JEE Main Full Syllabus Mock Test 01

📋 Test Information

• Exam: JEE Main Full Syllabus Mock Test
• Subjects: Physics, Chemistry, Mathematics
• Test Duration: 180 minutes (3 hours)
• Total Questions: 75
• Total Marks: 300
• Question Type: Multiple Choice Questions (MCQs)
• Marking Scheme: +4 for correct, -1 for incorrect

🎯 Test Structure

Section A: Physics (25 Questions, 100 Marks)

• Mechanics: 8 questions
• Thermodynamics: 3 questions
• Electrostatics: 4 questions
• Current Electricity: 3 questions
• Magnetism: 2 questions
• Optics: 3 questions
• Modern Physics: 2 questions

Section B: Chemistry (25 Questions, 100 Marks)

• Physical Chemistry: 8 questions
• Inorganic Chemistry: 8 questions
• Organic Chemistry: 9 questions

Section C: Mathematics (25 Questions, 100 Marks)

• Algebra: 8 questions
• Calculus: 6 questions
• Coordinate Geometry: 5 questions
• Trigonometry: 3 questions
• Vectors and 3D: 3 questions

📝 Section A: Physics

Part 1: Mechanics (8 Questions)

Q1. A particle moves in a circle of radius R with constant angular speed ω. The magnitude of average velocity over half revolution is:

(a) ωR (b) 2ωR/π (c) ωR/2 (d) 2ωR

Q2. A block of mass m is placed on a rough inclined plane with angle of inclination θ. The coefficient of friction between the block and plane is μ. The block just begins to slide down when:

(a) μ = tan θ (b) μ > tan θ (c) μ < tan θ (d) μ = cot θ

Q3. A uniform rod of length L and mass M is hinged at one end and released from horizontal position. When it passes through vertical position, the angular velocity is:

(a) √(3g/2L) (b) √(2g/L) (c) √(3g/L) (d) √(g/L)

Q4. The escape velocity from the surface of Earth is 11.2 km/s. If the radius of Earth becomes half, keeping mass constant, the escape velocity would be:

(a) 5.6 km/s (b) 11.2 km/s (c) 15.8 km/s (d) 22.4 km/s

Q5. A simple harmonic oscillator has amplitude A and time period T. The time taken to travel from x = A/2 to x = -A/2 is:

(a) T/6 (b) T/4 (c) T/3 (d) T/2

Q6. Two identical spheres of radius R are in contact and are kept on a rough horizontal surface. A horizontal force F is applied at the top of one sphere. The acceleration of the center of mass of the system is:

(a) F/2m (b) F/3m (c) F/4m (d) F/8m

Q7. A satellite revolves around Earth in elliptical orbit with perigee and apogee distances from Earth’s center as rp and ra respectively. The time period of satellite is proportional to:

(a) (rp + ra)³/² (b) (rp - ra)³/² (c) (rp × ra)³/² (d) (rp/ra)³/²

Q8. Water flows through a horizontal pipe of varying cross-section. The pressure difference between two points where cross-sectional areas are A₁ and A₂ (A₁ > A₂) is:

(a) (1/2)ρv²(A₂²/A₁² - 1) (b) (1/2)ρv²(1 - A₁²/A₂²) (c) (1/2)ρv²(A₁²/A₂² - 1) (d) (1/2)ρv²(1 - A₂²/A₁²)

Part 2: Thermodynamics (3 Questions)

Q9. An ideal gas expands isothermally from volume V₁ to V₂. The work done by the gas is:

(a) nRT ln(V₂/V₁) (b) nRT ln(V₁/V₂) (c) nRT(V₂ - V₁) (d) nRT(V₁ - V₂)

Q10. The efficiency of Carnot engine working between temperatures T₁ and T₂ (T₁ > T₂) is:

(a) 1 - T₂/T₁ (b) 1 - T₁/T₂ (c) T₂/T₁ (d) T₁/T₂

Q11. Two moles of an ideal gas expand adiabatically from temperature 300K to 200K. The work done by the gas is: (Given Cv = 3R/2)

