BITSAT Past Paper

BITSAT SOLVED PAPER-2021

PART-I

PHYSICS

1. An ideal monoatomic gas is taken round the cycle of ABCDA as shown in the p-V diagram.

The work done during the cycle is

(a)   pV

(b)   2pV

(c)   pV/2

(d)   zero

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2. The initial speed of a body of mass 2.0 kg is 5 m/s. A force acts for 4 s in the direction of motion of the body, as shown in force-time graph. The impulse of force is

(a)   8.50 Ns

(b)   8 Ns

(c)   5.5 Ns

(d)   6 Ns

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3. For a constant hydraulic stress on an object, the fractional change in the object’s volume (∆V/V) and its bulk modulus B are related as

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4. A shunt is connected in parallel with a galvanometer. Why?

(a)   To prevent galvanometer from strong current

(b)   To convert galvanometer into ammeter

(c)   To increase the range of ammeter

(d)   All of the above

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5. The phase difference between the V_out­ and V­_in of CE-amplifier circuit is

(a)   90°

(b)   180°

(c)   0°

(d)   270°

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6. If nth division of main scale coincides with (n + 1)th divisions of vernier scale. The least count of the vernier is (Given, one main scale division is equal to a units)

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7. A uniform rod AB of length L = 1 m is sliding along two mutually perpendicular surfaces OP and OQ as shown in figure.

When the rod subtends an angle θ = 30° with OQ, then the end B has a velocity √3 m/s. The velocity of end A at that time is

(a)   1 m /s

(b)   0.5 m/s

(c)   √3 m/s

(d)   1/√3 m/s

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8. A tray of mass (M) 12 kg is supported by a spring as shown in figure.

When the tray is pressed down and released, it executes SHM with a period of 1.5 s. When a block of mass m placed on the tray, then the period of SHM changes to 3.0 s. The mass of block is

(a)   36 kg

(b)   48 kg

(c)   12 kg

(d)   24 kg

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9. The phasor diagram of a load represents which circuit?

(a)   Purely capacitive

(b)   Purely inductive

(c)   R-L-C circuit with X_L more than X_C

(d)   R-L-C circuit with X_L less than X_C

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10. The equation of progressive wave is given by  Which one of the following is correct?

(a)   υ = 5 cm/s

(b)   λ = 18 cm

(c)   A = 0.04 cm

(d)   f = 50 Hz

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11. The property of light used in optical fibre cable is

(a)   total internal reflection

(b)   refraction

(c)   interference

(d)   polarization

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12. A man walks in a straight line for 5 mine with a velocity of 45 m/s. What is the speed with which he has to move in order to comeback to its original position in 1.5 min?

(a)   90 m/s

(b)   150 m/s

(c)   135 m/s

(d)   115 m/s

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13. From a solid sphere of mass M and radius R, spherical portion of radius R/2 is removed as shown in the figure.

Taking gravitational potential V = 0 at r = ∞, the potential at the centre of the cavity thus formed is

(a)   −GM/2R

(b)   −GM/R

(c)   −2GM/3R

(d)   −2GM/R

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14. Four charges equal to +Q are placed at the four corners of a square and a charge (−q) is at its centre. If the system is in equilibrium, then the value of –q is

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15. A force F = a + bx acts on a particle in the x-direction, where a and b are constants. The work done by this force during a displacement from x =0 to x = d is

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16. A proton has kinetic energy E = 100 eV which is equal to that of a photon. The wavelength of photon is λ₂ and that of proton is λ₁. The ratio λ₂/λ₁ is proportional to

(a)   E²

(b)   E^1/2

(c)   E⁻¹

(d)   E^−1/2

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17. A block of mass 10 kg rests on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of static friction between the block and the plane is 0.1. The friction force on the block is

(a)   4.9 N

(b)   49√3 N

(c)   49 N

(d)   0.1 × 49√3 N

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18. Which of the following graphs show the correct relation between conductivity and temperature for a metallic conductor?

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19. The radius of a muonic hydrogen atom is 2.5 × 10⁻¹³ The total atomic volume (in m³) of a mole of such hydrogen atoms is

(Take, π = 3.14)

(a)   3.94 × 10⁻¹⁴

(b)   3.09 × 10⁻¹⁴

(c)   4 × 10⁻¹⁴

(d)   3.9 × 10⁻¹⁴

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20. The angular momentum of a body placed at origin of mass 1 kg and having position vector  is

(a)   time dependent

(b)  

(c)  

(d)   0

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21. If the earth stops rotating about its axis, then what will be the change in the value of g at a place in the equatorial plane?

(Radius of earth = 6400 km)

(a)   3.7 cm/s²

(b)   9.8 m/s²

(c)   0

(d)   3.4 cm/s²

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22. Two cars approach a stationary observer from opposite sides as shown in the figure.

The observer hears to beats. If the frequency of the horn of the car B is 504 Hz, then the frequency of the horn of the car A will be

(a)   529.2 Hz

(b)   440.5 Hz

(c)   295.2 Hz

(d)   None of these

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23. 

In the following circuit, assuming point A to be at zero potential, then what is the potential at point B?

(a)   1 V

(b)   2 V

(c)   4 V

(d)   3 V

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24. Two plane mirrors A and B are aligned parallel to each other as shown in the figure.

A ray of light is incident at an angle 30° at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times, the ray undergoes reflection (excluding the first one) before it emerges out is

(a)   28

(b)   34

(c)   30

(d)   29

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25. A projectile is given an initial velocity of  where  is along the ground and  is along the vertical. If g = 10 m/s², then the equation of its trajectory is

(a)   y = x  + 5x²

(b)   y = x – 5x²

(c)   y = x² + 5x

(d)   y = x² – 5x

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26. Two drops of equal radius R coalesce to form a bigger drop. What is the ratio of surface energy of bigger drop to smaller one?

(a)   2^−1/3; 1

(b)   2^2/3 : 1

(c)   1 : 1

(d)   2^1/2 : 1

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27. Two particles A and B of masses m_A and m_B respectively, are having same charge and moving on same plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are v_A and v_B­ respectively and the trajectories are as shown in figure. Then,

(a)   m_A = m_B and v_A = v_B

(b)   m_Av_A > m_B­v_B

(c)   m_A < m_B and v_A < υ_B

(d)   m_Av_A < m_Bv_B

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28. The potential difference applied to an X-ray tube is decreased. As a result, in the emitted radiation,

(a)   the intensity increases

(b)   the intensity decreases

(c)   the minimum wavelength increases

(d)   the minimum wavelength decreases

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29. The ratio of the specific heats  in terms of degrees of freedom n is given by

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30. A cyclist speeding at 6 m/s in a circle of 18 m radius makes an angle θ with the vertical. The minimum possible value of coefficient of friction between the tyres and the ground is

(a)   12.041

(b)   0.2041

(c)   11.32

(d)   10.020

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31. Three particles each of mass m are kept at the vertices of an equilateral triangle of side b. Moment of inertia of the system about an axis passing through the centroid and perpendicular to its plane is

(a)   3 mb²

(b)   mb²

(c)   mb²/3

(d)  

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32. An electric dipole is placed at an angle of 30° in a non-uniform electric field. The dipole will experience

(a)   torque only

(b)   translational force only in the direction of the field

(c)   translational force only in a direction normal to the direction of the field

(d)   torque as well as a translational force

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33. Two coils A and B have a mutual inductance 0.001 H. The current changes in the first coil according to the equation i = i₀ sin ωt, where i₀ = 10A and ω = 10π rads⁻¹. The maximum value of emf in the second coil is

(a)   0.01 π V

(b)   1 πV

(c)   0.1 π V

(d)   0.05 π V

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34. The current in the circuit will be

(a)   0.125 A

(b)   0.1 A

(c)   0.5 A

(d)   0.25 A

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35. The bob of a pendulum of length 2m lies at P, when it reaches Q, it loses 10% of its total energy due to air resistance.

The velocity of bob at Q is

(a)   6 m/s

(b)   1 m/s

(c)   2 m/s

(d)   8 m/s

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36. A particle executes SHM with a frequency f. The frequency with which its kinetic energy oscillates is

(a)   f/2

(b)   f

(c)   2f

(d)   4f

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37. A radioactive sample at any instant has its disintegration rate 5000 disintegrations per min. After 5 min, the rate is 1250 disintegrations per min. Then, the disintegration constant (per min) is

(a)   0.4 log_e 2

(b)   0.2 log_e 2

(c)   0.1 log_e 2

(d)   0.8 log_e 2

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38. The separation between two parallel plates of capacitor is 1 mm. What is the electric potential generates between the plates of capacitor, when electric field of 2000 N/C is applied on it?

