**BITSAT SOLVED PAPER-2022**

**PART-I**

**PHYSICS**

1. The stopping potential (V_{0}) versus frequency (v) of a graph of photoelectric effect in a metal. From the graph, the planck’s constant (h) is.

(a) 6.60 × 10^{−}^{34} J-s

(b) 6.69 × 10^{−}^{34} J-s

(c) 6.62 × 10^{−}^{34} J-s

(d) 6.63 × 10^{−}^{34} J-s

2. In a resonance column first and second resonance are obtained at depths 24 cm and 78 cm the third resonance will be obtained at depth.

(a) 160 cm

(b) 132 cm

(c) 131 cm

(d) 152 cm

3. A submarine A travelling at 17 m/s is being chased along the line of its velocity by another submarine B travelling at 34 m/s. B sends a sonar signal of 600 Hz to detect A and receives a reflected sound of frequency v. The of v is

[Speed of sound in water = 1500 ms^{−}^{1}]

(a) 613.7 Hz

(b) 6137 Hz

(c) 62 Hz

(d) 539 Hz

4. Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of the waves in A and B is

(a) 1 : 2

(b) 1 : √2

(c) 1 : 2√2

(d) 3 : 2√2

5. In the diagram shown below, both the strings AB and CD are made of same material and have same cross-section. The pulleys are light and frictionless. If the speed of wave in string AB is v_{1} and in CD is v_{2}, then v_{1}/v_{2} is

(a) 1

(b) √2

(c) 2

(d) 1/√2

6. What will be the acceleration due to gravity at a depth d, where g is acceleration due to gravity on the surface of earth?

7. A direct current of 6 A is superimposed on an alternating current I = 10 sin ωt flowing through a wire. The effective value of t he resulting current will be

(a) 5√2

(b) 5√3

(c) 9.27

(d) 8.37

8. Which one of the following graphs represents the variation of electric potential with distance r from the centre of a non-conducting charged sphere of radius R?

9. For an insulator, the forbidden energy gap is

(a) Zero

(b) 1eV

(c) 2eV

(d) 5eV

10. A machine gun fires 300 bullets per min if the mass of each bullet is 10 g and the velocity of the bullets is 600 ms^{−}^{1}, the power (in kW) of the gun is

(a) 43200

(b) 9

(c) 72

(d) 7.2

11. Four holes of radius 5 cm are cut from a thin square plate of 20 cm and mass 1 kg. The moment of inertia of the remaining portion about Z-axis is

(a) 15 kg-m^{2}

(b) 0.37 kg-m^{2}

(c) 0.0017 kg-m^{2}

(d) 0.08 kg-m^{2}

12. A particle of mass m is projected with velocity υ at an angle θ with the horizontal. At its highest point, it explodes into two pieces of equal mass, one of the piece continue to move on the original trajectory, then the velocity of second piece is.

(a) 2 v cos θ

(b) v cos θ

(c) 3 v cos θ

(d)

13. In the circuit shown assume the diode to be ideal. When V_{i} increases from −2V to 6V, the change in current is (in mA)

(a) Zero

(b) 20

(c) 25/8

(d) 32

14. The de-Broglie wavelength of an electron moving with a velocity is equal to the wavelength of photon. The ratio of the kinetic energies of electron and photon is

(a) 1 : 4

(b) 1 : 3

(c) 1 : 2

(d) 2 : 1

15. In the circuit shown in the figure, the AC source gives a voltage V = 20 cos (2000 t) neglecting source resistance, the voltmeter and ammeter reading will be

(a) 0V, 0.47 A

(b) 2.82 V, 1.41 A

(c) 1.41 V, 0.47 A

(d) 1.5 V, 8.37 A

16. An electromagnetic wave is propagating along X-axis. At x = 1 cm and t = 18s, its electric vector |E| = 8 V/m, then the magnitude of its magnetic vector is

(a) 2.66 × 10^{−}^{8}

(b) 3 × 10^{−}^{7}

(c) 3.14 × 10^{−}^{8}

(d) 3.16 × 10^{−}^{7}

17. In the following circuit the equivalent resistance between X and Y is …….. Ω

(a) 5

(b) 12

(c) 16

(d) 20

18. A monoatomic gas of molar mass m is kept in a insulated container. Container is moving with velocity v. If the container is suddenly stopped, then the change in the temperature of the gas is