(a) 300R (b) -300R (c) 900R (d) -900R

Part 3: Electrostatics (4 Questions)

Q12. Two identical positive charges +Q are fixed at points (a,0) and (-a,0). A charge +q is released from rest at point (0,b). The initial acceleration of charge +q is:

(a) Qq/4πε₀ma² (b) Qq/4πε₀mb² (c) 2Qq/4πε₀m(a² + b²) (d) Qqb/4πε₀m(a² + b²)^(3/2)

Q13. A parallel plate capacitor has capacitance C when distance between plates is d. If distance is reduced to d/2, the new capacitance is:

(a) C/2 (b) C (c) 2C (d) 4C

Q14. Electric field inside a uniformly charged solid sphere at distance r from center (r < R) is:

(a) ρr/3ε₀ (b) ρr²/3ε₀ (c) ρR/3ε₀ (d) ρR²/3ε₀r

Q15. The electric potential at point P due to electric dipole of moment p at distance r (r » a) is:

(a) p cos θ/4πε₀r² (b) p sin θ/4πε₀r² (c) p cos θ/4πε₀r (d) p sin θ/4πε₀r

Part 4: Current Electricity (3 Questions)

Q16. A wire of resistance R is stretched to twice its original length. The new resistance is:

(a) R/2 (b) R (c) 2R (d) 4R

Q17. In the circuit shown, the current through 6Ω resistor is:

[Circuit diagram showing 12V battery with 6Ω and 3Ω resistors in parallel]

(a) 1 A (b) 2 A (c) 3 A (d) 4 A

Q18. A cell of emf E and internal resistance r is connected across external resistance R. The condition for maximum power transfer to R is:

(a) R = r (b) R = 2r (c) R = r/2 (d) R = 0

Part 5: Magnetism (2 Questions)

Q19. A long straight wire carries current I. The magnetic field at distance r from wire is:

(a) μ₀I/2πr (b) μ₀I/4πr (c) μ₀I/πr (d) μ₀I/r

Q20. A charged particle moves with velocity v perpendicular to uniform magnetic field B. The radius of circular path is:

(a) mv/qB (b) qB/mv (c) mv²/qB (d) qB/mv²

Part 6: Optics (3 Questions)

Q21. The refractive index of glass is 1.5. The speed of light in glass is:

(a) 2 × 10⁸ m/s (b) 3 × 10⁸ m/s (c) 4.5 × 10⁸ m/s (d) 1.5 × 10⁸ m/s

Q22. In Young’s double slit experiment, the distance between slits is 0.3 mm and distance to screen is 1 m. If wavelength of light is 600 nm, the fringe width is:

(a) 1 mm (b) 2 mm (c) 3 mm (d) 4 mm

Q23. A convex lens has focal length 20 cm. An object is placed 30 cm from lens. The image distance is:

(a) 40 cm (b) 50 cm (c) 60 cm (d) 70 cm

Part 7: Modern Physics (2 Questions)

Q24. The wavelength of photon having energy 3.0 eV is approximately:

(a) 414 nm (b) 4140 nm (c) 41.4 nm (d) 4.14 nm

Q25. The mass defect in nuclear reaction 2¹H + 2¹H → ⁴He is 0.018 amu. The energy released is:

(a) 16.7 MeV (b) 167 MeV (c) 1.67 MeV (d) 0.167 MeV

📝 Section B: Chemistry

Part 1: Physical Chemistry (8 Questions)

Q26. The pH of 0.01 M HCl solution is:

(a) 1 (b) 2 (c) 7 (d) 14

Q27. The rate constant of first order reaction is 2 × 10⁻³ s⁻¹. The half-life is:

(a) 346 s (b) 346.5 s (c) 347 s (d) 350 s

Q28. The osmotic pressure of 0.1 M glucose solution at 27°C is:

