JEE Main Practice Set 2
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 2: all 90 questions with answers
Try each question first, then open “Show answer” to check the correct option and explanation.
Q1.Solve for x: 7x + 10 = 66.
- A.9
- B.7
- C.10
- D.8
Show answer
Correct answer: D. 8
Subtract 10 from both sides: 7x = 56. Divide by 7: x = 8.
Q2.One root of x² − 18x + 80 = 0 is 8. The other root is:
- A.9
- B.18
- C.10
- D.11
Show answer
Correct answer: C. 10
Product of roots = 80. Other root = 80 ÷ 8 = 10.
Q3.The 8th term of an AP with first term 7 and common difference 7 is:
- A.64
- B.56
- C.49
- D.63
Show answer
Correct answer: B. 56
aₙ = a + (n−1)d = 7 + 7×7 = 56.
Q4.Slope of the line through (6, 7) and (9, 28) is:
- A.7
- B.8
- C.6
- D.9
Show answer
Correct answer: A. 7
Slope = (28−7) ÷ (9−6) = 21 ÷ 3 = 7.
Q5.Value of sin 90° is:
- A.0
- B.−1
- C.1/2
- D.1
Show answer
Correct answer: D. 1
sin 90° = 1.
Q6.A bag contains 8 red and 10 blue balls. Probability of drawing a red ball is:
- A.8/17
- B.11/19
- C.8/18
- D.10/19
Show answer
Correct answer: C. 8/18
P(red) = 8/18.
Q7.Determinant of matrix [[7, 1], [3, 8]] is:
- A.23
- B.53
- C.58
- D.50
Show answer
Correct answer: B. 53
det = ad − bc = 7×8 − 1×3 = 53.
Q8.Evaluate: log₂ₐₑₒₓ3(3^7) [log base 3].
- A.7
- B.8
- C.6
- D.21
Show answer
Correct answer: A. 7
logₐ(a^n) = n, so log_3(3^7) = 7.
Q9.Find 11P4.
- A.1980
- B.7928
- C.7912
- D.7920
Show answer
Correct answer: D. 7920
11P4 = 11!/(11−4)! = 11×10×9×8 = 7920.
Q10.Find 12C2.
- A.69
- B.63
- C.66
- D.24
Show answer
Correct answer: C. 66
nC2 = n(n−1)/2 = 12×11/2 = 66.
Q11.Simple interest on Rs 1500 at 9% p.a. for 3 years is:
- A.Rs 810
- B.Rs 405
- C.Rs 675
- D.Rs 270
Show answer
Correct answer: B. Rs 405
SI = P×R×T/100 = 1500×9×3/100 = Rs 405.
Q12.Area of a triangle with base 11 cm and height 9 cm is:
- A.49.5 cm²
- B.99 cm²
- C.55.5 cm²
- D.43.5 cm²
Show answer
Correct answer: A. 49.5 cm²
Area = (1/2) × base × height = (1/2) × 11 × 9 = 49.5 cm².
Q13.Solve for x: 8x + 11 = 83.
- A.10
- B.8
- C.11
- D.9
Show answer
Correct answer: D. 9
Subtract 11 from both sides: 8x = 72. Divide by 8: x = 9.
Q14.One root of x² − 21x + 108 = 0 is 9. The other root is:
- A.11
- B.21
- C.12
- D.13
Show answer
Correct answer: C. 12
Product of roots = 108. Other root = 108 ÷ 9 = 12.
Q15.The 9th term of an AP with first term 8 and common difference 8 is:
- A.81
- B.72
- C.64
- D.80
Show answer
Correct answer: B. 72
aₙ = a + (n−1)d = 8 + 8×8 = 72.
Q16.Slope of the line through (1, 8) and (4, 32) is:
- A.8
- B.9
- C.7
- D.10
Show answer
Correct answer: A. 8
Slope = (32−8) ÷ (4−1) = 24 ÷ 3 = 8.
Q17.Value of cos 90° is:
- A.1
- B.−1
- C.1/2
- D.0
Show answer
Correct answer: D. 0
cos 90° = 0.
