight lines are and . Then

(a) The lines are non-coplanar

(b) The lines are parallel and distinct

(c) The lines intersect in unique point

(d) The lines are coincident

110. The equation of the curve passing through the point (a, −1/a) and satisfying the differential equation is

(a) (x + a) (1 + ay) = −4a^{2}y

(b) (x + a) (1 − ay) = 4a^{2}y

(c) (x + a) (1 − ay) = −4a^{2}y

(d) None of these

111. The locus of the mid-point of a chord of the circle x^{2} + y^{2} = 4, which subtends a right angle at the origin is

(a) x + y = 2

(b) x^{2} + y^{2} = 1

(c) x^{2} + y^{2} = 2

(d) x + y = 1

112. With the usual notation is equal to

(a) 4 + √2 − √3

(b) 4 − √2 + √3

(c) 4 − √2 – √3

(d) none of these

113.

(a)

(b)

(c)

(d)

114. If

(a)

(b)

(c)

(d)

115. If f(x) = 3x^{4} + 4x^{3} – 12x^{2} + 12, then f(x) is

(a) increasing in (–∞,–2) and in (0, 1)

(b) increasing in (–2, 0) and in (1, ∞)

(c) decreasing in (–2, 0) and in (0, 1)

(d) decreasing in (–∞,–2) and in (1, ∞)

116. Consider Then number of possible solutions are :

(a) Zero

(b) Unique

(c) Infinite

(d) None of these

117. The distance of a point (2, 5 –3) from the plane is

(a) 13

(b) 13/7

(c) 13/5

(d) 37/7

118. The value of definite integral is

(a) 0

(b) π/4

(c) π/2

(d) π

119. For the following feasible region, the linear constraints are

(a) x ≥ 0, y ≥ 0, 3x + 2y ≥ 12, x + 3y ≥ 11

(b) x ≥ 0, y ≥ 0, 3x + 2y ≤ 12, x + 3y ≥ 11

(c) x ≥ 0, y ≥ 0, 3x + 2y ≤ 12, x + 3y ≤ 11

(d) None of these

120. The general solution of differential equation (e^{x} + 1) ydy = (y + 1) e^{x} dx is

(a) (y + 1) = k(e^{x} + 1)

(b) y + 1 = e^{x} + 1 + k

(c) y = log {k(y + 1) (e^{x} + 1)}

(d)

121. What is the slope of the normal at the point (at^{2}, 2at) of the parabola y^{2} = 4ax?

(a) 1/t

(b) t

(c) −t

(d) −1/t

122. is equal to

(a) π^{2}/32

(b) π^{2}/16

(c) π/32

(d) None of these

123. If , then what is x equal to?

(a) 3

(b) 2

(c) 1

(d) 0

- The limit

(a) is equal to 1/2

(b) is equal to −1/2

(c) is equal to 2

(d) does not exist

125. If 2 cos^{2} x + 3 sin x – 3 = 0, 0 ≤ x ≤ 180°, then x = 0

(a) 30°, 90°, 150°

(b) 60°, 120°, 180°

(c) 0°, 30°, 150°

(d) 45°, 90°, 135°

126. If the number of available constraints is 3 and the number of parameters to be optimized is 4, then

(a) The objective function can be optimized

(b) The constraint are short in number

(c) The solution is problem oriented

(d) None of these

127. If then y'(1) is equal to

(a) 0

(b) 1/2

(c) −1

(d) −1/4

128. The maximum area of rectangle inscribed in a circle of diameter R is

(a) R^{2}

(b) R^{2}/2

(c) R^{2}/4

(d) R^{2}/8

129. If A and B are two events, such that P (A ⋃ B) = 3/4, P(A ⋂ B) = 1/4, P(A^{c}) = 2/3 where A° stands for the complementary event of A, then P(B) is given by:

(a) 1/3

(b) 2/3

(c) 1/9

(d) 2/9

130. If then

(a) f is continuous at x, when k = 0

(b) f is not continuous at x = 0 for any real k.