(a)   2 V

(b)   2000 V

(c)   0.2 V

(d)   200 V

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39. Choose the correct statement.

(a)   The speed of light in the meta-material is υ = c|n|.

(b)   The speed of light in the meta-material is υ = c/|n|.

(c)   The speed of light in the meta-material is υ = c.

(d)   The wavelength of the light in the meta-material (λ_m) is given by λ_m = λ_air|n|.

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40. A T-shaped object with dimensions shown in figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

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PART II

Chemistry

41. The most volatile compound among the given option is

(a)   o-nitrophenol

(b)   p-nitrophenol

(c)   m-nitrophenol

(d)   can’t say

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42. What is the magnetic moment of Ti²⁺?

(Given : Atomic number = 22)

(a)   √8

(b)   √10

(c)   √6

(d)   √9

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43. Why only Xe can form compounds with fluorine among noble gases?

(a)   Large size

(b)   Low electronegativity

(c)   High ionization energy

(d)   Low electron gain enthalpy

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44. Which of the following inert gas is used as cryogenic agent?

(a)   He

(b)   Ne

(c)   Ar

(d)   Kr

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45. For the following reaction,

2A + 3B → 3C + 4D

Expression for rate of reaction is

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46. Cyclohexanol on reacting with H₂SO₄ and then heating gives

(a)   cyclohexene

(b)   cyclohexanone

(c)   cyclohexanol

(d)   None of these

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47. The major product obtained on reaction of 3-methylbutene with HCl is

(a)   2-chloro-2-methylbutane

(b)   3-chloro-2-methylbutane

(c)   1-chloro-2-methylbutane

(d)   3-chloro-3-methylbutane

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48. If Rydberg constant is same for all elements, the angular momentum and energy of Li²⁺ of which orbital is equal to angular momentum and energy of 1s-orbital of hydrogen atom?

(a)   3s

(b)   4s

(c)   2p

(d)   3d

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49. Sodium iodide reacts with ammonia to give

(a)   [Na(NH₃)₄]I

(b)   [Na(NH₃)₄]I₃

(c)   [Na(NH₃)I₃]I

(d)   [Na(NH₃)₃I]

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50. In photography, which compound is used as a fixing agent

(a)   sodium thiosulphate

(b)   ammonium thiosulphate

(c)   sodium chloride

(d)   Both (a) and (b)

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51. The compound formed on reaction of epoxy ethane with NH₃ and H₂O is

(a)   mono-ethanol amines

(b)   di-ethanol amines

(c)   tri-ethanol amines

(d)   All of these

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52. The process of removal of excess electrolyte from colloidal solution is

(a)   coagulation

(b)   dialysis

(c)   ultra-filtration

(d)   peptisation

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53. Maltase converts maltose into

(a)   glucose

(b)   sucrose

(c)   fructose

(d)   starch

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54. Starch is a polymer of

(a)   glucose

(b)   fructose

(c)   Both (a) and (b)

(d)   None of these

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55. Methyl alcohol can be distinguished from ethyl alcohol using

(a)   Fehling solution

(b)   Schiff’s reagent

(c)   Sodium hydroxide and iodine

(d)   Phthalein fusion test

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56. Sodium stearate (C₁₇H₃₅COO⁻Na⁺) is

(a)   anionic soap

(b)   cationic detergent

(c)   anionic detergent

(d)   Non-ionic soap

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57. Which is not an anti-fluorite structure

(a)   Rb₂S

(b)   BaF₂

(c)   K₂O

(d)   Li₂O

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58. The structure of ClF₃ is

(a)   T-shape

(b)   bent shape

(c)   linear

(d)   trigonal planar

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59. Which of the following is diamagnetic in nature?

(a)   O₂

(b)   O₂²⁻

(c)   N₂²⁺

(d)   B₂

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60. The correct order of bond order in SO₂, SO₃, SO₄²⁻, SO₃²⁻ is

(a)   SO₃²⁻ > SO₄²⁻ > SO₃ = SO₂

(b)   SO₄²⁻ > SO₃ > SO₂ > SO₃²⁻

(c)   SO₂ = SO₃ > SO₄²⁻ > SO₃²⁻

(d)   Can’t say

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61. Ionisation energy for H⁺ ion is proportional to rⁿ, then value of n is

(a)   1

(b)   −1

(c)   2

(d)   −2

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62. Role of BHA in food industries

(a)   prevent oxidation

(b)   prevent reduction

(c)   add sweeteners

(d)   None of these

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63. Permanganate ion (MnO₄⁻) is dark purple coloured though Mn is in +7 oxidation state with d⁰ This is due to

(a)   d – d transition

(b)   charge transfer from metal to ligand

(c)   charge transfer from ligand to metal

(d)   All of the above

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64. Rutherford model could not explain

(a)   electronic structure of an atom

(b)   stability of an atom

(c)   Both (a) and (b)

(d)   None of the above

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65. Which is true in case of [Ni(CO)₄]?

(a)   Hybridization of Ni is sp³

(b)   Hybridization of Ni is dsp²

(c)   Paramagnetic

(d)   Square planar

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66. SI unit of Boltzmann’s constant is

(a)   JK⁻¹

(b)   eVK⁻¹

(c)   ergK⁻¹

(d)   JK

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67. Acetone does not undergo which type of reaction?

(a)   Substitution reaction

(b)   Polymerization reaction

(c)   Condensation reaction

(d)   Addition reaction

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68. Magnetic moment of Co in [CoF₆]²⁻ of unpaired electron is

(a)   √35

(b)   √45

(c)   √40

(d)   √30

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69. Some statement about heavy water are given below

(1) Heavy water is used as a moderator in nuclear

(2) Heavy water is more associated than ordinary water.

(3) Heavy water in more effective solvent than ordinary water.

Which of the above statements are correct?

(a)   1 and 2

(b)   1, 2 and 3

(c)   2 and 3

(d)   1 and 3

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70. CH₃−CHCl−CH₂−C₃ has a chiral centre, which of the following represents its R configuration?

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71. In Victor Meyer’s method 0.2 g of an organic substance displaced 56 mL of air at STP the molecular weight of the compound is

(a)   56

(b)   112

(c)   80

(d)   28

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72. For the complete combustion of ethanol, C₂H₅OH(l) + 3O₂(g) → 2CO₂(g) + 3H₂O(l)the amount of heat produced as measured in bomb calorimeter is 1364.47 kJ mol⁻¹ at 25° Assuming ideality the enthalpy of combustion, ∆H_C, for the reaction will be

(R = 8.314 JK⁻¹ mol⁻¹)

(a)   −1366.95 kJ mol⁻¹

(b)   −1361.95 kJ mol⁻¹

(c)   −1460.50 kJ mol⁻¹

(d)   −1350.50 kJ mol⁻¹

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73. The incorrect expression among the following is

(a) 

(b)   In isothermal process, 

(c)  

(d)

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74. The solubility of Pb(OH)₂ in water is 6.7 × 10⁻⁶ Its solubility in a buffer solution of pH = 8 would be

(a)   1.2 × 10⁻²

(b)   1.6 × 10⁻³

(c)   1.6 × 10⁻²

(d)   1.2 × 10⁻³

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75. The density (in g mL⁻¹) of a 60 M sulphuric acid solution that is 29% H₂SO₄ (molar mass = 98 g mol⁻¹) by mass will be

(a)   1.64

(b)   1.88

(c)   1.22

(d)   1.45

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76. The relative lowering of vapour pressure of a dilute aqueous solution containing non-volatile solute is 0.0125. The molality of the solution is about

(a)   0.70

(b)   0.50

(c)   0.90

(d)   0.80

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77. Equal masses of methane and oxygen are mixed in an empty container at 25° The fraction of the total pressure exerted by oxygen is

(a)   2/3

(b)

(c)   1/3

(d)   1/2

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78. The molar conductivities of KCl NaCl and KNO₃ are 152, 128 and 111 S cm² mol⁻¹ What is the molar conductivity of NaNO₃?

(a)   101 S cm² mol⁻¹

(b)   87 S cm² mol⁻¹

(c)   −101 S cm² mol⁻¹

(d)   −391 S cm² mol⁻¹

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79. The approximate time duration in hours to electroplate 30 g of calcium form molten calcium chloride using a current of 5 A is (Atomic mass of Ca = 40)

(a)   80

(b)   10

(c)   16

(d)   8

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80. Given, the reduction potential of Na⁺, Mg²⁺, Al³⁺ and Ag⁺ as 

The least stable oxide is

(a)   Ag₂O

(b)   Al₂O₃

(c)   MgO

(d)   Na₂O

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PART III

(a) English Proficiency

Directions (Q. Nos. 81-83) Choose the word which best expresses the meaning of the underlined word in the sentence.