(a) mv^{2}/4R

(b) mv^{2}/2R

(c) mv^{2}/R

(d) mv^{2}/3R

19. A projectile is projected with the velocity of The horizontal range of the projectile will be

(a) 1.2 m

(b) 2.4 m

(c) 3.6 m

(d) 4.5 m

20. A transistor is connected in common-emitter (CE) configuration. The collector supply is 8V and the voltage drop across a resistor is 500 Ω in the collector circuit is 0.6 V. If the current gain factor α is 0.96, find the base current

(a) 25 μA

(b) 50 μA

(c) 20 μA

(d) 35 μA

21. A solid sphere of 80 kg radius 15 m moving in a space becomes a circular disc of radius 20 m in 1 h. The rate of change of moment of Inertia in this process is ………

22. If the B – H curves of two samples of X and Y of iron are as shown below, then which one of the following statement is correct?

(a) Both X and Y are suitable for making electromagnets.

(b) Both X and Y are suitable for making permanent magnet.

(c) X is suitable for making permanent magnet and Y for making electromagnet.

(d) X is suitable for making electromagnet and Y is suitable for permanent magnet.

23. In a radioactive material the activity at time t_{1}, is A_{1} and at a later time t_{2}, it is A_{2}. If the decay constant of the material is λ, then

24. A mosquito O is sitting infront of a glass rod having spherical end of radius of curvature 40 cm. The image would be formed at

(a) 40 cm left

(b) infinity

(c) 20 cm to the right

(d) 15 cm to the left

25. One mole of an ideal diatomic gas undergoes a process as shown in the figure. The molar specific heat of the gas in the process is

(a) 3R/2

(b) R/2

(c) 5R/2

(d) 7R/2

26. A capillary tube is attached horizontally to a constant heat arrangement. If the radius of the capillary tube is increased by 25%, then the rate of flow of liquid will change nearly by

(a) 100%

(b) 112%

(c) 124%

(d) 144%

27. In the arrangement shown in figure, when the switch S_{2} is open, the galvanometer, shows no deflection of l = 50 cm when the switch S_{2} is closed, the galvanometer shows no deflection for l = 0.416 m. The internal resistance (r) of 6 V cell is

(a) 2 Ω

(b) 3 Ω

(c) 5 Ω

(d) 9 Ω

28. In a young’s double slit arrangement frings are produced using light of wavelength 4000 Å. One slit is covered by a thin plate of glass of refractive index 1.4 and the other with another glass plate of same thickness but of refractive index 1.7. By doing so the central bright shifts to original sixth fringe from centre. Thickness of glass plate is ………. .

(a) 2 μm

(b) 8 μm

(c) 11 μm

(d) 16 μm

29. An electric current I enters and leaves a uniform circular wire of radius r through diametrically opposite points. A charged particle q moves along the axis of circular wire passes through its centre at speed v. The magnetic force on the particle when it passes through the centre has a magnitude.

30. An achromatic convergent doublet of two lenses in contact has a power of +5D. The power of converging lens is +6D. The ratio of the dispersive power of the convergent and divergent lenses is

(a) 3 : 7

(b) 2 : 3

(c) 1 : 5

(d) 5 : 3

**PART II**

**Chemistry**

31. Which one of the following is correct or3der of given isotopes?

(I) T_{2} > D_{2} > P_{2} (order of boiling point)

(II) T_{2} > D_{2} > P_{2} (order of bond energy)

(III) T_{2} = D_{2} = P_{2} (order of bond length)

(IV) T_{2} < D_{2} < P_{2} (order of reactivity with Cl_{2})

(a) I and II

(b) III and IV

(c) II, III and IV

(d) All of these

32. Ninhydrin gives yellow colour in paper chromatography with which amino acid?

(a) Tryptophan

(b) Proline

(c) Alanine

(d) Tyrosine

33. How will raise in temperature affects the viscosity of liquids and gases?

(a) Both increases

(b) Both decreases

(c) In case of liquids, decreases and in case of gases increases.

(d) In case of liquid, increases and in case of gases, decreases.