(a) 2.48 atm (b) 24.8 atm (c) 0.248 atm (d) 248 atm

Q29. The standard enthalpy of formation of CO₂ is -393.5 kJ/mol. The enthalpy change for reaction C + O₂ → CO₂ is:

(a) -393.5 kJ (b) +393.5 kJ (c) -787 kJ (d) +787 kJ

Q30. The equilibrium constant Kp for reaction N₂ + 3H₂ ⇌ 2NH₃ is related to Kc as:

(a) Kp = Kc(RT)⁻² (b) Kp = Kc(RT)² (c) Kp = Kc(RT) (d) Kp = Kc/RT

Q31. The molar conductivity of 0.1 M KCl solution at infinite dilution is 149.9 S cm²/mol. The molar conductivity at 0.1 M concentration is:

(a) 149.9 S cm²/mol (b) 129.9 S cm²/mol (c) 169.9 S cm²/mol (d) 109.9 S cm²/mol

Q32. The activation energy of reaction is 50 kJ/mol. The rate constant at 300K is 2 × 10⁻³ s⁻¹. The rate constant at 350K is approximately:

(a) 1 × 10⁻² s⁻¹ (b) 2 × 10⁻² s⁻¹ (c) 4 × 10⁻² s⁻¹ (d) 8 × 10⁻² s⁻¹

Q33. The heat of neutralization of strong acid and strong base is:

(a) -57.1 kJ/mol (b) +57.1 kJ/mol (c) -7.1 kJ/mol (d) +7.1 kJ/mol

Part 2: Inorganic Chemistry (8 Questions)

Q34. The electron configuration of Cr³⁺ ion is:

(a) [Ar] 3d³ (b) [Ar] 3d⁵ 4s¹ (c) [Ar] 3d⁴ (d) [Ar] 3d⁶

Q35. The coordination number of central atom in [Co(NH₃)₆]³⁺ is:

(a) 4 (b) 6 (c) 8 (d) 12

Q36. Which of the following has highest boiling point?

(a) H₂O (b) H₂S (c) H₂Se (d) H₂Te

Q37. The oxidation state of sulfur in H₂SO₄ is:

(a) +2 (b) +4 (c) +6 (d) -2

Q38. The structure of SF₄ is:

(a) Tetrahedral (b) Square planar (c) See-saw (d) Trigonal bipyramidal

Q39. Which of the following is a strong field ligand?

(a) H₂O (b) NH₃ (c) Cl⁻ (d) CN⁻

Q40. The magnetic moment of [Fe(CN)₆]⁴⁻ is:

(a) 0 BM (b) 1.73 BM (c) 4.9 BM (d) 5.92 BM

Q41. The lanthanide contraction is due to:

(a) Poor shielding of 4f electrons (b) Poor shielding of 5d electrons (c) High nuclear charge (d) Increased atomic radius

Part 3: Organic Chemistry (9 Questions)

Q42. The IUPAC name of CH₃-CH₂-CH=CH-CH₃ is:

(a) 2-pentene (b) 3-pentene (c) 2-pentene (d) pent-2-ene

Q43. Which of the following shows geometrical isomerism?

(a) CH₃CH=CHCH₃ (b) CH₃CH=CH₂ (c) CH₃CH₂CH=CH₂ (d) CH₃C≡CH

Q44. The major product of reaction between 2-methylpropene and HBr is:

(a) 2-bromo-2-methylpropane (b) 1-bromo-2-methylpropane (c) 2-bromo-1-methylpropane (d) 1-bromo-1-methylpropane

Q45. Which of the following reagents converts primary alcohol to aldehyde?