Q18.A bag contains 9 red and 11 blue balls. Probability of drawing a red ball is:
- A.9/19
- B.12/21
- C.9/20
- D.11/21
Show answer
Correct answer: C. 9/20
P(red) = 9/20.
Q19.Determinant of matrix [[8, 2], [4, 9]] is:
- A.26
- B.64
- C.69
- D.61
Show answer
Correct answer: B. 64
det = ad − bc = 8×9 − 2×4 = 64.
Q20.Evaluate: log₂ₐₑₒₓ5(5^8) [log base 5].
- A.8
- B.9
- C.7
- D.40
Show answer
Correct answer: A. 8
logₐ(a^n) = n, so log_5(5^8) = 8.
Q21.Find 12P2.
- A.66
- B.136
- C.128
- D.132
Show answer
Correct answer: D. 132
12P2 = 12!/(12−2)! = 12×11 = 132.
Q22.Find 13C2.
- A.81
- B.75
- C.78
- D.26
Show answer
Correct answer: C. 78
nC2 = n(n−1)/2 = 13×12/2 = 78.
Q23.Simple interest on Rs 1700 at 10% p.a. for 4 years is:
- A.Rs 1360
- B.Rs 680
- C.Rs 1080
- D.Rs 480
Show answer
Correct answer: B. Rs 680
SI = P×R×T/100 = 1700×10×4/100 = Rs 680.
Q24.Area of a triangle with base 12 cm and height 10 cm is:
- A.60 cm²
- B.120 cm²
- C.66 cm²
- D.54 cm²
Show answer
Correct answer: A. 60 cm²
Area = (1/2) × base × height = (1/2) × 12 × 10 = 60 cm².
Q25.Solve for x: 2x + 12 = 32.
- A.11
- B.9
- C.12
- D.10
Show answer
Correct answer: D. 10
Subtract 12 from both sides: 2x = 20. Divide by 2: x = 10.
Q26.One root of x² − 24x + 140 = 0 is 10. The other root is:
- A.13
- B.24
- C.14
- D.15
Show answer
Correct answer: C. 14
Product of roots = 140. Other root = 140 ÷ 10 = 14.
Q27.The 10th term of an AP with first term 9 and common difference 2 is:
- A.37
- B.27
- C.25
- D.29
Show answer
Correct answer: B. 27
aₙ = a + (n−1)d = 9 + 9×2 = 27.
Q28.Slope of the line through (2, 2) and (5, 29) is:
- A.9
- B.10
- C.8
- D.11
Show answer
Correct answer: A. 9
Slope = (29−2) ÷ (5−2) = 27 ÷ 3 = 9.
Q29.Value of sin 45° is:
- A.1/2
- B.√3/2
- C.1
- D.1/√2
Show answer
Correct answer: D. 1/√2
sin 45° = 1/√2.
Q30.A bag contains 10 red and 12 blue balls. Probability of drawing a red ball is:
- A.10/21
- B.13/23
- C.10/22
- D.12/23
Show answer
Correct answer: C. 10/22
P(red) = 10/22.
Q31.A body starts with velocity 7 m/s and has acceleration 7 m/s². Its velocity after 3 s is:
- A.21 m/s
- B.35 m/s
- C.10 m/s
- D.28 m/s
Show answer
Correct answer: D. 28 m/s
v = u + at = 7 + 7×3 = 28 m/s.
Q32.For u = 6 m/s, a = 2 m/s², t = 5 s, displacement is:
- A.65 m
- B.53 m
- C.55 m
- D.30 m
Show answer
Correct answer: C. 55 m
s = ut + ½At² = 6×5 + 0.5×2×5² = 55 m.
Q33.Net force needed to give 7 kg mass an acceleration of 8 m/s² is:
- A.15 N
- B.56 N
- C.64 N
- D.48 N
Show answer
Correct answer: B. 56 N
F = ma = 7×8 = 56 N.
Q34.Work done when force 35 N moves a body 8 m in its direction is:
- A.280 J
- B.315 J
- C.245 J
- D.43 J
Show answer
Correct answer: A. 280 J
W = F×d = 35×8 = 280 J.
Q35.A body does 350 J of work in 10 s. Its power is:
- A.70 W
- B.45 W
- C.30 W
- D.35 W
Show answer
Correct answer: D. 35 W
P = W/t = 350/10 = 35 W.