34. Which of the following compounds is thermodynamically is the most stable?

(a) BaCO_{3}

(b) MgCO_{3}

(c) SrCO_{3}

(d) CaCO_{3}

35. Glucose reacts with X number of molecules of phenyl hydrazine to yield osazone. The value of X is,

(a) three

(b) two

(c) one

(d) four

36. Nylon-6, 6 is obtained from

(a) adipic acid and hexamethylene diamine

(b) tetrafluoroethylene

(c) vinyl cyanide

(d) vinyl benzene

37. What is the hybridization of [CrF_{6}]^{3}^{−}?

(a) sp^{3}d

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

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

(d) d^{2}sp

38. OF an F_{2} can be compared in terms of

(a) OF is paramagnetic while F_{2} is diamagnetic

(b) OF is more stable towards dissociation into atoms

(c) Both (a) and (b) are correct

(d) None of the above is correct

39. ortho and para form of hydrogen have

(a) different physical and chemical properties

(b) identical physical properties but different chemical properties

(c) identical chemical properties but different physical properties

(d) identical chemical and physical properties

40. The structure of H_{2}O_{2} is

(a) planar, linear

(b) non-planar, linear

(c) planar, non-linear

(d) non-planar, non-linear

41. Match the species in Column I with their types in Column II.

**Codes**

(a) A→4, B→3, C→2, D→1

(b) A→1, B→2, C→3, D→1

(c) A→2, B→3, C→1, D→4

(d) A→3, B→1, C→2, D→4

42. In which pair or pairs is the stronger bond found in the first species?

(I) O_{2}^{2}^{−}, O_{2}; (II) N_{2}, N_{2}^{+}; (III) NO^{+}, NO^{−}

(a) I only

(b) II only

(c) I and II only

(d) II and III only

43. Select the correct statement about the complex [Co(NH_{3})_{5}SO_{4}]Br.

(a) Its ionization isomer is [Co(NH_{3})_{5}Br]SO_{4}.

(b) It gives yellow precipitate with AgNO_{3}.

(c) Its ionization isomer give while precipitate with BaCl_{2}.

(d) All the above are correct statements.

44. A certain metal sulphide, MS_{2}, is used extensively as a high temperature lubricant. If MS_{2} is 40.06% by mass sulphur, metal M has atomic mass.

(a) 160 u

(b) 64 u

(c) 40 u

(d) 96 u

45.

X and Y are

(a) benzene, benzaldehyde

(b) toluene, benzaldehyde

(c) toluene, benzoic acid

(d) benzene, benzoic acid

46. Ge(II) compounds are powerful reducing agents whereas Pb(IV) compounds are strong oxidants. It can be because

(a) Pb is more electropositive than Ge.

(b) ionization potential of lead is less than that of Ge.

(c) ionic radii of Pb^{2+} and Pb^{4+} are larger than that of Ge^{2+} and Ge^{4+}

(d) more pronounced inert pair effect in lead has.

47. Which compound has antifluorite structure?

(a) MnO_{4}

(b) Na_{2}O

(c) Na_{2}O_{2}

(d) Li_{2}O_{2}

48. 100 mL of 2 M of formic acid (pK_{a} = 3.74) is neutralize by NaOH, at the equivalence point pH is

(a) 7

(b) 6

(c) 9.5

(d) 8.87

49. The reaction of C_{6}H_{5}CH = CHCH_{3} with HBr produces

50. The number of 3C−2e^{−} bonds present in diborane is

(a) 1

(b) 2

(c) 3

(d) 4

51. Standard entropy of X_{2}, Y_{2} and XY_{2} are 60, 40 and 50 JK^{−}^{1} mol^{−}^{1}, respectively. For the reaction, to be at equilibrium, the temperature will be

(a) 1250 K

(b) 500 K

(c) 750 K

(d) 1000 K

52. The total number of P−OH bonds for pyrophosphoric acid

(a) 4

(b) 5

(c) 6

(d) 8

53. Using the standard electrode potential, find out the pair between which redox reaction is not feasible.

E^{⊝} values Fe^{3+}/Fe^{2+} = +0.77; I_{2}/I^{−} = + 0.54 Cu^{2+}/Cu = +0.34; Ag^{+}/Ag = 0.80 V

(a) Fe^{3+} and I^{−}

(b) Ag^{+} and Cu

(c) Fe^{3+} and Cu

(d) Ag and Fe^{3+}

54. What is [NH_{4}^{+}] in a solution that is 0.02 M NH_{3}01 M KOH ? [K_{b}(NH_{3}) = 1.8 × 10^{−}^{5}]

(a) 3.6 × 10^{−}^{5} M

(b) 1.8 × 10^{−}^{5} M

(c) 0.9 × 10^{−}^{5} M

(d) 7.2 × 10^{−}^{5} M

55. For an isomerization reaction A ⇋ B, the temperature dependence of equilibrium constant is given by

The value of ∆S° at Hook is, therefore

(a) 4R

(b) 5R

(c) 400R

(d) 2000R

56. In an adiabatic process, no transfer of heat takes place between system and surrounding. Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following.