81. Decay is an immutable factor of human life.

(a)   important

(b)   unique

(c)   unchangeable

(d)   awful

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82. It was an ignominious defect for the team.

(a)   shameful

(b)   admirable

(c)   unaccountable

(d)   worthy

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83. His conjecture was the better than mine.

(a)   guess

(b)   fact

(c)   surprise

(d)   doubt

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Directions (Q. Nos. 84-86) Fill in the blanks.

84. Freedom and equality are the ………. Rights of every human.

(a)   inalienable

(b)   inscrutable

(c)   incalculable

(d)   institutional

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85. Pradeep’s face spoke …………. of the happiness he was feeling.

(a)   elegantly

(b)   tons

(c)   volumes

(d)   much

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86. His speech was disappointing : it …………. All the major issues.

(a)   projected

(b)   revealed

(c)   skirted

(d)   analysed

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Directions (Q. Nos. 87-89) Choose the word which is closest to the opposite in meaning of the given italicized word.

87. Hydra is biologically believed to be immortal.

(a)   undying

(b)   perishable

(c)   ancient

(d)   eternal

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88. The Gupta rulers patronized all cultural activities and thus Gupta period was called the golden era in Indian History.

(a)   criticized

(b)   rejected

(c)   opposed

(d)   spurned

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89. This is a barbarous

(a)   bad

(b)   good

(c)   civilized

(d)   exemplary

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Directions (Q. Nos. 90-92) In each of the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence.

90. A person who does not believe in any religion

(a)   Philatelist

(b)   Rationalist

(c)   Atheist

(d)   Pagan

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91. A person who believes that pleasure is the chief good

(a)   Stoic

(b)   Hedonist

(c)   Epicure

(d)   Sensual

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92. One who loves mankind

(a)   Anthropologist

(b)   Philanthropist

(c)   Seismologist

(d)   Optometrist

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Directions (Q. Nos. 93-95) Choose the order of the sentence marked A, B, C, D and E to form a logical paragraph.

93. (A) Tasty and healthy food can help you bring out their best.

(B) One minute they are toddlers and next you see them in their next adventure.

(C) Your young ones seem to be growing so fast.

(D) Being their loving custodians, you always want to see them doing well.

(E) Their eyes sparkle with curiosity and endless questions on their tongues.

Codes

(a)   DBCEA

(b)   CADEB

(c)   CBEDA

(d)   ECABD

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94. (A) It is hoping that overseas friends will bring in big money and lift the morale of the people.

(B) But a lot needs to be done to kick start industrial revival.

(C) People had big hopes from the new government.

(D) So far government has only given an incremental push to existing policies and programmes.

(E) Government is to go for big time reforms, which it promised.

Codes

(a)   BCDAE

(b)   EADCB

(c)   DABEC

(d)   CDEAB

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95. (A) However, women hiring is catching up at a slow and steady rate in the recent times.

(B) Gender ratio has been inclined more towards male employees.

(C) As a result, recent reports have highlighted the rise in demand for women employees.

(D) Women constitute a little over half of world’s total population.

(E) But, their contribution to measured economic activity is far below the potential.

Codes

(a)   DEBAC

(b)   CDAEB

(c)   BCDEA

(d)   AEDBC

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(b) Logical Reasoning

96. Choose the correct answer figure which will make a complete square on joining with the problem figure.

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

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

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99. From the given four positions of a single dice, find the colour at the face opposite to the face having red colour.

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100. In the following questions, one or more dots are placed in the figure marked as (A). The figure is followed by four alternatives marked as (a), (b), (c) and (d). One out of these four options contains region(s) common to the circle, square, triangle, similar to that marked by the dot in figure (A).

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

G4T, J9R, M20P, P43N, S90L, ?

(a)   S90L

(b)   V185J

(c)   M20P

(d)   P43N

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102. Neeraj starts walking towards South. After walking 15 m, he turns towards North. After walking 20 m, he turns towards East and walks 10 m. He then turns towards South and walks 5 m. How far is he from his original position and in which direction?

(a)   10 m, East

(b)   10 m, South-East

(c)   10 m, West

(d)   10 m, North-East

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103. The average age of 8 men is increased by 2 yrs. when one of them whose age is 20 yr is replaced by a new man. What is the age of the new man?

(a)   28 y r

(b)   36 yr

(c)   34 yr

(d)   35 yr

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104. Shikha is mother-in-law of Ekta who is sister-in-law of Ankit. Pankaj is father of Sanjay, the only brother of Ankit. How is Shikha related to Ankit?

(a)   Mother-in-law

(b)   Aunt

(c)   Wife

(d)   Mother

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105. In a row of forty children, P is thirteenth from the left end and Q is ninth from the right end. How many children are there between P and R, if R is fourth to the left of Q?

(a)   12

(b)   13

(c)   14

(d)   15

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PART IV

Mathematics

106. If Re(z + 2) = |z – 2|, then the locus of z is

(a)   parabola

(b)   circle

(c)   ellipse

(d)   hyperbola

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107. If a ∈ R, b ∈ R, then the equation

x² – abx – a² = 0 has

(a)   one positive root and one negative root

(b)   Both positive roots

(c)   Both negative roots

(d)   Non-real roots

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108. If a + 2b + 3c = 12 (a, b, c ∈ R⁺), then the maximum value of ab²c³ is

(a)   2³

(b)   2⁴

(c)   2⁶

(d)   2⁵

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109. Sum of n terms of the infinite series

1.3² + 2.5² + 3.7² + … ∞ is

Show Answer

110. If log₇ 5 = a, log₅ 3 = b and log₃ 2 = c, then the logarithm of the number 70 to the base 225 is

Show Answer

111. The maximum number of points of intersection of 10 circles is

(a)   80

(b)   90

(c)   85

(d)   95

Show Answer

112. 

(a)   120

(b)   260

(c)   210

(d)   180

Show Answer

113. If p ≠ q ≠ r and  then the value of x which satisfy the equation is

(a)   x = p

(b)   x = q

(c)   x = r

(d)   x = 0

Show Answer

114. Matrix  if xyz = 60 and 8x + 4y + 3z = 20, then A(adj A) is equal to

Show Answer

115. If f(x) = 4x – x², x ∈ R, and f(a + 1) – f(a – 1) = 0, then a is equal to

(a)   0

(b)   2

(c)   1

(d)   3

Show Answer

116. Which of the following is not an equivalence relation in z?

(a)   aRb ⇔ a + b is an even integer

(b)   aRb ⇔ a − b is an even integer

(c)   aRb ⇔ a < b

(d)   aRb ⇔ a = b

Show Answer

117. Which of the following is always true?

(a)   (~ p ˅ ~ q) ≡ (p ˄ q)

(b)   (p → q) ≡ (~ p → ~ p)

(c)   ~(p → ~ q) ≡ (p ˄ ~ q)

(d)   ~(p ⟷ q) ≡ (p → q) → (q → p)

Show Answer

118. The solution of the inequation 4^{−x + 0.5} – 7.2^−x < 4, x ∈ R is

(a)   (−2, ∞)

(b)   (2, ∞)

(c)   (2, 7/2)

(d)   None of these

Show Answer

119. If  is identity in x, then

(a)   a₃ = 3/8, a₂ = 0

(b)   n =6, a₁ = 1/2

(c)   n = 5, a₁ = 3/4

(d)   ∑a_m = 1/4

Show Answer

120. Total number of solutions of  x ∈ [0, 3π] is equal to

(a)   1

(b)   2

(c)   3

(d)   0

Show Answer

121. The minimum value of (sin⁻¹ x)³ + (cos⁻¹ x)³ is equal to

(a)   π³/32

(b)   5π³/32

(c)   9π³/32

(d)   11π³/32

Show Answer

122. The origin is shifted to (1, 2). The equation y² – 8x – 4y + 12 = 0 changes to y² = 4ax, then a is equal to

(a)   1

(b)   2

(c)   −2

(d)   −1

Show Answer

123. The equations of the bisector of the angles between the straight lines 3x + 4y + 7 = 0 and 12x + 5y – 8 = 0 are

(a)   7x + 9y + 17 = 0, 99x + 77y + 51 = 0

(b)   7x – 9y – 17 = 0, 99x + 77y – 51 = 0

(c)   7x – 9y + 17 = 0, 99x + 77y + 51 = 0

(d)   None of the above

Show Answer

124. Equation of circle which passes through the points (1, −2) and (3, −4) and touch the X-axis is

(a)   x² + y² + 6x + 2y + 9 = 0

(b)   x² + y² + 10x + 20y + 25 = 0

(c)   x² + y² + 6x + 4y + 9 = 0

(d)   None of the above

Show Answer

125. If x = 9 is the chord of contact of the hyperbola x² – y² = 9, then the equation of the corresponding pair of tangent is

