JEE Main Practice Set 1
Original JEE Main-style full-length set with 90 unique questions: 30 Mathematics, 30 Physics, and 30 Chemistry following the official exam pattern.
Exam Pattern & Rules
Negative Marking: Yes, in Section A and Section B
Note: Paper contains 90 questions (30 per subject), with 75 attempted as per the current exam attempt structure.
Practice Set Details
JEE Main Practice Set 1: all 90 questions with answers
Try each question first, then open “Show answer” to check the correct option and explanation.
Q1.Solve for x: 2x + 5 = 11.
- A.4
- B.2
- C.5
- D.3
Show answer
Correct answer: D. 3
Subtract 5 from both sides: 2x = 6. Divide by 2: x = 3.
Q2.One root of x² − 8x + 15 = 0 is 3. The other root is:
- A.4
- B.8
- C.5
- D.6
Show answer
Correct answer: C. 5
Product of roots = 15. Other root = 15 ÷ 3 = 5.
Q3.The 8th term of an AP with first term 2 and common difference 2 is:
- A.19
- B.16
- C.14
- D.18
Show answer
Correct answer: B. 16
aₙ = a + (n−1)d = 2 + 7×2 = 16.
Q4.Slope of the line through (1, 2) and (4, 8) is:
- A.2
- B.3
- C.1
- D.4
Show answer
Correct answer: A. 2
Slope = (8−2) ÷ (4−1) = 6 ÷ 3 = 2.
Q5.Value of sin 0° is:
- A.1
- B.1/2
- C.√3/2
- D.0
Show answer
Correct answer: D. 0
sin 0° = 0.
Q6.A bag contains 3 red and 5 blue balls. Probability of drawing a red ball is:
- A.3/7
- B.6/9
- C.3/8
- D.5/9
Show answer
Correct answer: C. 3/8
P(red) = 3/8.
Q7.Determinant of matrix [[2, 1], [2, 3]] is:
- A.12
- B.4
- C.9
- D.1
Show answer
Correct answer: B. 4
det = ad − bc = 2×3 − 1×2 = 4.
Q8.Evaluate: log₂ₐₑₒₓ2(2^2) [log base 2].
- A.2
- B.3
- C.1
- D.4
Show answer
Correct answer: A. 2
logₐ(a^n) = n, so log_2(2^2) = 2.
Q9.Find 6P2.
- A.15
- B.34
- C.26
- D.30
Show answer
Correct answer: D. 30
6P2 = 6!/(6−2)! = 6×5 = 30.
Q10.Find 7C2.
- A.24
- B.18
- C.21
- D.14
Show answer
Correct answer: C. 21
nC2 = n(n−1)/2 = 7×6/2 = 21.
Q11.Simple interest on Rs 500 at 4% p.a. for 2 years is:
- A.Rs 80
- B.Rs 40
- C.Rs 120
- D.Rs 0
Show answer
Correct answer: B. Rs 40
SI = P×R×T/100 = 500×4×2/100 = Rs 40.
Q12.Area of a triangle with base 6 cm and height 4 cm is:
- A.12 cm²
- B.24 cm²
- C.18 cm²
- D.6 cm²
Show answer
Correct answer: A. 12 cm²
Area = (1/2) × base × height = (1/2) × 6 × 4 = 12 cm².
Q13.Solve for x: 3x + 6 = 18.
- A.5
- B.3
- C.6
- D.4
Show answer
Correct answer: D. 4
Subtract 6 from both sides: 3x = 12. Divide by 3: x = 4.
Q14.One root of x² − 11x + 28 = 0 is 4. The other root is:
- A.6
- B.11
- C.7
- D.8
Show answer
Correct answer: C. 7
Product of roots = 28. Other root = 28 ÷ 4 = 7.
Q15.The 9th term of an AP with first term 3 and common difference 3 is:
- A.31
- B.27
- C.24
- D.30
Show answer
Correct answer: B. 27
aₙ = a + (n−1)d = 3 + 8×3 = 27.
Q16.Slope of the line through (2, 3) and (5, 12) is:
- A.3
- B.4
- C.2
- D.5
Show answer
Correct answer: A. 3
Slope = (12−3) ÷ (5−2) = 9 ÷ 3 = 3.
Q17.Value of cos 0° is:
- A.0
- B.−1
- C.1/2
- D.1
Show answer
Correct answer: D. 1
cos 0° = 1.
Q18.A bag contains 4 red and 6 blue balls. Probability of drawing a red ball is:
- A.4/9
- B.7/11
- C.4/10
- D.6/11
Show answer
Correct answer: C. 4/10
P(red) = 4/10.
