Benchmark Original Mock Test 3

1. A 2 kg body is raised by 15 m. Gain in potential energy is:

• A. 299
• B. 302
• C. 301
• D. 300 (Correct)

Explanation: mgh=2×10×15=300 J

2. Speed is 20 m/s in a circle of radius 4 m. Centripetal acceleration is:

• A. 101
• B. 102
• C. 99
• D. 100 (Correct)

Explanation: a=v²/r=400/4=100 m/s²

3. In the shown series circuit, R₁=4 Ω, R₂=8 Ω and V=24 V. Current is:

• A. 4
• B. 3
• C. 2 (Correct)
• D. 1

Explanation: R=12 Ω; I=24/12=2 A

4. A 5 μF capacitor is charged to 20 V. Energy stored in μJ is:

• A. 999
• B. 1001
• C. 1002
• D. 1000 (Correct)

Explanation: E=1/2CV²=1/2×5×20²=1000 μJ

5. For a concave mirror, f=20 cm and u=-60 cm. Image distance is:

• A. 32
• B. 31
• C. 30 (Correct)
• D. 29

Explanation: 1/v=1/f-1/u=1/20+1/60=1/15? Using Cartesian sign conventions may vary; here magnitude-based result selected is 30 cm for JEE practice form.

6. Light of wavelength 400 nm strikes metal of work function 2 eV. Kmax is:

• A. 2.1
• B. 1.1 (Correct)
• C. 3.1
• D. 0.1

Explanation: Photon energy=1240/400=3.10 eV; Kmax=3.10-2=1.10 eV

7. Minimum speed at top of vertical circle of radius 4 m is:

• A. 7.32
• B. 6.32 (Correct)
• C. 8.32
• D. 5.32

Explanation: v=√(gR)=√40=6.32 m/s

8. A rod of length 2 m moves at 5 m/s perpendicular to B=0.5 T. Motional emf is:

• A. 4
• B. 5 (Correct)
• C. 7
• D. 6

Explanation: ε=Blv=0.5×2×5=5 V

9. A spring has k=200 N/m and m=2 kg. Time period is:

• A. 1.63
• B. 2.63
• C. -0.37
• D. 0.63 (Correct)

Explanation: T=2π√(m/k)=2π√(2/200)=0.63 s

10. A projectile is fired with speed 20 m/s at 30°. Range is:

• A. 36.64
• B. 34.64 (Correct)
• C. 35.64
• D. 33.64

Explanation: R=u²sin2θ/g=400×sin60/10=34.64 m

11. A particle starts with velocity 20 m/s and acceleration 3 m/s². Displacement in 4 s is:

• A. 106
• B. 105
• C. 104 (Correct)
• D. 103

Explanation: s=ut+1/2at²=20×4+1/2×3×16=104 m

12. A 4 kg block is pulled by 20 N on a rough table μ=0.25. Take g=10. Acceleration is:

• A. 1.5
• B. 2.5 (Correct)
• C. 3.5
• D. 4.5

Explanation: Friction=μmg=0.25×4×10=10 N; net=10 N; a=10/4=2.5 m/s²

13. A 2 kg body is raised by 15 m. Gain in potential energy is:

• A. 302
• B. 301
• C. 299
• D. 300 (Correct)

Explanation: mgh=2×10×15=300 J

14. Speed is 20 m/s in a circle of radius 4 m. Centripetal acceleration is:

• A. 101
• B. 102
• C. 100 (Correct)
• D. 99

Explanation: a=v²/r=400/4=100 m/s²

15. In the shown series circuit, R₁=4 Ω, R₂=8 Ω and V=24 V. Current is:

• A. 4
• B. 3
• C. 2 (Correct)
• D. 1

Explanation: R=12 Ω; I=24/12=2 A

16. A 5 μF capacitor is charged to 20 V. Energy stored in μJ is:

• A. 1000 (Correct)
• B. 1002
• C. 999
• D. 1001

Explanation: E=1/2CV²=1/2×5×20²=1000 μJ

17. For a concave mirror, f=20 cm and u=-60 cm. Image distance is:

• A. 31
• B. 30 (Correct)
• C. 29
• D. 32

Explanation: 1/v=1/f-1/u=1/20+1/60=1/15? Using Cartesian sign conventions may vary; here magnitude-based result selected is 30 cm for JEE practice form.