(a)   9x² – 8y² + 18x – 9 = 0

(b)   9x² – 8y² – 18x + 9 = 0

(c)   9x² – 8y² – 18x – 9 = 0

(d)   9x² – 8y² + 18x + 9 = 0

Show Answer

126. The points with position vectors  and  are collinear, if a is

(a)   −8

(b)   4

(c)   2

(d)   82/9

Show Answer

127. Let a, b, c be vectors of lengths 3, 4, 5 respectively and a be perpendicular to (b + c), to (c + a) and c to (a + b), then the value of (a + b + c) is

(a)   2√5

(b)   2√2

(c)   10√5

(d)   5√2

Show Answer

128. For non-zero vectors, a, b, c; |(a × b) ∙ c| = |a| |b| |c| holds if and only if

(a)   a ∙ b = 0, b ∙ c = 0

(b)   b ∙ c = 0, c ∙ a = 0

(c)   c ∙ a = 0, a ∙ b = 0

(d)   a ∙ b = b ∙ c = c ∙ a = 0

Show Answer

129. Angle between the diagonals of a cube is

(a)   π/3

(b)   π/2

(c)   cos⁻¹(1/3)

(d)   cos⁻¹(1/√3)

Show Answer

130. Consider the two lines

The unit vector perpendicular to both the lines L₁ and L₂ is

Show Answer

131. The distance between the line  and the plane  is

(a)   10/9

(b)   10/3√3

(c)   10/3

(d)   None of these

Show Answer

132. Two cards are drawn from a pack of 52 cards. What is the probability that either both are red or both are kings?

(a)   7/13

(b)   63/221

(c)   55/221

(d)   3/26

Show Answer

133. If A and B are two independent events such that P(A) = 1/2 and P(B) = 1/5, then which of the following is correct?

Show Answer

134. Box 1 contains 5 red and 2 blue balls, while box II contains 2 red and 6 blue balls. A fair coin is tossed. If it turns up head, a ball is drawn from box I, else a ball is drawn from box II. The probability ball drawn is from box I, if it is blue, is

(a)   27/56

(b)   8/29

(c)   21/29

(d)   29/56

Show Answer

135. For a random variable X, E(X) = 3 and E(X²) = 11. The variable of X is

(a)   8

(b)   5

(c)   2

(d)   1

Show Answer

136. The sum of 10 items is 12 and the sum of their squares is 18, then the standard deviation will be

(a)   −3/5

(b)   6/5

(c)   4/5

(d)   3/5

Show Answer

137. The height of the chimney when it is found that on walking towards it 50 m in the horizontal line through its base, the angle of elevation of its top changes from 30° to 60° is

(a)   25 m

(b)   25√2 m

(c)   25√3 m

(d)   None of these

Show Answer

138. The value of  is

(a)   1/2

(b)   2

(c)   √2

(d)   None of these

Show Answer

139. If  is differentiable at x = 1, then

(a)   a = 1, b = 1

(b)   a = 1, b = 0

(c)   a = 2, b = 0

(d)   a = 2, b = 1

Show Answer

140. The slope the tangent to the curve x = t² + 3t – 8 y = 2t² – 2t – 5 at the point t = 2 is

(a)   7/6

(b)   5/6

(c)   6/7

(d)   1

Show Answer

141. is equal to

Show Answer

142. is equal to

Show Answer

143. The area of one curvilinear triangle formed by curves y = sin x, y = cos x and X-axis, is

(a)   2 sq units

(b)   (2 + √2) sq units

(c)   (2 – √2) sq units

(d)   None of the above

Show Answer

144. Solution of  given that y = 1 when x = 1 is

Show Answer

145. If  is

(a)   1

(b)   −1

(c)  

(d) 

Show Answer

146. The maximum value of the function y = x(x – 1)², is

(a)   0

(b)   4/27

(c)   −4

(d)   None of these

Show Answer

147. The solution of  satisfying y(1) = 0, is

(a)   tan y = (x – 2)e^x log x

(b)   sin y = e^x(x – 1) x⁻¹

(c)   tan y = (x – 1)e^x x⁻³

(d)   sin y = e^x(x – 1)x⁻³

Show Answer

148. The runs of two players for 10 innings each are as follows

The more consistent player is

(a)   player A

(b)   player B

(c)   both player A and B

(d)   None of the above

Show Answer

149. The linear programming problem minimize z = 3x + 2y subject to constraints x + y ≥ 8, 3x + 5y ≤ 15, x ≥ 0 and y ≥ 0, has

(a)   one solution

(b)   no feasible solution

(c)   two solutions

(d)   infinitely many solution

Show Answer

150. Find the area enclosed by the loop in the curve 4y² = 4x² – x³.

(a)   128/5

(b)   15/128

(c)   130/17

(d)   17/130

Show Answer

BITSAT SOLVED PAPER-2020

PART-I

PHYSICS

1. Three solenoid coils of same dimensions, same number of turns and same number of layers of winding are taken. Coil 1 has inductance L₁ wounded by Mn wire of resistance 6 Ωm⁻¹, coil 2 with inductance L₂ wounded by similar wire but in reverse direction in each layer. Coil 3 with inductance L₃ wounded by a superconducting wire. The relation between their self inductances will be

(a)   L₁ = L₂, L₃ = 0

(b)   L₁ = L₂ = L₃

(c)   L₁ = L₃, L₂ = 0

(d)   L₁ > L₂ > L₃

Show Answer

2. Three capacitors C₁, C₂ and C₃ are connected as shown in the figure below. If capacitor C₃ breaks down electrically, then the change in total charge on the combination of capacitors, is

Show Answer

3. A black body radiates energy at the rate EWm⁻² at high temperature T K. When the temperature is reduced to (T/4) K, then the new radiant energy is

(a)   E/256

(b)   4E

(c)   E/4

(d)   E/16

Show Answer

4. The length of the rectangle is l = 15.2 cm and breadth is b = 2.9 cm and the minimum possible measurement by scale = 0.1 cm. Then, the area of the rectangle is

(Taking, significant figures into consideration)

(a)   44.08 cm²

(b)   24.8 cm²

(c)   44 cm²

(d)   94.008 cm²

Show Answer

5. In an adiabatic process, where pressure is decreased by 3/4%, if  then the volume increases by

(a)   3/4%

(b)   9/16%

(c)   16/9%

(d)   4/3%

Show Answer

6. The vibrations of a string of length 60 cm fixed at both ends are represented by the equation

where, x and y are cm and t is in second. Calculate the velocity of the particle at x = 7.5 cm and t = 0.25 s.

(a)   4  m/s

(b)   Zero

(c)   16 m/s

(d)   9.8 m/s

Show Answer

7. A charge +q is placed at the origin O of XY-axes as shown in the figure. The work done in taking a charge Q from A to B along the straight line AB is

Show Answer

8. The hydrogen-like element that has a spectrum whose lines have wavelength four times shorter than those of atomic hydrogen is

(a)   lithium

(b)   helium

(c)   berilliyum

(d)   potassium

Show Answer

9. Two small conducting spheres of equal radius have charges +20 μC and −40 μC respectively and placed at a distance R from each other experience force F₁. If they are brought in contact and separated to the same distance, they experience force F₂. The ratio of F₁ to F₂ is

(a)   1 : 4

(b)   8 : 1

(c)   −8 : 1

(d)   1 : 8

Show Answer

10. A Carnot engine has the same efficiency between 600 K to 300 K and 1600 K to x K, then the value of x is

(a)   1600 K

(b)   800 K

(c)   819 K

(d)   900 K

Show Answer

11. A ball of mass 0.5 kg is thrown up with initial speed 16 ms⁻¹ and reaches maximum height of 9 m. How much energy is dissipated by air drag acting on the ball during the ascent?

(a)   199 J

(b)   19.9 J

(c)   20.9 J

(d)   9.9 J

Show Answer

12. In the circuit shown, if the 10 Ω resistor is replaced by a resistor of 15 Ω, then what is the amount of current drawn from the battery?