Q19.Determinant of matrix [[3, 2], [3, 4]] is:
- A.15
- B.6
- C.11
- D.3
Show answer
Correct answer: B. 6
det = ad − bc = 3×4 − 2×3 = 6.
Q20.Evaluate: log₂ₐₑₒₓ3(3^3) [log base 3].
- A.3
- B.4
- C.2
- D.9
Show answer
Correct answer: A. 3
logₐ(a^n) = n, so log_3(3^3) = 3.
Q21.Find 7P3.
- A.70
- B.216
- C.204
- D.210
Show answer
Correct answer: D. 210
7P3 = 7!/(7−3)! = 7×6×5 = 210.
Q22.Find 8C2.
- A.31
- B.25
- C.28
- D.16
Show answer
Correct answer: C. 28
nC2 = n(n−1)/2 = 8×7/2 = 28.
Q23.Simple interest on Rs 700 at 5% p.a. for 3 years is:
- A.Rs 210
- B.Rs 105
- C.Rs 255
- D.Rs 30
Show answer
Correct answer: B. Rs 105
SI = P×R×T/100 = 700×5×3/100 = Rs 105.
Q24.Area of a triangle with base 7 cm and height 5 cm is:
- A.17.5 cm²
- B.35 cm²
- C.23.5 cm²
- D.11.5 cm²
Show answer
Correct answer: A. 17.5 cm²
Area = (1/2) × base × height = (1/2) × 7 × 5 = 17.5 cm².
Q25.Solve for x: 4x + 7 = 27.
- A.6
- B.4
- C.7
- D.5
Show answer
Correct answer: D. 5
Subtract 7 from both sides: 4x = 20. Divide by 4: x = 5.
Q26.One root of x² − 14x + 45 = 0 is 5. The other root is:
- A.8
- B.14
- C.9
- D.10
Show answer
Correct answer: C. 9
Product of roots = 45. Other root = 45 ÷ 5 = 9.
Q27.The 10th term of an AP with first term 4 and common difference 4 is:
- A.45
- B.40
- C.36
- D.44
Show answer
Correct answer: B. 40
aₙ = a + (n−1)d = 4 + 9×4 = 40.
Q28.Slope of the line through (3, 4) and (6, 16) is:
- A.4
- B.5
- C.3
- D.6
Show answer
Correct answer: A. 4
Slope = (16−4) ÷ (6−3) = 12 ÷ 3 = 4.
Q29.Value of sin 30° is:
- A.0
- B.1
- C.√3/2
- D.1/2
Show answer
Correct answer: D. 1/2
sin 30° = 1/2.
Q30.A bag contains 5 red and 7 blue balls. Probability of drawing a red ball is:
- A.5/11
- B.8/13
- C.5/12
- D.7/13
Show answer
Correct answer: C. 5/12
P(red) = 5/12.
Q31.A body starts with velocity 2 m/s and has acceleration 2 m/s². Its velocity after 3 s is:
- A.6 m/s
- B.10 m/s
- C.5 m/s
- D.8 m/s
Show answer
Correct answer: D. 8 m/s
v = u + at = 2 + 2×3 = 8 m/s.
Q32.For u = 1 m/s, a = 2 m/s², t = 4 s, displacement is:
- A.28 m
- B.18 m
- C.20 m
- D.4 m
Show answer
Correct answer: C. 20 m
s = ut + ½At² = 1×4 + 0.5×2×4² = 20 m.
Q33.Net force needed to give 2 kg mass an acceleration of 3 m/s² is:
- A.5 N
- B.6 N
- C.9 N
- D.3 N
Show answer
Correct answer: B. 6 N
F = ma = 2×3 = 6 N.
Q34.Work done when force 10 N moves a body 3 m in its direction is:
- A.30 J
- B.40 J
- C.20 J
- D.13 J
Show answer
Correct answer: A. 30 J
W = F×d = 10×3 = 30 J.
Q35.A body does 100 J of work in 5 s. Its power is:
- A.40 W
- B.25 W
- C.15 W
- D.20 W
Show answer
Correct answer: D. 20 W
P = W/t = 100/5 = 20 W.
Q36.A body of mass 3 kg moves at 4 m/s. Its momentum is:
- A.8 kg·m/s
- B.7 kg·m/s
- C.12 kg·m/s
- D.15 kg·m/s
Show answer
Correct answer: C. 12 kg·m/s
p = mv = 3×4 = 12 kg·m/s.