(c)

(d) None of these

131. is equal to

(a)

(b)

(c)

(d) None of these

132. The equation of chord of the circle x^{2} + y^{2} = 8x bisected at the point (4, 3) is

(a) x = 3

(b) y = 3

(c) x = −3

(d) y = −3

133. x and y are positive number. Let g and a be G.M. and Am of these numbers. Also let G be G. M. of x + 1 and y + 1. If and g are roots of equation x^{2} – 5x + 6 = 0, then

(a) x = 2, y = 3/4

(b) x = 3/4, y = 12

(c) x = 5/2, y = 8/5

(d) x = y = 2

134. The co-efficient of x^{n} in the expansion of

(a)

(b)

(c)

(d)

135. A pair of tangents are drawn from the origin to the circle x^{2} + y^{2} + 20(x + y) + 20 = 0, then the equation of the pair of tangent are

(a) x^{2} + y^{2} – 5xy = 0

(b) x^{2} + y^{2} + 2x + y = 0

(c) x^{2} + y^{2} – xy + 7 = 0

(d) 2x^{2} + 2y^{2} + 5xy = 0

136. If the sum of a certain number of terms of the A.P. 25, 22, 19, …..is 116. then the last term is

(a) 0

(b) 2

(c) 4

(d) 6

137. If 1, a and P are in A.P. and 1, g and P are in G.P., then

(a) 1 + 2a + g^{2} = 0

(b) 1 + 2a – g^{2} = 0

(c) 1 – 2a – g^{2} = 0

(d) 1 – 2a + g^{2} = 0

138. If y = sin x + e^{x}, then is equal to

(a)

(b)

(c)

(d) (−sin x + e^{x})^{−}^{1}

139. The foci of the hyperbola 4x^{2} – 9y^{2} – 1 = 0 are

(a) (±√13, 0)

(b) (±√13/6, 0)

(c) (0, ±√13/6)

(d) None of these

140. From the top of a cliff 50 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 45°. The height of tower is

(a) 50 m

(b) 50√3 m

(c) 50(√3 – 1)m

(d)

141. The coefficient of x^{2} tem in the binomial expansion of is:

(a) 70/243

(b) 60/423

(c) 50/13

(d) none of these

142. The value of λ, for which the circle x^{2} + y^{2} + 2λr + 6y + 1 = 0 intersects the circle x^{2} + y^{2} + 4x + 2y = 0 orthogonally, is

(a) 11/8

(b) −1

(c) −5/4

(d) 5/2

143. The value of is

(a)

(b)

(c) 1

(d) None of these

144. If f(x) = a – x^{n})^{1/n}, where a > 0 and n ∈ N, then fof(x) is equal to:

(a) a

(b) x

(c) x^{n}

(d) a^{n}

145. Sum of n terms of the series 8 + 88 + 888 + … equals

(a)

(b)

(c)

(d) None of these

146. The modulus of the complex number z such that |z + 3 – i| = 1 and arg(z) = π is equal to

(a) 3

(b) 2

(c) 9

(d) 4

147. Bag P contains 6 red and 4 blue balls and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?

(a) 7/15

(b) 8/15

(c) 4/19

(d) 8/19

148. The number of 4-digit number that can be formed with the digits, 1, 2, 3, 4 and 5 in which at least 2 digits are identical, is

(a) 505

(b) 4^{5} – 5!

(c) 600

(d) None of these

149. Consider the system of linear equations;

x_{1} + 2x_{2} + x_{3} = 3

2x_{1} + 3x_{2} + x_{3} = 3

3x_{1} + 5x_{2} + 2x_{3} = 1

The system has

(a) exactly 3 solutions

(b) a unique solution

(c) no solution

(d) infinite solutions

150. What is the value of y so that the line through (3, y) and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?

(a) 6

(b) 7

(c) 5

(d) 9

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