(a)   100 A

(b)   10 A

(c)   1 A

(d)   2.4 A

Show Answer

13. A time dependent force F(= 8t) acts on a particle of mass 2 kg. If the particle starts form rest, the work done by the force during the first 1 s will be

(a)   0.4 J

(b)   4 J

(c)   19 J

(d)   4.5 J

Show Answer

14. If L, R, C and V represent inductance, resistance, capacitance and potential difference respectively, then dimensions L/RCV are the same as those of

(a)   current

(b)   1/current

(c)   charge

(d)   1/charge

Show Answer

15. The magnetic field of a beam emerging from a fitter facing a flood light is given by

B = 10 × 10⁻⁸ sin(1 × 10⁷ z – 3.6 × 10¹⁵ t)T. The average intensity of the beam is

(a)   1.82 W/m²

(b)   1.19 W/m²

(c)   1.18 W/m²

(d)   1.17 W/m²

Show Answer

16. From the velocity-time graph of a body moving in a straight line, the distance travelled and the average velocity in the time interval t = 0 to t = 20 s are, respectively,

(a)   0, 0

(b)   120 m, 60 m

(c)   60 m, 0

(d)   0, 60 m

Show Answer

17. A thin equi-convex lens is made of glass of refractive index 1.5 and its focal length is 0.2 m. If it acts as a concave lens of focal length 0.5 m when dipped in a liquid, the refractive index of the liquid is

(a)   17/8

(b)   15/8

(c)   13/8

(d)   9/8

Show Answer

18. A moving coil galvanometer has a resistance of 60 Ω and it indicates full deflection on passing a current of 4.5 mA. A voltmeter is made using this galvanometer and a 4.5 kΩ The maximum voltage, that can be measured using this voltmeter, will be close to

(a)   21 V

(b)   20.5 V

(c)   20 V

(d)   19.5 V

Show Answer

19. The combination of the gates shown in following figure yields

(a)   NAND gate

(b)   OR gate

(c)   NOT gate

(d)   XOR gate

Show Answer

20. A vessel contains one mole of O₂ gas (molar mass 32) at a temperature T. The pressure of the gas is p. An identical vessel containing one mole of He gas (molar mass 4) at a temperature 2T has a pressure of

(a)   p/8

(b)   p

(c)   2p

(d)   8p

Show Answer

21. The acceleration of a particle in m/s² is given by a = (3t² – 2t + 1), where t is in second. If the particle starts with a velocity v = 1 m/s at t = 1s, then velocity of the particle at the end of 4s is

(a)   40 m/s

(b)   52 m/s

(c)   48 m/s

(d)   84 m/s

Show Answer

22. The figure shows graphs of pressure (p) versus density (d) for an ideal gas at two temperatures T₁ and T₂, then

(a)   T₁ > T₂

(b)   T₁ < T₂

(c)   T₁ = T₂

(d)   None of these

Show Answer

23. Two spheres of the same material and same radii r are touching each other. The gravitational force between the spheres is proportional to

(a)   1/r²

(b)   r²

(c)   1/r⁴

(d)   r⁴

Show Answer

24. A spherical lens of power −4 D is placed at a distance of 15 cm from another spherical lens of power 5 D. A beam of parallel light falls on the first spherical lens. The final image formed is

(a)   real and at a distance of 40 cm from the lens of power 5 D

(b)   real and at a distance of 10 cm from the lens of power −4 D

(c)   virtual and at a distance of 40 cm from the lens of power −5 D

(d)   None of the above

Show Answer

25. The wheel of a car, accelerated uniformly from rest, rotates through 5 rad during the first second. The angle (in rad) rotated during the next second is

(a)   15

(b)   7.5

(c)   12.5

(d)   20

Show Answer

26. Lights of two different frequencies whose photons have energies 1.5 eV and 2.5 eV respectively illuminate a metallic surface whose work function is 0.5 eV successively. Ratio of maximum speeds of emitted electrons will be

(a)   3 : 2

(b)   2 : 3

(c)   √3 : √2

(d)   √2 : √3

Show Answer

27. When a body is dropped from a height h, then it hits the ground with a momentum p. If the same body is dropped from a height which is three times more than previous height, the percentage change in momentum when it hits the ground is

(a)   25%

(b)   50%

(c)   75%

(d)   100%

Show Answer

28. The reading of the ammeter for a germanium diode in the given circuit is

(a)   0.94 A

(b)   0

(c)   2.8 A

(d)   5 A

Show Answer

29. The decay constants of two radioactive substances X and Y are 4λ and λ At t = 0, a sample has the same number of two nuclei. The time taken for the ratio of number of nuclei to become 1/e³ will be

(a)   1/3λ

(b)   1/2λ

(c)   2/3λ

(d)   3/2λ

Show Answer

30. The magnitude of the force vector acting on a unit length of a thin wire carrying a current I = 10 A at a point O, if the wire is bent in the form of a semi-circle (shown below) with radius R = 20 π cm, is

(a)   30 μN/m

(b)   40 μN/m

(c)   50 μN/m

(d)   60 μN/m

Show Answer

31. A long cylindrical iron core of cross-sectional area 5 cm² is inserted into a long solenoid having 4000 turns/metre and carrying a current 5 A. The magnetic field inside the core is π Find the pole strength developed.

(a)   1000 A-m

(b)   1240 A-m

(c)   882 A-m

(d)   760 A-m

Show Answer

32. A plane requires for take off a speed of 72 kmh⁻¹, the run on the ground being 50 m. The mass of the plane is 10000 kg and the coefficient of friction between the plane and the ground is 0.2. Assume that the plane accelerates uniformly during take off. The minimum force required by the engine of the plane for take off is

(a)   4.43 × 10⁴ N

(b)   5.96 × 10⁴ N

(c)   2.25 × 10⁴ N

(d)   3.45 × 10⁴ N

Show Answer

33. In a fluorescent lamp choke, 120 V of reverse voltage is produced when the choke current changes uniformly 0.50 A to 0.20 A in a duration of 0.030 ms. The self inductance of the choke (in mH) is estimated to be

(a)   12 H

(b)   12 × 10⁻³ mH

(c)   12 × 10⁻³ H

(d)   0

Show Answer

34. A man grows into a giant such that his linear dimensions increase by a factor of 8. Assuming that his density remains same, the stress in his leg will change by a factor of

(a)   1/8

(b)   8

(c)   36

(d)   64

Show Answer

35. When 2 moles of a monoatomic gas are mixed with 3 moles of a diatomic gas, the value of adiabatic exponent for the mixture is

(a)   15/16

(b)   7/5

(c)   31/21

(d)   38/59

Show Answer

36. A simple pendulum is placed inside a lift, the lift is moving with a uniform acceleration. If the time periods of the pendulum, while the lift is moving upwards and downwards are in the ratio of 1 : 3, then the acceleration of the lift is

[Take, acceleration due to gravity, g = 10 m/s²]

(a)   4 m/s²

(b)   6 m/s²

(c)   8 m/s²

(d)   10 m/s²

Show Answer

37. A satellite is moving around the earth with speed υ in a circular orbit of radius r. If the orbit radius is decreased by 2%, its speed will increase by

(a)   1%

(b)   2%

(c)   1.5%

(d)   1.414%

Show Answer

38. In the circuit shown in figure, the AC source has angular frequency ω = 2000 rad s⁻¹. The amplitude of the current will be nearest to

(a)   2.85 A

(b)   3 A

(c)   0.5 A

(d)   3.625 A

Show Answer

39. The work done by a force acting on a body is as shown in the following graph. The total work done in covering an initial distance of 40 m is

(a)   500 J

(b)   600 J

(c)   400 J

(d)   800 J

Show Answer

40. A potential wire, 10 m long, has a resistance of 40 Ω. It is connected in series with a resistance box and a 4 V storage cell. If the potential gradient along the wire is 0.4 mVcm⁻¹, the resistance unplugged in the box is

(a)   220 Ω

(b)   360 Ω

(c)   760 Ω

(d)   848.3 Ω

Show Answer

PART II

Chemistry

41. In a set of reactions, m-bromobenzoic acid gives a product D. Identify the product D.

Show Answer

42. A volume of 50.00 mL of a weak acid of unknown concentration is titrated with 10 M solution of NaOH. The equivalence point is reached after 39.30 mL of NaOH solution h as been added. At the half equivalence point (19.65 mL) the pH is 4.85. Thus, initial concentration of the acid and its pK_a values are

[HA]                pK_a

(a)   0.1 M          4.85

(b)   0.079 M      4.85

(c)   0.1 M          3.70

(d)   0.097 M      2.93

Show Answer

43. 1-phenyl-1, 3-dibromopropane on treatment with alc. KOH gives diastereomeric mixture in which compound (A) is major product. (A) gives the following reaction

Show Answer

44. Which of the following statement is incorrect?

(a)   α-D-fructose and β-D-fructose are enantiomers of each other.