(a) q = 0, ∆T ≠ 0, W = 0

(b) q ≠ 0, ∆T = 0, W = 0

(c) q = 0, ∆T = 0, W = 0

(d) q = 0, ∆T < 0, W ≠ 0

57. The given graph represents the variation of compressibility factor (Z) = pV/nRT, for three real gases A, B and C. Identify the only incorrect statement.

(a) For the gas A, a = 0 and the dependence on p is linear at all pressure.

(b) For the gas B, b = 0 and its dependence on p is linear at all pressure.

(c) For the gas C, which is typical real gas for which neither, a nor b = 0. By knowing the minima and point of the intersection, with Z = 1, a and b can be calculated.

(d) At high pressure the slope is positive for all real gases.

58. Which one of the following statements in relation to the hydrogen atom is correct?

(a) 3s, 3p and 3d-orbitals all have the same energy.

(b) 3s and 3p-orbitals are of lower energy than 3d-orbital.

(c) 3p-orbital is lower in energy than 3d-orbital.

(d) 3s-orbital is lower in energy than 3p-orbital.

59. In the molecules CH_{4}, NF_{3}, NH_{4}^{+} and H_{2}O

(a) number of lone pairs are same

(b) all have same hybridization of centre of atom

(c) the bond angles are same

(d) number of bond pairs are same

60. 0.20 g of an organic compound gave 0.12 g of AgBr By using Carius method, the percentage of bromine in the compound will be

(a) 34.06%

(b) 44.04%

(c) 54%

(d) 25%

**PART III**

**(a) English Proficiency**

**Directions **(Q. Nos. 61-64) Choose the word which best expresses the meaning of the underlined word in the sentence.

61. __Forthrightness__ in speech may not always be a desirable quality.

(a) Outspokenness

(b) Obliqueness

(c) Mendacity

(d) Equivocation

62. The __inexorable__ demands of the workers brought the company to a closure.

(a) Unreasonable

(b) Relentless

(c) Monetary

(d) Violent

63. __Select the one which best expresses the same sentence in Passive/Active voice__.

Then her face was bowed.

(a) Then she was being bowed her face.

(b) Her face was bowed by them.

(c) Then she bowed her face.

(d) Then her face has been bowed.

64. The complex form of the sentence given below would be

Spare the rod and spoil the child.

(a) The child is spoiled if the rod is spared.

(b) The child becomes spoiled when the rod is spared.

(c) The child is spoiled whenever the rod is spared.

(d) The child is spoiled when the rod is spared.

**Directions **(Q. Nos. 65-66) Choose the word which is closest to the opposite in meaning of the given italicized word.

65. The attack on the freedom of the press is a *retrograde*

(a) progressive

(b) stubborn

(c) punitive

(d) aggressive

66. The leader might have had some *covert* reason for the change of his political affiliations.

(a) Unjustifiable

(b) Obvious

(c) Inexplicable

(d) Flimsy

**Directions **(Q. Nos. 67-68) In the following questions, out of the four alternatives, choose the one which can be substituted for the given word/sentence.

67. Regard for others as a principle of action or selflessly.

(a) Gynicism

(b) Nepotism

(c) Philanthropy

(d) Altruism

68. Code of diplomatic etiquette and precedence is

(a) Formalism

(b) Statesmanship

(c) Protocol

(d) Hierarchy

**Directions **(Q. Nos. 69-70) Choose the order of the sentences marked A, B, C and D to form a logical paragraph.

69. (A) Now under liberated economy they are learning to compete domestically and globally.

(B) In India corporations until recently achieved success by avoiding competition, using protected and regulated domestic markets.

(C) The trend is irreversible.