(a) PCC (b) KMnO₄ (c) K₂Cr₂O₇ (d) H₂SO₄

Q46. The basicity order for the following amines is: I. CH₃NH₂ II. (CH₃)₂NH III. (CH₃)₃N

(a) I > II > III (b) III > II > I (c) II > I > III (d) I = II = III

Q47. The polymer formed by polymerization of ethene is:

(a) Polythene (b) Polystyrene (c) PVC (d) Teflon

Q48. The reaction of benzene with concentrated HNO₃ in presence of H₂SO₄ gives:

(a) Nitrobenzene (b) Phenol (c) Benzoic acid (d) Chlorobenzene

Q49. Which of the following is used as antiseptic?

(a) DDT (b) BHC (c) Iodine (d) Chlorine

Q50. The configuration of 2-bromobutane is:

(a) R (b) S (c) Meso (d) Racemic

📝 Section C: Mathematics

Part 1: Algebra (8 Questions)

Q51. The roots of equation x² + 5x + 6 = 0 are:

(a) -2, -3 (b) 2, 3 (c) -1, -6 (d) 1, 6

Q52. The value of log₂ 8 is:

(a) 2 (b) 3 (c) 4 (d) 8

Q53. The sum of first n natural numbers is:

(a) n(n+1)/2 (b) n(n+1) (c) n² (d) n(n-1)/2

Q54. The value of sin² 30° + cos² 30° is:

(a) 0 (b) 1/2 (c) 1 (d) 2

Q55. The determinant |1 2 3; 4 5 6; 7 8 9| is equal to:

(a) 0 (b) 1 (c) 2 (d) 3

Q56. The solution of inequality x² - 5x + 6 < 0 is:

(a) 2 < x < 3 (b) x < 2 or x > 3 (c) x ≤ 2 or x ≥ 3 (d) 2 ≤ x ≤ 3

Q57. The value of (1 + i)² is:

(a) 2i (b) -2i (c) 2 (d) -2

Q58. The term independent of x in expansion of (x + 1/x)⁶ is:

(a) 20 (b) 15 (c) 6 (d) 1

Part 2: Calculus (6 Questions)

Q59. The derivative of sin x is:

(a) cos x (b) -cos x (c) -sin x (d) sin x

Q60. The integral of x² dx is:

(a) x³/3 + C (b) x³ + C (c) 2x³/3 + C (d) x² + C

Q61. The limit lim(x→0) sin x/x is:

(a) 0 (b) 1 (c) -1 (d) ∞

Q62. The maximum value of function f(x) = -x² + 4x + 5 is:

(a) 5 (b) 9 (c) 13 (d) 17

Q63. The derivative of log x is:

(a) 1/x (b) x (c) -1/x (d) -x

Q64. The area under curve y = x² between x = 0 and x = 2 is:

(a) 4/3 (b) 8/3 (c) 2 (d) 4

Part 3: Coordinate Geometry (5 Questions)

Q65. The distance between points (1, 2) and (4, 6) is:

(a) 3 (b) 4 (c) 5 (d) 6

Q66. The equation of line passing through origin and slope 2 is:

(a) y = 2x (b) y = x/2 (c) x = 2y (d) x = y/2

Q67. The center of circle x² + y² - 4x + 6y - 12 = 0 is:

(a) (2, -3) (b) (-2, 3) (c) (4, 6) (d) (-4, -6)

Q68. The focus of parabola y² = 4ax is:

(a) (a, 0) (b) (-a, 0) (c) (0, a) (d) (0, -a)

Q69. The eccentricity of ellipse x²/9 + y²/16 = 1 is:

(a) 3/4 (b) 4/3 (c) 5/4 (d) 4/5

Part 4: Trigonometry (3 Questions)

Q70. The value of sin 90° is:

(a) 0 (b) 1/2 (c) 1 (d) √3/2

Q71. The value of cos 60° is:

(a) 0 (b) 1/2 (c) √3/2 (d) 1

Q72. The value of tan 45° is:

(a) 0 (b) 1 (c) √3 (d) 1/√3

Part 5: Vectors and 3D (3 Questions)

Q73. The magnitude of vector 2i + 3j + 6k is:

(a) 1 (b) 7 (c) √7 (d) 49

Q74. The dot product of vectors i + j and i - j is:

(a) 0 (b) 1 (c) 2 (d) -1

Q75. The angle between vectors i and j is:

(a) 0° (b) 45° (c) 90° (d) 180°

🔑 Answer Key

Physics Answers:

1. (b) 2ωR/π
2. (a) μ = tan θ
3. (a) √(3g/2L)
4. (c) 15.8 km/s
5. (c) T/3
6. (b) F/3m
7. (c) (rp × ra)³/²
8. (a) (1/2)ρv²(A₂²/A₁² - 1)
9. (a) nRT ln(V₂/V₁)
10. (a) 1 - T₂/T₁
11. (b) -300R
12. (d) Qqb/4πε₀m(a² + b²)^(3/2)
13. (c) 2C
14. (a) ρr/3ε₀
15. (a) p cos θ/4πε₀r²
16. (d) 4R
17. (b) 2 A
18. (a) R = r
19. (a) μ₀I/2πr
20. (a) mv/qB
21. (a) 2 × 10⁸ m/s
22. (b) 2 mm
23. (c) 60 cm
24. (a) 414 nm
25. (a) 16.7 MeV

Chemistry Answers:

26. (b) 2
27. (b) 346.5 s
28. (a) 2.48 atm
29. (a) -393.5 kJ
30. (a) Kp = Kc(RT)⁻²
31. (b) 129.9 S cm²/mol
32. (c) 4 × 10⁻² s⁻¹
33. (a) -57.1 kJ/mol
34. (a) [Ar] 3d³
35. (b) 6
36. (a) H₂O
37. (c) +6
38. (c) See-saw
39. (d) CN⁻
40. (a) 0 BM
41. (a) Poor shielding of 4f electrons
42. (d) pent-2-ene
43. (a) CH₃CH=CHCH₃
44. (a) 2-bromo-2-methylpropane
45. (a) PCC
46. (c) II > I > III
47. (a) Polythene
48. (a) Nitrobenzene
49. (c) Iodine
50. (d) Racemic

Mathematics Answers:

51. (a) -2, -3
52. (b) 3
53. (a) n(n+1)/2
54. (c) 1
55. (a) 0
56. (a) 2 < x < 3
57. (a) 2i
58. (a) 20
59. (a) cos x
60. (a) x³/3 + C
61. (b) 1
62. (b) 9
63. (a) 1/x
64. (b) 8/3
65. (c) 5
66. (a) y = 2x
67. (a) (2, -3)
68. (a) (a, 0)
69. (d) 4/5
70. (c) 1
71. (b) 1/2
72. (b) 1
73. (b) 7
74. (a) 0
75. (c) 90°

📊 Performance Analysis

Score Interpretation:

• 240-300 marks: Excellent performance (Expected JEE Main rank: < 1000)
• 180-239 marks: Good performance (Expected JEE Main rank: 1000-10000)
• 120-179 marks: Average performance (Expected JEE Main rank: 10000-50000)
• Below 120 marks: Need significant improvement

Time Management:

• Physics: 60 minutes (2.4 minutes per question)
• Chemistry: 60 minutes (2.4 minutes per question)
• Mathematics: 60 minutes (2.4 minutes per question)

Section-wise Strategy:

1. Start with your strongest subject
2. Don’t spend more than 3 minutes on any question initially
3. Mark difficult questions for review
4. Ensure no negative marking for unattempted questions

💡 Test Preparation Tips

Before the Test:

1. Revise all formulas and key concepts
2. Practice time management with mock tests
3. Get adequate sleep before test day
4. Reach test center early to avoid stress

During the Test:

1. Read questions carefully
2. Use elimination technique for MCQs
3. Manage time section-wise
4. Don’t panic if some questions are difficult

After the Test:

1. Analyze mistakes thoroughly
2. Identify weak areas for improvement
3. Practice similar questions
4. Track progress over time

All the best for your JEE Main preparation! 🎯