(b)   D-glyceraldehyde and L-glyceraldehyde are enantiomers of each other.

(c)   The reserve carbohydrate of animals is glycogen.

(d)   Aldohexoses which react with phenyl hydrazine to give identical osazones are C-2 epimers.

Show Answer

45. Which of the following is not a mixed pair of oxides?

(a)   Mn₃O₄ and Co₃O₄

(b)   Co₃O₄ and Pb₃O₄

(c)   Pb₃O₄ and Mn₃O₄

(d)   Fe₃O₄ and Fe₂O₃

Show Answer

46. A solution of copper sulphate is electrolyzed between copper electrodes by a current of 10.0A passing for one hour. Which of the following statements is correct regarding the changes that occur at the electrodes and in the solution?

(a)   11.84 g of copper will deposit on the cathode

(b)   11.84 g of copper will deposit on the anode

(c)   11.84 g copper will deposit on the anode as well as on the cathode

(d)   copper will not deposit on any of the electrode

Show Answer

47. 

Identify structure of compound (D).

Show Answer

48. Which of the following statement is correct?

(a)   ∆S for  is positive.

(b)   ∆E < 0 for combustion of CH₄ (g) in a sealed container with rigid adiabatic system.

(c)   ∆G is always zero for a reversible process in a closed system.

(d)   ∆G° for an ideal gas reaction is a function of pressure.

Show Answer

49. Which of the following statements on critical constants of gases are correct?

(I) Larger the T_c/p_c value of a gas, larger would be the included volume.

(II) Critical temperature (T_c) of g as is greater than its Boyle  temperature (T_B).

(III) At the critical point in the van der Waal’s gas isotherm, 

Select the correct answer using the codes given below.

(a)   Both I and II

(b)   Both I and III

(c)   Both II and III

(d)   I, II and III

Show Answer

50. In the given reaction,

Product (D) is

(a)   a positional isomer of X

(b)   identical to X

(c)   chain isomer of X

(d)   an oxidation product of X

Show Answer

51. 

(B) is identified by the characteristic colour of the flame. (A) and (B) are respectively.

(a)   H₃BO₃ and Na₂B₄O₇

(b)   B(OC₂H₅)₃ and H₃BO₃

(c)   NaBO₂ and H₃BO₃

(d)   H₃BO₃ and B(OC₂H₅)₃

Show Answer

52. How many mL of perhydrol is required to produce sufficient oxygen which can be used to completely convert 2 L of SO₂ gas?

(a)   10 mL

(b)   5 mL

(c)   20 mL

(d)   30 mL

Show Answer

53. At the top of a mountain the thermometer reads 0°C and the barometer reads 710 mm Hg. At the bottom of the mountain the temperature is 30°C and the pressure is 760 mm Hg. The ratio of the density of air at the top to that of the bottom is

(a)   1 : 1.04

(b)   0.4 : 1

(c)   1.04 : 1

(d)   1 : 04

Show Answer

54. Match the following columns.

Codes

(a)   A-5; B-4; C-3; D-2; E-1

(b)   A-5; B-3; C-4; D-2; E-1

(c)   A-5; B-3; C-4; D-1; E-2

(d)   A-4; B-3; C-5; D-2; E-1

Show Answer

55. Most acidic hydrogen is present in

Show Answer

56. The process of ‘eutrophication’ is due to the

(a)   increase in concentration of insecticide in H₂O

(b)   increase in concentration of fluoride ion in H₂O

(c)   reduction in concentration of the dissolved oxygen in water due to phosphate pollution in water.

(d)   attack of younger leaves of a plant by peroxyacetyl nitrate

Show Answer

57. Ionization energy of H-atom is 13.6 eV. The wavelengths of the spectral line emitted when an electron in Be³⁺ comes from 5^th energy level to 2^nd energy level is

(a)   43.5 nm

(b)   4350 nm

(c)   4.35 nm

(d)   435 nm

Show Answer

58. The enthalpies of combustion of carbon and carbon monoxide in excess of oxygen at 298 K and constant pressure are −5 kJ/mol and −280.0 kJ/mol respectively. The heat of formation of carbon monoxide at constant volume is

(a)   +111.7 kJ/mol

(b)   −1111.7 kJ/mol

(c)   −111.7 kJ/mol

(d)   −11.7 kJ/mol

Show Answer

59. If the quantum number l could have the value n also then, Sc(21) would have electronic configuration as (other rules strictly followed)

(a)   1s² 1p⁶ 2s² 2p⁶ 2d³ 3s²

(b)   1s² 1p⁶ 2s² 2p⁶ 3s² 2d³

(c)   1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹ 4s²

(d)   1s² 2s² 2p⁶ 3s² 3p⁶ 3d³

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60. 1.1 mole of A mixed with 2.2 moles of B and the mixture is kept in a 1 L flask and the equilibrium, A + 2B ⇌ 2C + D is reached. If at equilibrium 0.2 mole of C is formed then the value of K_C will be

(a)   0.1

(b)   0.01

(c)   0.001

(d)   1

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61. Choose the correct chemical reaction among the following:

(a)   CaCN₂ + H₂O → Ca(OH)₂ + C₂H₂ + NH₃

(b)   2NH₃ + CaSO₄ + CO₂ + H₂O → CaCN₂+(NH₄)₂SO₄

(c)   CaCl₂ + Na₂SO₄ → CaSO₄ + 2NaCl

(d)   CaC₂ + H₂O → Ca(OH)₂ + 2NaCl

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62. Which of the following reactions represents disproportionation?

(a)   CrO₅ → Cr³⁺ + O₂

(b)   IO₃⁻ + I⁻ + H⁺ → I₂

(c)   CrO₂Cl₂ + NaOH → Na₂CrO₄ + NaCl + H₂O

(d)   Na₂S₂O₃ + H₂SO₄ → Na₂SO₄ + SO₂ + S₈ + H₂O

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63. 

Compound C is

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64. On the basis of Ellingham diagram, which of the following is not correct?

(a)   Entropy change for all metal oxides is roughly same.

(b)   Below the boiling point, T∆S factor is same irrespective of metal.

(c)   Above ∆G = 0 line, oxide decomposes into metal and oxygen.

(d)   If randomness increases the slope increases.

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65. Which of the following is not explained by adsorption?

(a)   When acetic acid solution is shaken with charcoal the concentration of acid decreases.

(b)   The white ppt. of Mg(OH)₂ attains blue colour when precipitated in the presence of magneson reagent.

(c)   An aqueous solution of NaOH attains pink colour with a drop of phenolphthalein.

(d)   When animal charcoal is shaken with coloured methylene blue solution, the solution turns colourless.

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66. Identify ‘A’ and ‘B’ in the following reaction

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67. An element occurs in two crystalline forms α and β. The α-from has an fcc with a = 3.68 Å and β form has a bcc with a = 2.92 Å. Calculate the ratio of their densities.

(a)   1 : 1

(b)   1 : 2

(c)   2 : 1

(d)   2 : 3

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68. The molar heat of vaporization of water at 100°C is 40.585 kJ/mol. The temperature at which a solution containing 5.60 g of Al₂(SO₄)₃ per 1000 g of water boil is …. . (Assuming the degree of ionization of salt to be 1).

(a)   1000.042°C

(b)   10.0042°C

(c)   100.042°C

(d)   105°C

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69. An organic base C₈H₁₁(X) reacts with nitrous acid at 0°C to give a clear solution. Heating the solution with KCN and cuprous cyanide followed by continued heating with conc. HCl gives a crystalline solid. Heating this solid with alkaline potassium permanganate gives a compound which dehydrates on heating to an anhydride (C₈H₄O₃). Compound X is

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70. The final product of the following reaction is/are

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71. The correct order of pseudohalide, polyhalide and interhalogen is

(a)   BrI₂⁻, OCN⁻, IF₅

(b)   IF₅, BrI₂⁻, OCN⁻

(c)   OCN⁻, IF₂, BrI₂⁻

(d)   OCN⁻, BrI₂⁻, IF₅

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72. An inorganic halide (A) reacts with water to form two acids (B) and (C). (A) also reacts with NaOH to form two salts (D) and (E) which remain in solution. The solution gives white precipitate with both AgNO₃ and BaCl₂ solutions respectively. (A) is a useful organic reagent. The compound (A) is

(a)   SOCl₂

(b)   SO₂Cl₂

(c)   S₂Cl₂

(d)   SF₄

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73. Following statements regarding the periodic trends of chemical reactivity to the alkali metals and the halogens are given. Which of these statements gives the correct picture?