(D) Business leaders are preparing themselves to meet competitive challenges, and to avoid being swept away.

(a) BADC

(b) BDCA

(c) BDAC

(d) CDBA

70. (A) Recovery was given inadequate attention and consequently some bank branches regularly incurred heavy losses and their parent bodies had to bale them out.

(B) As a result, banks indulged in extensive lending to borrowers who had little or no potential to make repayments.

(C) To fulfill the social objectives laid down by the masters of nationalization, banks were asked to lend to identified priority sectors.

(D) 1992-93 results showed that the loss making branches of public sector banks increased from 10,000 to 13,000 and the quantum of losses showed at Rs. 3,369 crores.

(a) BACD

(b) DABC

(c) CBAD

(d) BCAD

**(b) Logical Reasoning**

71. Select the figure that can replace the question mark (?) in the following series.

72. ‘A + B’ means ‘A is the mother of B’.

‘A – B’ means ‘A is the brother of B’.

‘A × B’ means ‘A is the father of B’.

‘A ÷ B’ means ‘A is the daughter of B’.

If, P – K × Y – J ÷ S + R, then which of the following statement is not correct?

(a) K is husband of S

(b) Y is son of S

(c) J is daughter of P

(d) P is paternal uncle of R

73. Three different positions of the same dice are shown, the six faces of which are numbered from 1 to 6. Select the number that will be on the face opposite to the one showing ‘6’.

(a) 2

(b) 4

(c) 5

(d) 3

74. Select the option in which the given figure X is embedded (rotation is now allowed).

75. Select the letter-cluster that can replace the question mark (?) in the following series.

TULG, WRPC, ZOTY, CLXU, ?

(a) FIBQ

(b) FICR

(c) FJCQ

(d) GIAQ

76. How many triangles are there in the given figure?

(a) 33

(b) 18

(c) 31

(d) 29

77. The average marks of 50 students in a class was found to be 64. If the marks of two students were incorrectly entered as 38 and 42 instead of 83 and 24, respectively, then what is the correct average?

(a) 64.54

(b) 62.32

(c) 61.24

(d) 61.86

78. Select the correct mirror image of the given figure when the mirror is placed on the right of the figure.

79. Six friends A, B, C, D, E and F are sitting around a round table facing the centre. A sits second to the right of B, E sits second to the left of C. B doesn’t sit adjacent to E. D does not sit opposite to E or C. Who sits to the immediate left of E?

(a) A

(b) D

(c) B

(d) C

80. Five friends A, B, C, D and E bought cars which were priced differently. B’s car was costlier than C’s car but was less costly than E’s car. A’s car was costlier than D’s car but less costly than C’s car. Whose car was the 2^{nd} costliest?

(a) E

(b) A

(c) B

(d) C

81. In the following questions, complete the missing segment by selecting the appropriate figure from the given alternatives, (a), (b), (c) and (d).

82. In each of the following question, find out which of the answer figures (a), (b), (c) and (d) completes the figure matrix?

**Directions **(Q. No. 83-84) In the following questions two statements are given followed by two conclusions I and II. You have to consider the two statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any follow from the given statements.

**Give Answer**

(a) Only conclusion I follows

(b) Only conclusion II follows

(c) Both conclusions I and II follow

(d) Either conclusion I or II follows

83. **Statements** 60% of government employees went on strike.

Mr. Gopal is government employee.

**Conclusions**

(I) Mr. Gopal went on strike.

(II) Mr. Gopal did not participate in the strike.

84. **Statements**

Lawyers marry only fair girls.

Shobha is very fair.

**Conclusions**

(I) Shobha is marked to a lawyer.

(II) Shobha is not married to a lawyer.

85. In the question given below, find out which of the figures can be formed from the pieces given in the problem figure.

86. Select the option in which the words share the same relationship as that shared by the given pair of words.

Barometer : Pressure

(a) Ammeter : Current

(b) Thermometer : Volume

(c) Voltmeter : Heat

(d) Scale : Seconds

87. Select the option in which the words share the same relationship as that shared by the given set of words.

Cat : Lion : Jaguar

(a) Shark : Dolphin : Bat

(b) Sport; Athlete : Javelin

(c) Monkey : Chimpenzee : Gorilla

(d) Reptile : Snake : Toad

88. ‘Needle’ is related to ‘Sew’ in the same way as ‘Microscope’ is related to ‘……….’.