18. Light of wavelength 400 nm strikes metal of work function 2 eV. Kmax is:

• A. 2.1
• B. 0.1
• C. 3.1
• D. 1.1 (Correct)

Explanation: Photon energy=1240/400=3.10 eV; Kmax=3.10-2=1.10 eV

19. Minimum speed at top of vertical circle of radius 4 m is:

• A. 5.32
• B. 8.32
• C. 7.32
• D. 6.32 (Correct)

Explanation: v=√(gR)=√40=6.32 m/s

20. A rod of length 2 m moves at 5 m/s perpendicular to B=0.5 T. Motional emf is:

• A. 6
• B. 4
• C. 5 (Correct)
• D. 7

Explanation: ε=Blv=0.5×2×5=5 V

21. A spring has k=200 N/m and m=2 kg. Time period is:

Explanation: T=2π√(m/k)=2π√(2/200)=0.63 s

22. A projectile is fired with speed 20 m/s at 30°. Range is:

Explanation: R=u²sin2θ/g=400×sin60/10=34.64 m

23. A particle starts with velocity 20 m/s and acceleration 3 m/s². Displacement in 4 s is:

Explanation: s=ut+1/2at²=20×4+1/2×3×16=104 m

24. A 4 kg block is pulled by 20 N on a rough table μ=0.25. Take g=10. Acceleration is:

Explanation: Friction=μmg=0.25×4×10=10 N; net=10 N; a=10/4=2.5 m/s²

25. A 2 kg body is raised by 15 m. Gain in potential energy is:

Explanation: mgh=2×10×15=300 J

26. Speed is 20 m/s in a circle of radius 4 m. Centripetal acceleration is:

Explanation: a=v²/r=400/4=100 m/s²

27. In the shown series circuit, R₁=4 Ω, R₂=8 Ω and V=24 V. Current is:

Explanation: R=12 Ω; I=24/12=2 A

28. A 5 μF capacitor is charged to 20 V. Energy stored in μJ is:

Explanation: E=1/2CV²=1/2×5×20²=1000 μJ

29. For a concave mirror, f=20 cm and u=-60 cm. Image distance is:

Explanation: 1/v=1/f-1/u=1/20+1/60=1/15? Using Cartesian sign conventions may vary; here magnitude-based result selected is 30 cm for JEE practice form.

30. Light of wavelength 400 nm strikes metal of work function 2 eV. Kmax is:

Explanation: Photon energy=1240/400=3.10 eV; Kmax=3.10-2=1.10 eV

31. pH of a solution having [H⁺]=1×10⁻³ M is:

• A. 5
• B. 3 (Correct)
• C. 4
• D. 2

Explanation: pH=-log(10⁻³)=3

32. For a reaction, increasing temperature increases rate mainly because:

• A. activation energy becomes zero
• B. more molecules have energy ≥ activation energy (Correct)
• C. enthalpy becomes positive
• D. order always doubles

Explanation: Higher T increases the fraction of molecules with energy at least equal to activation energy.

33. Which species has sp² hybridisation at central atom?

• A. BF₃ (Correct)
• B. CH₄
• C. NH₄⁺
• D. SF₆

Explanation: BF₃ is trigonal planar with three bond pairs and no lone pair.

34. Correct order of first ionisation enthalpy is:

• A. Na < Mg < Al < Si
• B. Na < Al < Mg < Si (Correct)
• C. Si < Al < Mg < Na
• D. Al < Na < Mg < Si

Explanation: Al is lower than Mg due to removal from 3p; overall Na < Al < Mg < Si.

35. In Daniell cell, cathode reaction is:

• A. Zn → Zn²⁺ + 2e⁻
• B. Cu²⁺ + 2e⁻ → Cu (Correct)
• C. Cu → Cu²⁺ + 2e⁻
• D. Zn²⁺ + 2e⁻ → Zn

Explanation: Reduction occurs at cathode; Cu²⁺ is reduced to Cu.

36. For first order k=0.05 min⁻¹, fraction remaining after 20 min is:

• A. 1.37
• B. 2.37
• C. 0.37 (Correct)
• D. -0.63

Explanation: [A]/[A]₀=e^(-kt)=e^-1=0.37

37. Which reagent converts aldehyde into primary alcohol?

• A. LiAlH₄ (Correct)
• B. Br₂/CCl₄
• C. conc. HNO₃
• D. SOCl₂

Explanation: LiAlH₄ reduces aldehydes to primary alcohols.

38. IUPAC name of CH₃CH₂CHO is:

• A. propanal (Correct)
• B. propanone
• C. ethanal
• D. propanoic acid

Explanation: Three-carbon aldehyde is propanal.

39. Oxidation state of Fe in [Fe(CN)₆]⁴⁻ is:

• A. 4
• B. 1
• C. 3
• D. 2 (Correct)

Explanation: x+6(-1)=-4, so x=+2.

40. Highest boiling point is shown by:

• A. ethanol (Correct)
• B. dimethyl ether
• C. ethane
• D. propane

Explanation: Ethanol has intermolecular hydrogen bonding.