Q37.Kinetic energy of 2 kg body moving at 4 m/s is:
- A.14 J
- B.16 J
- C.8 J
- D.24 J
Show answer
Correct answer: B. 16 J
KE = ½mv² = 0.5×2×4² = 16 J.
Q38.Voltage across a 3 Ω resistor carrying 2 A current is:
- A.6 V
- B.9 V
- C.3 V
- D.7 V
Show answer
Correct answer: A. 6 V
V = IR = 2×3 = 6 V.
Q39.Two resistors 4 Ω and 6 Ω connected in series. Total resistance is:
- A.24 Ω
- B.2 Ω
- C.12 Ω
- D.10 Ω
Show answer
Correct answer: D. 10 Ω
Series: R = R₁ + R₂ = 4 + 6 = 10 Ω.
Q40.Power of a lens with focal length 20 cm is:
- A.6 D
- B.0.2 D
- C.5 D
- D.20 D
Show answer
Correct answer: C. 5 D
P = 1/f = 1/0.2 m = 5 D.
Q41.Wave speed for frequency 50 Hz and wavelength 2 m is:
- A.52 m/s
- B.100 m/s
- C.150 m/s
- D.80 m/s
Show answer
Correct answer: B. 100 m/s
v = fλ = 50×2 = 100 m/s.
Q42.Gravitational force doubles when one mass doubles:
- A.doubles
- B.halves
- C.quadruples
- D.unchanged
Show answer
Correct answer: A. doubles
F ∝ m₁×m₂; doubling one mass doubles F.
Q43.A body starts with velocity 3 m/s and has acceleration 3 m/s². Its velocity after 4 s is:
- A.12 m/s
- B.18 m/s
- C.7 m/s
- D.15 m/s
Show answer
Correct answer: D. 15 m/s
v = u + at = 3 + 3×4 = 15 m/s.
Q44.For u = 2 m/s, a = 3 m/s², t = 5 s, displacement is:
- A.62.5 m
- B.44.5 m
- C.47.5 m
- D.10 m
Show answer
Correct answer: C. 47.5 m
s = ut + ½At² = 2×5 + 0.5×3×5² = 47.5 m.
Q45.Net force needed to give 3 kg mass an acceleration of 4 m/s² is:
- A.7 N
- B.12 N
- C.16 N
- D.8 N
Show answer
Correct answer: B. 12 N
F = ma = 3×4 = 12 N.
Q46.Work done when force 15 N moves a body 4 m in its direction is:
- A.60 J
- B.75 J
- C.45 J
- D.19 J
Show answer
Correct answer: A. 60 J
W = F×d = 15×4 = 60 J.
Q47.A body does 150 J of work in 6 s. Its power is:
- A.50 W
- B.31 W
- C.20 W
- D.25 W
Show answer
Correct answer: D. 25 W
P = W/t = 150/6 = 25 W.
Q48.A body of mass 4 kg moves at 5 m/s. Its momentum is:
- A.15 kg·m/s
- B.9 kg·m/s
- C.20 kg·m/s
- D.24 kg·m/s
Show answer
Correct answer: C. 20 kg·m/s
p = mv = 4×5 = 20 kg·m/s.
Q49.Kinetic energy of 3 kg body moving at 5 m/s is:
- A.34.5 J
- B.37.5 J
- C.15 J
- D.52.5 J
Show answer
Correct answer: B. 37.5 J
KE = ½mv² = 0.5×3×5² = 37.5 J.
Q50.Voltage across a 4 Ω resistor carrying 3 A current is:
- A.12 V
- B.16 V
- C.8 V
- D.9 V
Show answer
Correct answer: A. 12 V
V = IR = 3×4 = 12 V.
Q51.Two resistors 5 Ω and 7 Ω connected in series. Total resistance is:
- A.35 Ω
- B.2 Ω
- C.14 Ω
- D.12 Ω
Show answer
Correct answer: D. 12 Ω
Series: R = R₁ + R₂ = 5 + 7 = 12 Ω.
Q52.Power of a lens with focal length 30 cm is:
- A.4.33 D
- B.0.3 D
- C.3.33 D
- D.30 D
Show answer
Correct answer: C. 3.33 D
P = 1/f = 1/0.3 m = 3.33 D.
Q53.Wave speed for frequency 70 Hz and wavelength 3 m is:
- A.73 m/s
- B.210 m/s
- C.280 m/s
- D.180 m/s
Show answer
Correct answer: B. 210 m/s
v = fλ = 70×3 = 210 m/s.