(a) Laboratory

(b) Lens

(c) Science

(d) Magnify

89. Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number.

14 : 289 : : 17 : 400 : : 21 : ?

(a) 576

(b) 504

(c) 570

(d) 441

90. Select the letter-cluster that can replace the question mark (?) in the following series.

TXB, QWE, NVH, KUK, ?

(a) ITM

(b) JTM

(c) HTN

(d) HSN

**PART IV**

**Mathematics**

91. If α be a root of the equation 4x^{2} + 2x – 1 = 0, then the other root of the equation is

(a) 4α^{3} + 2α

(b) 4α^{2} – 2α

(c) 4α^{3} – 3α

(d) 4α^{3} + 3α

92. If A = {x : x is a multiple of 4}. And,

B + { x : x is a multiple of 6}, then A ∩ B consist of multiple of

(a) 16

(b) 12

(c) 8

(d) 4

93. If |w| = 2, then the set of points is contained in or equal to the set of points z satisfying

(a) Im(z) = 0

(b) |Im(z)| ≤ 1

(c) |Re(z)| ≤ 2

(d) |z| ≤ 3

94. The value of is

(a) 1/6

(b) 1/8

(c) 1/10

(d) 1/12

95. Let a_{1}, a_{2}, ….. a_{40} be in AP and h_{1}, h_{2}, …. H_{10} be in HP. If a_{1} = h_{1} = 2 and a_{10} = h_{10} = 3, then a_{4}h_{7} is

(a) 2

(b) 3

(c) 5

(d) 6

96. The number of terms in the expansion of (1 + 5√2x)^{9} + (1 – 5√2x)^{9}, is

(a) 5

(b) 7

(c) 9

(d) 10

97. The number of different seven-digit numbers that can be written using only the three digit 1, 2 and 3 with the condition that the digit 2 occurs twice in each number is

(a) ^{7}C_{2}2^{5}

(b) ^{7}p_{2}2^{5}

(c) ^{7}C_{2}5^{2}

(d) None of these

98. Given 2x – y + 2z = 2, x – 2y + z = −4, x + y + λz = 4, then the value of λ such that the given system of equation has no solution is

(a) −3

(b) 1

(c) 0

(d) 3

99. Let and 10 If B is the inverse of A, then the value of α is

(a) 4

(b) −4

(c) 3

(d) 5

100. If x ∈ (0, π/2), then the value of is equal to

(a) x − cos^{−}^{1} (7 cos x)

(b) x + sin^{−}^{1} (7 cos x)

(c) x + cos^{−}^{1} (6 cos x)

(d) x + cos^{−}^{1} (7 cos x)

101. A running track of 440 ft is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is to be maximum, then the lengths of its side are

(a) 70 ft and 110 ft

(b) 80 ft and 120 ft

(c) 35 ft and 110 ft

(d) 35 ft and 120 ft

102. find general solution

(a) y = tan x(log|cosec x – cot x| + cos x + c)

(b) y = sec^{2} x + tan x + c

(c) y = log|sec x + tan x| + cosec x + c

(d) y = tan^{2} x + sin x + c

103. If the straight line y = mx + c touches the parabola y^{2} – 4ax + 4a^{3} = 0, then c is

104. A normal is drawn at the point P to the parabola y^{2} = 8x, which is inclined at 60° with the straight line y = 8. Then the point P lies on the straight line

(a) 2x + y – 12 – 4√3 = 0

(b) 2x – y – 12 + 4√3 = 0

(c) 2x – y – 12 – 4√3 = 0

(d) None of these

105. The value of is

106. The area of the region bounded by the parabola (y – 2)^{2} = (x – 1), the tangent to the parabola at the point (2, 3) and the X-axis is

(a) 3

(b) 6

(c) 9

(d) 12

107. are two non-collinear unit vectors such that Then the value of is equal to

108. A six faced die is a biased one. It is thrice more likely to show an odd numbers than show an even number. It is thrown twice. The probability that the sum of the numbers in two throws is even, is

(a) 5/9

(b) 5/8

(c) 1/2

(d) None of these

109. The sum of all the solution of the equation θ ∈ [0, 6π]

(a) 15π

(b) 30π

(c) 100π/3

(d) None of these

110. Let α be the solution of in (0, π/4). If the shadow of a vertical pole is 1/√3 of its height, then the altitude of the sun is

