Benchmark Original Mock Test 8

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

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

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

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

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

Explanation: mgh=2×10×15=300 J

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

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

Explanation: a=v²/r=400/4=100 m/s²

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

• A. 1
• B. 2 (Correct)
• C. 3
• D. 4

Explanation: R=12 Ω; I=24/12=2 A

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

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

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

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

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

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.

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

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

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

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

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

Explanation: v=√(gR)=√40=6.32 m/s

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

• A. 5 (Correct)
• B. 4
• C. 7
• D. 6

Explanation: ε=Blv=0.5×2×5=5 V

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

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

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

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

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

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

12. 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

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

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

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

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

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

Explanation: mgh=2×10×15=300 J

15. 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

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

• A. 3
• B. 2 (Correct)
• C. 4
• D. 1

Explanation: R=12 Ω; I=24/12=2 A

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

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

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

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

• A. 32
• B. 30 (Correct)
• C. 31
• 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.

19. 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

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

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

Explanation: v=√(gR)=√40=6.32 m/s

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

Explanation: ε=Blv=0.5×2×5=5 V

22. 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

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

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

24. 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

25. 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

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

Explanation: mgh=2×10×15=300 J

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

Explanation: a=v²/r=400/4=100 m/s²

28. 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

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

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

30. 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.

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

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

Explanation: n=MV=0.2×0.5=0.1 mol

32. 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

33. 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.

34. 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.

35. 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.

36. 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.

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

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

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

38. 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.

39. IUPAC name of CH₃CH₂CHO is:

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

Explanation: Three-carbon aldehyde is propanal.

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

• A. 2 (Correct)
• B. 1
• C. 3
• D. 4

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

41. Highest boiling point is shown by:

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

Explanation: Ethanol has intermolecular hydrogen bonding.

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

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

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

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

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

Explanation: n=MV=0.2×0.5=0.1 mol

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

• A. 5
• B. 4
• C. 3 (Correct)
• D. 2

Explanation: pH=-log(10⁻³)=3

45. 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.

46. 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.

47. 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.

48. 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.

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

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

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

50. 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.

51. IUPAC name of CH₃CH₂CHO is:

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

Explanation: Three-carbon aldehyde is propanal.

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

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

53. Highest boiling point is shown by:

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

Explanation: Ethanol has intermolecular hydrogen bonding.

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

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

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

Explanation: n=MV=0.2×0.5=0.1 mol

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

Explanation: pH=-log(10⁻³)=3

57. 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.

58. 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.

59. 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.

60. 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.

61. Coefficient of x³ in (1+x)⁷ is:

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

Explanation: C(7,3)=35

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

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

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

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

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

Explanation: f'(x)=3x²+2, so f'(2)=14

64. Evaluate ∫ from 1 to 4 of x² dx:

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

Explanation: [x³/3]₁⁴=(64-1)/3=21

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

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

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

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

• A. 6 (Correct)
• B. 7
• C. 5
• D. 8

Explanation: √(4+16+16)=6

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

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

Explanation: det(kA)=k²det(A)=9×5=45

68. Number of arrangements of letters of LEVEL is:

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

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

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

• A. 6
• B. 4
• C. 5 (Correct)
• D. 7

Explanation: |z|=√(3²+4²)=5

70. 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.

71. Value of 3 sin30° is:

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

Explanation: sin30°=1/2, so value=1.5

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

• A. 1 (Correct)
• B. 0
• C. 2
• D. 3

Explanation: D=b²-4ac=25-24=1

73. Coefficient of x³ in (1+x)⁷ is:

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

Explanation: C(7,3)=35

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

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

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

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

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

Explanation: f'(x)=3x²+2, so f'(2)=14

76. Evaluate ∫ from 1 to 4 of x² dx:

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

Explanation: [x³/3]₁⁴=(64-1)/3=21

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

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

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

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

• A. 5
• B. 6 (Correct)
• C. 8
• D. 7

Explanation: √(4+16+16)=6

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

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

Explanation: det(kA)=k²det(A)=9×5=45

80. Number of arrangements of letters of LEVEL is:

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

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

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

Explanation: |z|=√(3²+4²)=5

82. 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.

83. Value of 3 sin30° is:

Explanation: sin30°=1/2, so value=1.5

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

Explanation: D=b²-4ac=25-24=1

85. Coefficient of x³ in (1+x)⁷ is:

Explanation: C(7,3)=35

86. 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

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

Explanation: f'(x)=3x²+2, so f'(2)=14

88. Evaluate ∫ from 1 to 4 of x² dx:

Explanation: [x³/3]₁⁴=(64-1)/3=21

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

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

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

Explanation: √(4+16+16)=6