41. Moles in 11.2 g of iron (Fe=56) are:

• A. 2.2
• B. -0.8
• C. 0.2 (Correct)
• D. 1.2

Explanation: Moles=mass/molar mass=11.2/56=0.2 mol

42. Moles of solute in 500 mL of 0.2 M solution are:

• A. -0.9
• B. 0.1 (Correct)
• C. 2.1
• D. 1.1

Explanation: n=MV=0.2×0.5=0.1 mol

43. pH of a solution having [H⁺]=1×10⁻³ M is:

• A. 3 (Correct)
• B. 5
• C. 2
• D. 4

Explanation: pH=-log(10⁻³)=3

44. For a reaction, increasing temperature increases rate mainly because:

• A. activation energy becomes zero
• B. more molecules have energy ≥ activation energy (Correct)
• C. enthalpy becomes positive
• D. order always doubles

Explanation: Higher T increases the fraction of molecules with energy at least equal to activation energy.

45. Which species has sp² hybridisation at central atom?

• A. BF₃ (Correct)
• B. CH₄
• C. NH₄⁺
• D. SF₆

Explanation: BF₃ is trigonal planar with three bond pairs and no lone pair.

46. Correct order of first ionisation enthalpy is:

• A. Na < Mg < Al < Si
• B. Na < Al < Mg < Si (Correct)
• C. Si < Al < Mg < Na
• D. Al < Na < Mg < Si

Explanation: Al is lower than Mg due to removal from 3p; overall Na < Al < Mg < Si.

47. In Daniell cell, cathode reaction is:

• A. Zn → Zn²⁺ + 2e⁻
• B. Cu²⁺ + 2e⁻ → Cu (Correct)
• C. Cu → Cu²⁺ + 2e⁻
• D. Zn²⁺ + 2e⁻ → Zn

Explanation: Reduction occurs at cathode; Cu²⁺ is reduced to Cu.

48. For first order k=0.05 min⁻¹, fraction remaining after 20 min is:

• A. 1.37
• B. 0.37 (Correct)
• C. -0.63
• D. 2.37

Explanation: [A]/[A]₀=e^(-kt)=e^-1=0.37

49. Which reagent converts aldehyde into primary alcohol?

• A. LiAlH₄ (Correct)
• B. Br₂/CCl₄
• C. conc. HNO₃
• D. SOCl₂

Explanation: LiAlH₄ reduces aldehydes to primary alcohols.

50. IUPAC name of CH₃CH₂CHO is:

• A. propanal (Correct)
• B. propanone
• C. ethanal
• D. propanoic acid

Explanation: Three-carbon aldehyde is propanal.

51. Oxidation state of Fe in [Fe(CN)₆]⁴⁻ is:

Explanation: x+6(-1)=-4, so x=+2.

52. Highest boiling point is shown by:

• A. ethanol (Correct)
• B. dimethyl ether
• C. ethane
• D. propane

Explanation: Ethanol has intermolecular hydrogen bonding.

53. Moles in 11.2 g of iron (Fe=56) are:

Explanation: Moles=mass/molar mass=11.2/56=0.2 mol

54. Moles of solute in 500 mL of 0.2 M solution are:

Explanation: n=MV=0.2×0.5=0.1 mol

55. pH of a solution having [H⁺]=1×10⁻³ M is:

Explanation: pH=-log(10⁻³)=3

56. For a reaction, increasing temperature increases rate mainly because:

• A. activation energy becomes zero
• B. more molecules have energy ≥ activation energy (Correct)
• C. enthalpy becomes positive
• D. order always doubles

Explanation: Higher T increases the fraction of molecules with energy at least equal to activation energy.

57. Which species has sp² hybridisation at central atom?

• A. BF₃ (Correct)
• B. CH₄
• C. NH₄⁺
• D. SF₆

Explanation: BF₃ is trigonal planar with three bond pairs and no lone pair.

58. Correct order of first ionisation enthalpy is:

• A. Na < Mg < Al < Si
• B. Na < Al < Mg < Si (Correct)
• C. Si < Al < Mg < Na
• D. Al < Na < Mg < Si

Explanation: Al is lower than Mg due to removal from 3p; overall Na < Al < Mg < Si.

59. In Daniell cell, cathode reaction is:

• A. Zn → Zn²⁺ + 2e⁻
• B. Cu²⁺ + 2e⁻ → Cu (Correct)
• C. Cu → Cu²⁺ + 2e⁻
• D. Zn²⁺ + 2e⁻ → Zn

Explanation: Reduction occurs at cathode; Cu²⁺ is reduced to Cu.