(a) α

(b) α/2

(c) 2α

(d) α/3

111. For each parabola y = x^{2} + px + q, meeting coordinate axes at 3-distinct points, if circles are drawn through these points, then the family of circles must pass through

(a) (1, 0)

(b) (0, 1)

(c) (1, 1)

(d) (p, q)

112. The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is

(a) 40

(b) 60

(c) 80

(d) 100

113. Let a_{1}, a_{2}, a_{3} …. Be a harmonic progression with a_{1} = 5 and a_{20} = 25. The least positive integer n for which a_{n} < 0, is

(a) 22

(b) 23

(c) 24

(d) 25

114. If the plane 3x + y + 2z + 6 = 0 is parallel to the line then the value of 3a + 3b is

(a) 1/2

(b) 3/2

(c) 3

(d) 4

115. Let a, b be the solutions of x^{2} + px + 1 = 0 and c, d be the solution of x^{2} + qx + 1 = 0. If (a – c) (b – c) and (a + d) (b + d) are the solution of x^{2} + ax + β = 0, then β is equal to

(a) p + q

(b) p – q

(c) p^{2} + q^{2}

(d) q^{2} – p^{2}

116. If then

(a) a = 1, b = 1

(b) a = sin 2θ, b = cos 2θ

(c) a = cos 2θ, b = sin 2θ

(d) None of these

117. The value of is

(a)

(b)

(c) e/24

(d) None of these

118. The locus of the mid-point of the chord if contact of tangents drawn from points lying on the straight line 4x – 5y = 20 to the circle x^{2} + y^{2} = 9 is

(a) 20(x^{2} + y^{2}) – 36x + 45y = 0

(b) 20(x^{2} + y^{2}) + 36x – 45y = 0

(c) 36(x^{2} + y^{2}) – 20x + 45y = 0

(d) 36(x^{2} + y^{2}) + 20x – 45y = 0

119. Let and f(0) = 0, then the value of f(1) be

(a) log(1 + √2)

(b)

(c)

(d) None of these

120. The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are

(a) 2 and 9

(b) 3 and 8

(c) 4 and 7

(d) 5 and 6

121. In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. If the middle term of AP be equal to the middle term of the GP, then the middle term of the entire sequence is

(a) −10/31

(b) 10/31

(c) 32/31

(d) −31/32

122. If p ≠ a, q ≠ b, r ≠ c and the system of equations

px + ay + az = 0

bx + qy + bz = 0

cx + cy + rz = 0

has a non-trivial solution, then the value of is

(a) 1

(b) 2

(c) 1/2

(d) 0

123. If g(x) = x^{2} + x – 2 and then f(x) is equal to

(a) 2x – 3

(b) 2x + 3

(c) 2x^{2} + 3x + 1

(d) 2x^{2} – 3x + 1

124. The smallest positive integral value of n such that is purely imaginary, is equal to

(a) 4

(b) 3

(c) 2

(d) 8

125. A house subtends a right angle at the window of a opposite house and the angle of elevation of the window from the bottom of the first house is 60. If the distance between two houses be 6 m, then the height of the first house is

(a) 8√3 m

(b) 6√3 m

(c) 4√3 m

(d) None of these

126. A spherical balloon is filled with 4500π cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic meters per minute then the rate (in meters per minute) at which the radius of the balloon decreases 49 min after the leakage began is

(a) 9/7

(b) 7/9

(c) 2/9

(d) 9

127. If in a ∆ABC, 2b^{2} = a^{2} + c^{2}, then is equal to

128. If the sum of the coefficients in the expansion of (x + y)^{n} is 1024, then the value of greatest coefficient in the expansion is

(a) 356

(b) 252

(c) 210

(d) 120

129. The area enclosed by the curves y = sin x + cos x and y = |cos x – sin x| over the interval [0, π/2] is

(a) 4(√2 – 1)

(b) 2√2(√2 – 1)

(c) 2(√2 + 1)

(d) 2√2(√2 + 1)

130. If α, β, γ ∈ [0, π] and if α, β, γ are in AP, then is equal to

(a) sin β

(b) cos β

(c) cot β

(d) 2 cos β

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