(a)   The reactivity decreases in the alkali metals but increases in the halogens with increase in atomic number down the group.

(b)   In both the alkali metals and the halogens the chemical reactivity decreases with increase in atomic number down the group.

(c)   Chemical reactivity increases with increase in atomic number down the group in both the alkali metals and halogens.

(d)   In alkali metals the reactivity increases but in the halogens it decreases with increase in atomic number down the group.

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74. According to IUPAC nomenclature sodium nitroprusside is named as

(a)   sodiumpentacyanonitrosylferrate (II)

(b)   sodiumpentacyanonitrosylferrate (III)

(c)   Sodiumnitroferricyanide

(d)   Sodiumnitroferrocyanide

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75. A(g) → P(g) + Q(g) + R(g),

Follow first order kinetics with a half-life of 69.3 s at 500°C. Starting from the gas ‘A’ an container at 500°C and at a pressure of 0.4 atm, the total pressure of the system after 230 s will be

(a)   1.15 atm

(b)   1.32 atm

(c)   1.22 atm

(d)   1.12 atm

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76. Which of the following gives paracetamol on acetylation?

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77. In qualitative analysis when H₂S passed through an aqueous solution of salt acidified with dilute HCl, a black ppt. is obtained. On boiling the precipitate with dil. HNO₃, it forms a solution of blue colour. Addition of excess of aqueous solution of NH₃ to this solution gives

(a)   deep blue ppt. of Cu(OH)₂

(b)   deep blue solution of [Cu(NH₃)₄]²⁺

(c)   deep blue solution of Cu(NO₃)₂

(d)   deep blue solution of Cu(OH)₂ ∙ Cu(NO₃)₂

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78. Titration of 0.1467 g of primary standard Na₂C₂O₄ required 28.85 mL of KMnO₄ Calculate the molar concentration of KMnO₄ solution.

(a)   0.01518 M

(b)   0.001518 M

(c)   0.15180 M

(d)   1.5180 M

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79. Which of the following facts about the complex [Cr(NH₃)₆]Cl₃ is wrong?

(a)   The complex involves d²sp³ hybridization and its octahedral in shape.

(b)   The complex is paramagnetic.

(c)   The complex is an outer orbital complex.

(d)   The complex gives white precipitate with silver nitrate solution.

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80. Sulphuric acid is a diabasic acid. It ionizes in two stages and hence, has two dissociation constants K_a1 and K_a2. Which of the following is the correct observation regarding K_a1and K_a2?

(a)   K_a1 > K_a2

(b)   K_a1 < K_a2

(c)   K_a1 = K_a2

(d)   K_a1 = 1.2 × 10⁻², K_a2 > 10

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PART III

(a) English Proficiency

Directions (Q. Nos. 81-83) In the following questions, find out which part of a sentence has an error. If there is no error, mark part (d) as your answer.

81. The road a./to famous monument b./ passes through a forest. c./ No error d

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82. The master did not known a./who of the servants b./broke the glass c./No error d

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83. Had I come a./to know about his difficulties b./I would have certainly helped c./No error d

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

84. He trekking was net ……………. Obstacles.

(a)   with

(b)   from

(c)   by

(d)   of

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85. She has not got ….. the shock of losing her father.

(a)   over

(b)   at

(c)   from

(d)   with

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Directions (Q. Nos. 86-88) Select the word or phrase which is closest to the opposite in meaning of the italicized word or phrase.

86. Yuvraj Singh is suffering from a BENIGN cancer.

(a)   Unfriendly

(b)   Friendly

(c)   Fatal

(d)   Malignant

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87. He is a NOTED figure of film industry.

(a)   Known

(b)   Unknown

(c)   Famous

(d)   Infamous

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88. SAGACIOUS decisions taken at right time in one’s career has long effects.

(a)   Foolish

(b)   Intelligent

(c)   Thoughtful

(d)   Intuitive

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Directions (Q. Nos. 89 and 90) Choose the word nearest in meaning to the italicized word.

89. The actor got PEEVISH on asking personal questions.

(a)   Irritated

(b)   Happy

(c)   Shy

(d)   Satisfied

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90. The engineer ROUGHED OUT his ideas on a piece of paper while he talked.

(a)   Shaped soughly

(b)   Rejected

(c)   Drew a quick plan

(d)   Describe inaccurately

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

The Centre and the States must become partners in the planning process to determine national priorities together. The process of planning would undergo a change in view of the changes in domestic economic situation and momentous trends emerging in the world. The development of human resource and the building up of an institutional framework would have to receive priority attention. The role of the government would also have to be examined so as to fully involve the people in the process of nation-building. The main task would be to ensure that the real initiative is transferred to the people. The private sector which would register expansion hereafter should keep this objective firmly in view. The need for an effective population policy is an urgent necessity in the country’s planning strategy. The family welfare programme should not be treated as the Centre’s responsibility alone. The States should evolve a suitable mechanism for closer involvement of the Government agencies, Zilla Parishads and Panchayats for making the family welfare programme a success.

91. Which one of the following statements is correct?

(a)   Effective family welfare programme is Centre’s responsibility alone.

(b)   Population policy and planning process are interlinked.

(c)   Family welfare programme should be left to the State Governments alone.

(d)   The State Government should use punitive measures to control population.

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92. What should be given priority attention?

(a)   Role of the Government

(b)   Decentralization of power

(c)   Involvement of people in labour welfare

(d)   Human resource and institutional framework

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93. Which one of the following statements is not correct?

(a)   Role of the government in nation-building should be examined.

(b)   Real initiatives should be transferred to the people.

(c)   There should be no role for the government as far as planning is concerned.

(d)   The Centre and the States must become equal partners in the planning process.

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94. What would force the planning process to undergo a change?

(a)   Free market forces

(b)   Domestic economic situation and world trends

(c)   Domestic compulsions

(d)   International pressures

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95. Which of the following is implied by the expression ‘momentous trends’?

(a)   GDP growth of the country

(b)   Memorable historical events

(c)   Important changes in the international scene

(d)   Improvement of foreign exchange reserves

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(b) Logical Reasoning

96. Find out the wrong number.

2, 6, 12, 72, 865, 62208

(a)   72

(b)   12

(c)   62208

(d)   865

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97. Each of P, Q, T, A and B has different heights. T is taller than P and B but shorter than A and Q. P is not the shortest, who is the tallest?

(a)   A

(b)   Q

(c)   A or Q

(d)   P or B

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98. Identify the missing part of the question figure and select it from given answer figures.

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99. Select the related word from the given alternatives.

Mechanic : Spanner : : Carpenter : ?

(a)   tree

(b)   wood

(c)   furniture

(d)   saw

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100. How many rectangles are there in the following figure?

(a)   8

(b)   18

(c)   17

(d)   20

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101. In the following question find the odd letters/group from the given alternatives.

(a)   BADC

(b)   JILK

(c)   NMPO

(d)   VUWX

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102. Find out which of the answer figures (a), (b), (c) and (d) completes the figure matrix?

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103. Among the four answer figures, which one can be formed from the cut out pieces given below in the question figures?

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104. A piece of paper is folded and cut as shown below in the question figures. From the given answer figures, indicates how it will appear when opened.

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105. In the following question three dots are placed in the figure marked as (A). The figure is followed by four alternatives marked as (a), (b), (c) and (d). One out of these four options contains region(s) common to the circle, square, triangle, similar to that marked by the dot in figure (A).

