Benchmark Original Mock Test 6

JEE Main · Full Length · 90 Questions · 180 Min

3 Hours (180 Min)

Duration

300 Marks

Total Marks

90 (30 per subject)

Questions

General Instructions

Section A has 20 MCQ questions per subject — all compulsory. +4 for correct, −1 for wrong.
Section B has 10 integer questions per subject. Attempt any 5. +4 for correct, 0 for wrong/unattempted.
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Physics — Projectile Motion
1. A projectile is fired with speed 20 m/s at 30°. Range is:
- A. 35.64
- B. 36.64
- C. 34.64 (Correct)
- D. 33.64
Explanation: R=u²sin2θ/g=400×sin60/10=34.64 m
Physics — Kinematics
2. A particle starts with velocity 20 m/s and acceleration 3 m/s². Displacement in 4 s is:
- A. 103
- B. 106
- C. 104 (Correct)
- D. 105
Explanation: s=ut+1/2at²=20×4+1/2×3×16=104 m
Physics — Laws of Motion
3. A 4 kg block is pulled by 20 N on a rough table μ=0.25. Take g=10. Acceleration is:
- A. 2.5 (Correct)
- B. 3.5
- C. 4.5
- D. 1.5
Explanation: Friction=μmg=0.25×4×10=10 N; net=10 N; a=10/4=2.5 m/s²
Physics — Work Energy
4. A 2 kg body is raised by 15 m. Gain in potential energy is:
- A. 299
- B. 301
- C. 302
- D. 300 (Correct)
Explanation: mgh=2×10×15=300 J
Physics — Circular Motion
5. Speed is 20 m/s in a circle of radius 4 m. Centripetal acceleration is:
- A. 99
- B. 100 (Correct)
- C. 102
- D. 101
Explanation: a=v²/r=400/4=100 m/s²
Physics — Current Electricity
6. In the shown series circuit, R₁=4 Ω, R₂=8 Ω and V=24 V. Current is:
- A. 3
- B. 4
- C. 2 (Correct)
- D. 1
Explanation: R=12 Ω; I=24/12=2 A
Physics — Capacitance
7. A 5 μF capacitor is charged to 20 V. Energy stored in μJ is:
- A. 1001
- B. 1002
- C. 1000 (Correct)
- D. 999
Explanation: E=1/2CV²=1/2×5×20²=1000 μJ
Physics — Ray Optics
8. For a concave mirror, f=20 cm and u=-60 cm. Image distance is:
- A. 31
- B. 30 (Correct)
- C. 32
- 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.
Physics — Modern Physics
9. Light of wavelength 400 nm strikes metal of work function 2 eV. Kmax is:
- A. 2.1
- B. 0.1
- C. 1.1 (Correct)
- D. 3.1
Explanation: Photon energy=1240/400=3.10 eV; Kmax=3.10-2=1.10 eV
Physics — Circular Motion
10. 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
Physics — EMI
11. 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. 6
- D. 7
Explanation: ε=Blv=0.5×2×5=5 V
Physics — SHM
12. A spring has k=200 N/m and m=2 kg. Time period is:
- A. 2.63
- B. -0.37
- C. 1.63
- D. 0.63 (Correct)
Explanation: T=2π√(m/k)=2π√(2/200)=0.63 s
Physics — Projectile Motion
13. A projectile is fired with speed 20 m/s at 30°. Range is:
- A. 33.64
- B. 35.64
- C. 36.64
- D. 34.64 (Correct)
Explanation: R=u²sin2θ/g=400×sin60/10=34.64 m
Physics — Kinematics
14. A particle starts with velocity 20 m/s and acceleration 3 m/s². Displacement in 4 s is:
- A. 105
- B. 103
- C. 104 (Correct)
- D. 106
Explanation: s=ut+1/2at²=20×4+1/2×3×16=104 m
Physics — Laws of Motion
15. 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. 4.5
- C. 2.5 (Correct)
- D. 3.5
Explanation: Friction=μmg=0.25×4×10=10 N; net=10 N; a=10/4=2.5 m/s²
Physics — Work Energy