Q54.Gravitational force when separation is tripled becomes:
- A.1/9 of original
- B.1/3 of original
- C.3 times
- D.9 times
Show answer
Correct answer: A. 1/9 of original
F ∝ 1/r²; 3× distance → F/9.
Q55.A body starts with velocity 4 m/s and has acceleration 4 m/s². Its velocity after 5 s is:
- A.20 m/s
- B.28 m/s
- C.9 m/s
- D.24 m/s
Show answer
Correct answer: D. 24 m/s
v = u + at = 4 + 4×5 = 24 m/s.
Q56.For u = 3 m/s, a = 4 m/s², t = 6 s, displacement is:
- A.114 m
- B.86 m
- C.90 m
- D.18 m
Show answer
Correct answer: C. 90 m
s = ut + ½At² = 3×6 + 0.5×4×6² = 90 m.
Q57.Net force needed to give 4 kg mass an acceleration of 5 m/s² is:
- A.9 N
- B.20 N
- C.25 N
- D.15 N
Show answer
Correct answer: B. 20 N
F = ma = 4×5 = 20 N.
Q58.Work done when force 20 N moves a body 5 m in its direction is:
- A.100 J
- B.120 J
- C.80 J
- D.25 J
Show answer
Correct answer: A. 100 J
W = F×d = 20×5 = 100 J.
Q59.A body does 200 J of work in 7 s. Its power is:
- A.57.14 W
- B.35.57 W
- C.23.57 W
- D.28.57 W
Show answer
Correct answer: D. 28.57 W
P = W/t = 200/7 = 28.57 W.
Q60.A body of mass 5 kg moves at 6 m/s. Its momentum is:
- A.24 kg·m/s
- B.11 kg·m/s
- C.30 kg·m/s
- D.35 kg·m/s
Show answer
Correct answer: C. 30 kg·m/s
p = mv = 5×6 = 30 kg·m/s.
Q61.If [H⁺] = 10⁻1 mol/L, the pH of the solution is:
- A.2
- B.13
- C.3
- D.1
Show answer
Correct answer: D. 1
pH = −log[H⁺] = −log(10⁻1) = 1.
Q62.Molar mass of H₂O is:
- A.20 g/mol
- B.22 g/mol
- C.18 g/mol
- D.16 g/mol
Show answer
Correct answer: C. 18 g/mol
Add atomic masses: molar mass of H₂O = 18 g/mol.
Q63.Oxidation state of sulfur in H₂SO₄ is:
- A.−2
- B.+6
- C.+4
- D.+2
Show answer
Correct answer: B. +6
S in H₂SO₄ = +6.
Q64.Formula of compound formed by Na⁺ and O²⁻ is:
- A.Na₂O
- B.NaO
- C.NaO₂
- D.Na₂O₂
Show answer
Correct answer: A. Na₂O
Na(+1) and O(−2): Na₂O.
Q65.Gas evolved when zinc reacts with dilute HCl is:
- A.oxygen
- B.nitrogen
- C.carbon dioxide
- D.hydrogen
Show answer
Correct answer: D. hydrogen
Zn + 2HCl → ZnCl₂ + H₂↑.
Q66.Which is a strong acid?
- A.H₂CO₃
- B.HF
- C.HCl
- D.CH₃COOH
Show answer
Correct answer: C. HCl
HCl ionises completely in water.
Q67.Functional group in ethanol is:
- A.−CO− (ketone)
- B.−OH (hydroxyl)
- C.−COOH (carboxyl)
- D.−CHO (aldehyde)
Show answer
Correct answer: B. −OH (hydroxyl)
C₂H₅OH has a hydroxyl group.
Q68.Which element belongs to Group 1 (alkali metals)?
- A.Potassium
- B.Calcium
- C.Magnesium
- D.Aluminium
Show answer
Correct answer: A. Potassium
K is in Group 1.
Q69.Number of moles in 18 g of H₂O (M = 18 g/mol) is:
- A.2
- B.3
- C.2.5
- D.1
Show answer
Correct answer: D. 1
n = mass/M = 18/18 = 1 mol.
Q70.Electronic configuration 2,8,1 corresponds to:
- A.Magnesium (Mg)
- B.Lithium (Li)
- C.Sodium (Na)
- D.Potassium (K)
Show answer
Correct answer: C. Sodium (Na)
2+8+1=11 → Na.
Q71.Which is a covalent compound?
- A.CaCl₂
- B.Water (H₂O)
- C.NaCl
- D.MgO
Show answer
Correct answer: B. Water (H₂O)
Water has covalent O−H bonds.