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PART IV

Mathematics

106. If A = {x : x² = 1} and B = {x : x⁴ = 1}, then A ∆ B is equal to

(a)   {−i, i}

(b)   {−1, i}

(c)   {−1, 1, −i, i}

(d)   None of these

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107. If 2f(xy) = (f(x))^y + (f(y))^x for all x, y ∈ R and f(1) = a (≠1). Then  is equal to

(a)   (aⁿ – 1)/(a – 1)

(b)   a(a^{n – 1} – 1)/(a – 1)

(c)   a(aⁿ – 1)/(a – 1)

(d)   (aⁿ – 1)/a + 1

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108. Let f(x) = x – 3 and g(x) = 4 – x. Then the set of values of x for which

|f(x) + g(x)| < |f(x)| + |g(x)| is true, is given by:

(a)   R

(b)   R – (3, 4)

(c)   R – [3, 4]

(d)   None of these

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109. If a₁, a₂, a₃, …., a₂₀ are AM’s between 13 and 67 then the maximum value of a₁ ∙ a₂ ∙ a₃ …, a₂₀ is

(a)   (20)²⁰

(b)   (40)²⁰

(c)   (60)²⁰

(d)   (80)²⁰

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110. If p, q, r are in AP and the positive, the roots of the quadratic equation px² + qx + r = 0 are all real for

(a) 

(b) 

(c)   All p and r

(d)   No p and r

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111. The value of  is equal to

(a)   ⁴⁷C₆

(b)   ⁵²C₅

(c)   ⁵²C₄

(d)   None of these

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112. The number of numbers divisible by 3 that can be formed by four different even digits is

(a)   36

(b)   18

(c)   0

(d)   None of these

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113. If n(A) = 1000, n(B) = 500, n (A ∩ B) ≥ 1 and n (A ∪ B) = P, then

(a)   500 ≤ P ≤ 1000

(b)   1001 ≤ P ≤ 1498

(c)   1000 ≤ P ≤ 1498

(d)   1000 ≤ P ≤ 1499

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114. is equal to

(a)   R – {0}

(b)   R – {0, 1, 3}

(c)   R – 3{0, −1, −3}

(d)   R – {0, −1, −3, 1/2}

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115. Let f(x) be a polynomial function of second degree. If f(1) = f(−1) and a, b, c are in AP, then f ꞌ(a), f ʹ(b) and f ʹ(c) are in

(a)   AP

(b)   GP

(c)   Arithmetic-Geometric progression

(d)   None of the above

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116. The value of  is

(a)   5 – 2log 2

(b)   4 – 2log 2

(c)   3 – 2log 2

(d)   2 – 2log 2

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117. The coefficient of x⁸ in the polynomial (x – 1) (x – 2) ….(x – 10)

(a)   2640

(b)   1320

(c)   1370

(d)   2740

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118. If  then z¹⁴ is

(a)   2⁷

(b)   2⁷i

(c)   (−2)⁷

(d)   (−2)⁷i

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119. The solution of the equation  is

(a)   2y = sin y(1 – 2cx²)

(b)   2x = cot y(1 + 2cx²)

(c)   2x = sin y(1 – 2cx²)

(d)   2x sin y  = 1 – 2cx²

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120. The value of the definite integral 

(a)   1 – π/4

(b)   1 + π/4

(c)   π + 1/4

(d)   None of these

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121. If a and b are two vectors such that |a| = 1, |b| = 4 and a ∙ b = 2, if c = (2a × b) – 3b, then angle between b and c

(a)   π/6

(b)   π/3

(c)   2π/3

(d)   5π/6

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122. Let x₁ and x₂ be the real roots of the equation x² – (k – 2)x + (k² + 3k + 5) = 0, then maximum value of x₁² + x₂² is

(a)   19

(b)   22

(c)   18

(d)   17

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123. Circle centered at origin and having radius π units is divided by the curve y = sin x in two parts. Then area of upper parts equals to

(a)   π²/2

(b)   π³/4

(c)   π³/2

(d)   π³/8

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124. The root of the equation 2(1 + i)x² – 4(2 – i)x – 5 – 3i = 0, where i = √−1, which has greater modulus, is

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125. The equation (cos β – 1)x² + (cos β)x + sin β = 0 in the variable x has real roots, then β lies in the interval

(a)   (0, 2π)

(b)   (−π, 0)

(c)   (−π/2, π/2)

(d)   (0, π)

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126. A ordered pair (α, β) for which the system of linear (1 + α)x + βy + z = 2, αx + (1 + β)y + z = 3 and αx + βy + 2z = 2 has a unique solution.

(a)   (1, −3)

(b)   (−3, 1)

(c)   (2, 4)

(d)   (−4, 2)

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127. A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. If flies off horizontally straight way from the point O. After one second, the elevation of the bird from O is reduced to 30°, then the speed (in m/s) of the bird is

(a)   40(√2 – 1)

(b)   40(√3 – √2)

(c)   20√2

(d)   20(√3 – 1)

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128. If one GM, g and two AM’s p and q are inserted between two numbers a and b, then (2p – q) (p – 2q) is equal to

(a)   g²

(b)   −g²

(c)   2g

(d)   3g²

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129. When x¹⁰⁰ is divided by x² – 3x + 2 the remainder is (2^k+1 – 1)x – 2(2^k – 1), then k is

(a)   97

(b)   99

(c)   100

(d)   101

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130. The mean of five observation is 5 and their variance is 9.20. If three of the given five observation are 1, 3 and 8, then a ratio of other two observations is

(a)   4 : 9

(b)   6 : 7

(c)   5 : 8

(d)   10 : 3

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131. How many three digit number satisfy the property that the middle digit is arithmetic mean of the first and the last digit.

(a)   41

(b)   45

(c)   43

(d)   44

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132. If z = re^iθ, then arg(e^iz) is

(a)   −r sin θ

(b)   r cos θ

(c)   e^{−r sin θ}

(d)   −r cos θ

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133. If 4 dice are rolled, then the number of ways of getting the sum 10 is

(a)   56

(b)   64

(c)   72

(d)   80

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134. Distance of point A(1, 2) measured parallel to the line 3x – y = 10 from the line x + y + 5 = 0, is

(a)   2√5

(b)   2√10

(c)   4√5

(d)   4√10

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135. Let f(x) = a₀ + a₁x² + a₂x⁴ + a₃x⁶ + … + a_nx²ⁿ be a polynomial in a real variable x with 0 < a₁ < a₂ < a₃ < … < a_n, the function f(x) has

(a)   neither a maxima nor a minima

(b)   only one maxima

(c)   both maxima and minima

(d)   only one minima

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136. If f(x) = 2x³ + x⁴ + log x and g is the inverse of f, then g’(3) is equal to

(a)   1/9

(b)   1/7

(c)   1/11

(d)   1/8

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137. A line passing through P(3, 7, 1) and R(2, 5, 7) meet the plane 3x + 2y + 11z – 9 = 0 at Q. Then PQ is equal to

(a)   5√41/59

(b)   √41/59

(c)   50√41/59

(d)   25√41/59

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138. equals to

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139. If  then find z component of a vector r, which is coplanar with a and b, r ∙ b = 0 and r ∙ a = 7.

(a)   0

(b)   3

(c)   6

(d)   5/2

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140. If x, y, z are three consecutive positive integers, x – z + 2 = 0, then  is equal to

(a)   log_e x

(b)   log_e y

(c)   log_e z

(d)   None of these

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141. The solution of differential equation (xy⁵ + 2y)dx – xdy = 0, is

(a)   9x⁸ + 4x⁹y⁴ = 9y⁴C

(b)   9x⁸ – 4x⁹y⁴ – 9y⁴C = 0

(c)   x⁸(9 + 4y⁴) = 10y⁴C

(d)   None of these

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142. The solution set of  is

(a)   [0, 1] ∪ (3, 4)

(b)   [0, 1] ∪ [3, 4]

(c)   [−1, 1] ∪ (3, 4]

(d)   None of these

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143. Let  the  is

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144. If  then  is equal to

(a)   50

(b)   47

(c)   44

(d)   53

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145. The number of distinct solutions of the equation  in the interval [0, 2π] is

(a)   8

(b)   10

(c)   6

(d)   15

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146. If the tangent at a point  to the ellipse 16x² + 11y² = 256 is also a tangent to x² + y² – 2x = 15, then ϕ equals

(a)   π/3

(b)   π/6

(c)   − π/6

(d)   π/4

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147. The distance of point of intersection of the tangents to the parabola x = 4y – y² drawn at the points where it is meet by Y-axis, from its focus is

(a)   11/4

(b)   17/4

(c)   13/4

(d)   3

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148. The value of the sum  is

(a)   5

(b)   4

(c)   3

(d)   2

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149. A curve passes through (2, 0) and the slope of the tangent at P(x, y) is equal to  then the equation of the curve is

(a)   y = x² – 2x

(b)   y = x³ – 8

(c)   y² = x² + 2x

(d)   y² = 5x² – 6

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150. Consider matrix  if A⁻¹ = αI + βA, when α, β ∉ R, then (α + β) is equal to (where A⁻¹ denotes the inverse of matrix A)

(a)   1

(b)   4/3

(c)   5/3

(d)   1/3

Show Answer