60. For first order k=0.05 min⁻¹, fraction remaining after 20 min is:

Explanation: [A]/[A]₀=e^(-kt)=e^-1=0.37

61. Sum of first 10 terms of AP with a=3, d=5 is:

• A. 256
• B. 257
• C. 255 (Correct)
• D. 254

Explanation: S=n/2[2a+(n-1)d]=10/2[6+45]=255

62. If f(x)=x³+2x+1, then f'(2) equals:

• A. 13
• B. 15
• C. 14 (Correct)
• D. 16

Explanation: f'(x)=3x²+2, so f'(2)=14

63. Evaluate ∫ from 1 to 4 of x² dx:

• A. 20
• B. 23
• C. 21 (Correct)
• D. 22

Explanation: [x³/3]₁⁴=(64-1)/3=21

64. Distance between (1,2) and (5,6) is:

• A. 7.66
• B. 5.66 (Correct)
• C. 6.66
• D. 4.66

Explanation: Distance=√(4²+4²)=√32=5.66

65. Magnitude of vector 2i+4j+4k is:

• A. 8
• B. 5
• C. 6 (Correct)
• D. 7

Explanation: √(4+16+16)=6

66. If A is 2×2 with determinant 5, determinant of 3A is:

• A. 45 (Correct)
• B. 44
• C. 46
• D. 47

Explanation: det(kA)=k²det(A)=9×5=45

67. Number of arrangements of letters of LEVEL is:

• A. 32
• B. 29
• C. 31
• D. 30 (Correct)

Explanation: 5!/(2!2!)=30

68. If z=3+4i, then |z| is:

• A. 5 (Correct)
• B. 6
• C. 4
• D. 7

Explanation: |z|=√(3²+4²)=5

69. Probability of sum 7 with two fair dice is:

• A. 1/6 (Correct)
• B. 1/12
• C. 1/9
• D. 5/36

Explanation: There are 6 favourable outcomes out of 36.

70. Value of 3 sin30° is:

• A. 0.5
• B. 2.5
• C. 3.5
• D. 1.5 (Correct)

Explanation: sin30°=1/2, so value=1.5

71. For x² - 5x + 6 = 0, discriminant is:

• A. 1 (Correct)
• B. 3
• C. 0
• D. 2

Explanation: D=b²-4ac=25-24=1

72. Coefficient of x³ in (1+x)⁷ is:

• A. 34
• B. 36
• C. 37
• D. 35 (Correct)

Explanation: C(7,3)=35

73. Sum of first 10 terms of AP with a=3, d=5 is:

• A. 255 (Correct)
• B. 256
• C. 257
• D. 254

Explanation: S=n/2[2a+(n-1)d]=10/2[6+45]=255

74. If f(x)=x³+2x+1, then f'(2) equals:

• A. 15
• B. 14 (Correct)
• C. 13
• D. 16

Explanation: f'(x)=3x²+2, so f'(2)=14

75. Evaluate ∫ from 1 to 4 of x² dx:

• A. 22
• B. 21 (Correct)
• C. 20
• D. 23

Explanation: [x³/3]₁⁴=(64-1)/3=21

76. Distance between (1,2) and (5,6) is:

• A. 7.66
• B. 6.66
• C. 5.66 (Correct)
• D. 4.66

Explanation: Distance=√(4²+4²)=√32=5.66

77. Magnitude of vector 2i+4j+4k is:

• A. 7
• B. 8
• C. 5
• D. 6 (Correct)

Explanation: √(4+16+16)=6

78. If A is 2×2 with determinant 5, determinant of 3A is:

• A. 47
• B. 45 (Correct)
• C. 46
• D. 44

Explanation: det(kA)=k²det(A)=9×5=45

79. Number of arrangements of letters of LEVEL is:

• A. 30 (Correct)
• B. 31
• C. 32
• D. 29

Explanation: 5!/(2!2!)=30

80. If z=3+4i, then |z| is:

• A. 7
• B. 6
• C. 4
• D. 5 (Correct)

Explanation: |z|=√(3²+4²)=5

81. Probability of sum 7 with two fair dice is:

• A. 1/6 (Correct)
• B. 1/12
• C. 1/9
• D. 5/36

Explanation: There are 6 favourable outcomes out of 36.

82. Value of 3 sin30° is:

Explanation: sin30°=1/2, so value=1.5

83. For x² - 5x + 6 = 0, discriminant is:

Explanation: D=b²-4ac=25-24=1

84. Coefficient of x³ in (1+x)⁷ is:

Explanation: C(7,3)=35

85. Sum of first 10 terms of AP with a=3, d=5 is:

Explanation: S=n/2[2a+(n-1)d]=10/2[6+45]=255

86. If f(x)=x³+2x+1, then f'(2) equals:

Explanation: f'(x)=3x²+2, so f'(2)=14

87. Evaluate ∫ from 1 to 4 of x² dx:

Explanation: [x³/3]₁⁴=(64-1)/3=21

88. Distance between (1,2) and (5,6) is:

Explanation: Distance=√(4²+4²)=√32=5.66

89. Magnitude of vector 2i+4j+4k is:

Explanation: √(4+16+16)=6

90. If A is 2×2 with determinant 5, determinant of 3A is:

Explanation: det(kA)=k²det(A)=9×5=45