16. A 2 kg body is raised by 15 m. Gain in potential energy is:
- A. 301
- B. 299
- C. 302
- D. 300 (Correct)
Explanation: mgh=2×10×15=300 J
Physics — Circular Motion
17. Speed is 20 m/s in a circle of radius 4 m. Centripetal acceleration is:
- A. 101
- B. 100 (Correct)
- C. 99
- D. 102
Explanation: a=v²/r=400/4=100 m/s²
Physics — Current Electricity
18. In the shown series circuit, R₁=4 Ω, R₂=8 Ω and V=24 V. Current is:
- A. 2 (Correct)
- B. 1
- C. 3
- D. 4
Explanation: R=12 Ω; I=24/12=2 A
Physics — Capacitance
19. A 5 μF capacitor is charged to 20 V. Energy stored in μJ is:
- A. 1000 (Correct)
- B. 1001
- C. 1002
- D. 999
Explanation: E=1/2CV²=1/2×5×20²=1000 μJ
Physics — Ray Optics
20. For a concave mirror, f=20 cm and u=-60 cm. Image distance is:
- A. 31
- B. 30 (Correct)
- C. 32
- 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.
Physics — Modern Physics
21. 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
Physics — Circular Motion
22. Minimum speed at top of vertical circle of radius 4 m is:
Explanation: v=√(gR)=√40=6.32 m/s
Physics — EMI
23. 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
Physics — SHM
24. 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
Physics — Projectile Motion
25. A projectile is fired with speed 20 m/s at 30°. Range is:
Explanation: R=u²sin2θ/g=400×sin60/10=34.64 m
Physics — Kinematics
26. 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
Physics — Laws of Motion
27. 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
Physics — Work Energy
28. A 2 kg body is raised by 15 m. Gain in potential energy is:
Explanation: mgh=2×10×15=300 J
Physics — Circular Motion
29. Speed is 20 m/s in a circle of radius 4 m. Centripetal acceleration is:
Explanation: a=v²/r=400/4=100 m/s²
Physics — Current Electricity
30. 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
Chemistry — Organic Properties
31. Highest boiling point is shown by:
- A. ethanol (Correct)
- B. dimethyl ether
- C. ethane
- D. propane
Explanation: Ethanol has intermolecular hydrogen bonding.
Chemistry — Mole Concept
32. Moles in 11.2 g of iron (Fe=56) are:
- A. 1.2
- B. -0.8
- C. 2.2
- D. 0.2 (Correct)
Explanation: Moles=mass/molar mass=11.2/56=0.2 mol
Chemistry — Solutions
33. Moles of solute in 500 mL of 0.2 M solution are:
- A. 1.1
- B. 0.1 (Correct)
- C. 2.1
- D. -0.9
Explanation: n=MV=0.2×0.5=0.1 mol
Chemistry — Ionic Equilibrium
34. pH of a solution having [H⁺]=1×10⁻³ M is:
- A. 5
- B. 2
- C. 3 (Correct)
- D. 4
Explanation: pH=-log(10⁻³)=3
Chemistry — Chemical Kinetics
35. 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.
Chemistry — Chemical Bonding
36. 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.
Chemistry — Periodic Properties
37. 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.
Chemistry — Electrochemistry
38. 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.
Chemistry — Chemical Kinetics
39. For first order k=0.05 min⁻¹, fraction remaining after 20 min is:
- A. 1.37
- B. -0.63
- C. 2.37
- D. 0.37 (Correct)
Explanation: [A]/[A]₀=e^(-kt)=e^-1=0.37
Chemistry — Organic Chemistry