Q72.Common name of NaHCO₃ is:
- A.baking soda
- B.washing soda
- C.bleaching powder
- D.quicklime
Show answer
Correct answer: A. baking soda
NaHCO₃ = baking soda.
Q73.If [H⁺] = 10⁻2 mol/L, the pH of the solution is:
- A.3
- B.12
- C.1
- D.2
Show answer
Correct answer: D. 2
pH = −log[H⁺] = −log(10⁻2) = 2.
Q74.Molar mass of CO₂ is:
- A.46 g/mol
- B.48 g/mol
- C.44 g/mol
- D.40 g/mol
Show answer
Correct answer: C. 44 g/mol
Add atomic masses: molar mass of CO₂ = 44 g/mol.
Q75.Oxidation state of nitrogen in NH₃ is:
- A.+5
- B.−3
- C.+3
- D.0
Show answer
Correct answer: B. −3
H is +1 (×3), so N = −3.
Q76.Formula of magnesium chloride is:
- A.MgCl₂
- B.MgCl
- C.Mg₂Cl
- D.MgCl₃
Show answer
Correct answer: A. MgCl₂
Mg(+2) needs 2 Cl(−1).
Q77.Gas evolved when Na₂CO₃ reacts with HCl is:
- A.hydrogen
- B.oxygen
- C.chlorine
- D.carbon dioxide
Show answer
Correct answer: D. carbon dioxide
Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂↑.
Q78.Which is a weak acid?
- A.H₂SO₄
- B.HCl
- C.CH₃COOH
- D.HNO₃
Show answer
Correct answer: C. CH₃COOH
Acetic acid ionises partially.
Q79.Functional group in ethanoic acid is:
- A.−NH₂ (amine)
- B.−COOH (carboxyl)
- C.−OH (hydroxyl)
- D.−CO− (ketone)
Show answer
Correct answer: B. −COOH (carboxyl)
CH₃COOH has a carboxyl group.
Q80.Atomic number of carbon is:
- A.6
- B.12
- C.14
- D.8
Show answer
Correct answer: A. 6
Carbon has 6 protons.
Q81.Number of moles in 88 g of CO₂ (M = 44 g/mol) is:
- A.3
- B.1
- C.3.5
- D.2
Show answer
Correct answer: D. 2
n = mass/M = 88/44 = 2 mol.
Q82.Electronic configuration 2,8,8 corresponds to:
- A.Sulphur (S)
- B.Potassium (K)
- C.Argon (Ar)
- D.Chlorine (Cl)
Show answer
Correct answer: C. Argon (Ar)
2+8+8=18 → Ar.
Q83.Bond angle in water molecule is approximately:
- A.109.5°
- B.104.5°
- C.180°
- D.120°
Show answer
Correct answer: B. 104.5°
Water is V-shaped; bond angle ≈ 104.5°.
Q84.Chemical name of common salt (NaCl) is:
- A.sodium chloride
- B.sodium carbonate
- C.sodium hydroxide
- D.sodium sulfate
Show answer
Correct answer: A. sodium chloride
NaCl = sodium chloride.
Q85.If [H⁺] = 10⁻3 mol/L, the pH of the solution is:
- A.4
- B.11
- C.2
- D.3
Show answer
Correct answer: D. 3
pH = −log[H⁺] = −log(10⁻3) = 3.
Q86.Molar mass of NH₃ is:
- A.16 g/mol
- B.18 g/mol
- C.17 g/mol
- D.14 g/mol
Show answer
Correct answer: C. 17 g/mol
Add atomic masses: molar mass of NH₃ = 17 g/mol.
Q87.Oxidation state of carbon in CO₂ is:
- A.0
- B.+4
- C.+2
- D.−2
Show answer
Correct answer: B. +4
O is −2 (×2), so C = +4.
Q88.Formula of aluminium oxide is:
- A.Al₂O₃
- B.AlO
- C.Al₃O₂
- D.AlO₃
Show answer
Correct answer: A. Al₂O₃
Al(+3) and O(−2): Al₂O₃.
Q89.Gas evolved when NH₄Cl reacts with Ca(OH)₂ is:
- A.hydrogen
- B.nitrogen
- C.HCl
- D.ammonia
Show answer
Correct answer: D. ammonia
2NH₄Cl + Ca(OH)₂ → CaCl₂ + 2H₂O + 2NH₃↑.
Q90.pH of pure water at 25°C is:
- A.14
- B.1
- C.7
- D.0
Show answer
Correct answer: C. 7
Pure water [H⁺]=[OH⁻]=10⁻⁷; pH=7.