40. 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.
Chemistry — Organic Nomenclature
41. IUPAC name of CH₃CH₂CHO is:
- A. propanal (Correct)
- B. propanone
- C. ethanal
- D. propanoic acid
Explanation: Three-carbon aldehyde is propanal.
Chemistry — Coordination Compounds
42. 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.
Chemistry — Organic Properties
43. Highest boiling point is shown by:
- A. ethanol (Correct)
- B. dimethyl ether
- C. ethane
- D. propane
Explanation: Ethanol has intermolecular hydrogen bonding.
Chemistry — Mole Concept
44. Moles in 11.2 g of iron (Fe=56) are:
- A. 1.2
- B. 2.2
- C. 0.2 (Correct)
- D. -0.8
Explanation: Moles=mass/molar mass=11.2/56=0.2 mol
Chemistry — Solutions
45. Moles of solute in 500 mL of 0.2 M solution are:
- A. 0.1 (Correct)
- B. 1.1
- C. 2.1
- D. -0.9
Explanation: n=MV=0.2×0.5=0.1 mol
Chemistry — Ionic Equilibrium
46. pH of a solution having [H⁺]=1×10⁻³ M is:
- A. 4
- B. 2
- C. 3 (Correct)
- D. 5
Explanation: pH=-log(10⁻³)=3
Chemistry — Chemical Kinetics
47. 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.
Chemistry — Chemical Bonding
48. 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.
Chemistry — Periodic Properties
49. 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.
Chemistry — Electrochemistry
50. 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.
Chemistry — Chemical Kinetics
51. For first order k=0.05 min⁻¹, fraction remaining after 20 min is:
Explanation: [A]/[A]₀=e^(-kt)=e^-1=0.37
Chemistry — Organic Chemistry
52. 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.
Chemistry — Organic Nomenclature
53. IUPAC name of CH₃CH₂CHO is:
- A. propanal (Correct)
- B. propanone
- C. ethanal
- D. propanoic acid
Explanation: Three-carbon aldehyde is propanal.
Chemistry — Coordination Compounds
54. Oxidation state of Fe in [Fe(CN)₆]⁴⁻ is:
Explanation: x+6(-1)=-4, so x=+2.
Chemistry — Organic Properties
55. Highest boiling point is shown by:
- A. ethanol (Correct)
- B. dimethyl ether
- C. ethane
- D. propane
Explanation: Ethanol has intermolecular hydrogen bonding.
Chemistry — Mole Concept
56. Moles in 11.2 g of iron (Fe=56) are:
Explanation: Moles=mass/molar mass=11.2/56=0.2 mol
Chemistry — Solutions
57. Moles of solute in 500 mL of 0.2 M solution are:
Explanation: n=MV=0.2×0.5=0.1 mol
Chemistry — Ionic Equilibrium
58. pH of a solution having [H⁺]=1×10⁻³ M is:
Explanation: pH=-log(10⁻³)=3
Chemistry — Chemical Kinetics
59. 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.
Chemistry — Chemical Bonding
60. 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.
Mathematics — Trigonometry
61. Value of 3 sin30° is:
- A. 2.5
- B. 1.5 (Correct)
- C. 3.5
- D. 0.5
Explanation: sin30°=1/2, so value=1.5
Mathematics — Quadratic Equations
62. For x² - 5x + 6 = 0, discriminant is:
- A. 2
- B. 0
- C. 1 (Correct)
- D. 3
Explanation: D=b²-4ac=25-24=1
Mathematics — Binomial Theorem
63. Coefficient of x³ in (1+x)⁷ is:
- A. 34
- B. 35 (Correct)
- C. 37
- D. 36
Explanation: C(7,3)=35
Mathematics — Sequences
64. Sum of first 10 terms of AP with a=3, d=5 is:
- A. 256
- B. 254
- C. 257
- D. 255 (Correct)
Explanation: S=n/2[2a+(n-1)d]=10/2[6+45]=255
Mathematics — Differentiation
65. If f(x)=x³+2x+1, then f'(2) equals:
- A. 14 (Correct)
- B. 15
- C. 16
- D. 13
Explanation: f'(x)=3x²+2, so f'(2)=14
Mathematics — Definite Integration
66. 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
Mathematics — Coordinate Geometry
67. Distance between (1,2) and (5,6) is:
- A. 5.66 (Correct)
- B. 6.66
- C. 7.66
- D. 4.66
Explanation: Distance=√(4²+4²)=√32=5.66
Mathematics — Vectors
68. Magnitude of vector 2i+4j+4k is:
- A. 6 (Correct)
- B. 7
- C. 8
- D. 5
Explanation: √(4+16+16)=6
Mathematics — Matrices and Determinants
69. 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
Mathematics — Permutations
70. Number of arrangements of letters of LEVEL is:
- A. 30 (Correct)
- B. 31
- C. 29
- D. 32
Explanation: 5!/(2!2!)=30
Mathematics — Complex Numbers
71. If z=3+4i, then |z| is:
- A. 6
- B. 7
- C. 5 (Correct)
- D. 4
Explanation: |z|=√(3²+4²)=5
Mathematics — Probability
72. 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.
Mathematics — Trigonometry
73. 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
Mathematics — Quadratic Equations
74. For x² - 5x + 6 = 0, discriminant is:
- A. 2
- B. 1 (Correct)
- C. 3
- D. 0
Explanation: D=b²-4ac=25-24=1
Mathematics — Binomial Theorem
75. Coefficient of x³ in (1+x)⁷ is:
- A. 35 (Correct)
- B. 34
- C. 37
- D. 36
Explanation: C(7,3)=35
Mathematics — Sequences
76. Sum of first 10 terms of AP with a=3, d=5 is:
- A. 257
- B. 256
- C. 255 (Correct)
- D. 254
Explanation: S=n/2[2a+(n-1)d]=10/2[6+45]=255
Mathematics — Differentiation
77. 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
Mathematics — Definite Integration
78. Evaluate ∫ from 1 to 4 of x² dx:
- A. 21 (Correct)
- B. 23
- C. 22
- D. 20
Explanation: [x³/3]₁⁴=(64-1)/3=21
Mathematics — Coordinate Geometry
79. Distance between (1,2) and (5,6) is:
- A. 6.66
- B. 5.66 (Correct)
- C. 7.66
- D. 4.66
Explanation: Distance=√(4²+4²)=√32=5.66
Mathematics — Vectors
80. Magnitude of vector 2i+4j+4k is:
- A. 6 (Correct)
- B. 5
- C. 8
- D. 7
Explanation: √(4+16+16)=6
Mathematics — Matrices and Determinants
81. If A is 2×2 with determinant 5, determinant of 3A is:
Explanation: det(kA)=k²det(A)=9×5=45
Mathematics — Permutations
82. Number of arrangements of letters of LEVEL is:
Explanation: 5!/(2!2!)=30
Mathematics — Complex Numbers
83. If z=3+4i, then |z| is:
Explanation: |z|=√(3²+4²)=5
Mathematics — Probability
84. 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.
Mathematics — Trigonometry
85. Value of 3 sin30° is:
Explanation: sin30°=1/2, so value=1.5
Mathematics — Quadratic Equations
86. For x² - 5x + 6 = 0, discriminant is:
Explanation: D=b²-4ac=25-24=1
Mathematics — Binomial Theorem
87. Coefficient of x³ in (1+x)⁷ is:
Explanation: C(7,3)=35
Mathematics — Sequences
88. 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
Mathematics — Differentiation
89. If f(x)=x³+2x+1, then f'(2) equals:
Explanation: f'(x)=3x²+2, so f'(2)=14
Mathematics — Definite Integration
90. Evaluate ∫ from 1 to 4 of x² dx:
Explanation: [x³/3]₁⁴=(64-1)/3=21