Q36.A body of mass 8 kg moves at 9 m/s. Its momentum is:
- A.63 kg·m/s
- B.17 kg·m/s
- C.72 kg·m/s
- D.80 kg·m/s
Show answer
Correct answer: C. 72 kg·m/s
p = mv = 8×9 = 72 kg·m/s.
Q37.Kinetic energy of 7 kg body moving at 9 m/s is:
- A.276.5 J
- B.283.5 J
- C.63 J
- D.346.5 J
Show answer
Correct answer: B. 283.5 J
KE = ½mv² = 0.5×7×9² = 283.5 J.
Q38.Voltage across a 8 Ω resistor carrying 7 A current is:
- A.56 V
- B.64 V
- C.48 V
- D.17 V
Show answer
Correct answer: A. 56 V
V = IR = 7×8 = 56 V.
Q39.Two resistors 9 Ω and 11 Ω connected in series. Total resistance is:
- A.99 Ω
- B.2 Ω
- C.22 Ω
- D.20 Ω
Show answer
Correct answer: D. 20 Ω
Series: R = R₁ + R₂ = 9 + 11 = 20 Ω.
Q40.Power of a lens with focal length 70 cm is:
- A.2.43 D
- B.0.7 D
- C.1.43 D
- D.70 D
Show answer
Correct answer: C. 1.43 D
P = 1/f = 1/0.7 m = 1.43 D.
Q41.Wave speed for frequency 150 Hz and wavelength 7 m is:
- A.157 m/s
- B.1050 m/s
- C.1200 m/s
- D.980 m/s
Show answer
Correct answer: B. 1050 m/s
v = fλ = 150×7 = 1050 m/s.
Q42.Standard acceleration due to gravity at Earth's surface is:
- A.9.8 m/s²
- B.6.7 m/s²
- C.11.2 m/s²
- D.3.7 m/s²
Show answer
Correct answer: A. 9.8 m/s²
g ≈ 9.8 m/s² at Earth's surface.
Q43.A body starts with velocity 8 m/s and has acceleration 8 m/s². Its velocity after 4 s is:
- A.32 m/s
- B.48 m/s
- C.12 m/s
- D.40 m/s
Show answer
Correct answer: D. 40 m/s
v = u + at = 8 + 8×4 = 40 m/s.
Q44.For u = 1 m/s, a = 3 m/s², t = 6 s, displacement is:
- A.78 m
- B.57 m
- C.60 m
- D.6 m
Show answer
Correct answer: C. 60 m
s = ut + ½At² = 1×6 + 0.5×3×6² = 60 m.
Q45.Net force needed to give 8 kg mass an acceleration of 9 m/s² is:
- A.17 N
- B.72 N
- C.81 N
- D.63 N
Show answer
Correct answer: B. 72 N
F = ma = 8×9 = 72 N.
Q46.Work done when force 40 N moves a body 9 m in its direction is:
- A.360 J
- B.400 J
- C.320 J
- D.49 J
Show answer
Correct answer: A. 360 J
W = F×d = 40×9 = 360 J.
Q47.A body does 400 J of work in 5 s. Its power is:
- A.160 W
- B.85 W
- C.75 W
- D.80 W
Show answer
Correct answer: D. 80 W
P = W/t = 400/5 = 80 W.
Q48.A body of mass 9 kg moves at 10 m/s. Its momentum is:
- A.80 kg·m/s
- B.19 kg·m/s
- C.90 kg·m/s
- D.99 kg·m/s
Show answer
Correct answer: C. 90 kg·m/s
p = mv = 9×10 = 90 kg·m/s.
Q49.Kinetic energy of 8 kg body moving at 10 m/s is:
- A.392 J
- B.400 J
- C.80 J
- D.480 J
Show answer
Correct answer: B. 400 J
KE = ½mv² = 0.5×8×10² = 400 J.
Q50.Voltage across a 9 Ω resistor carrying 8 A current is:
- A.72 V
- B.81 V
- C.63 V
- D.19 V
Show answer
Correct answer: A. 72 V
V = IR = 8×9 = 72 V.
Q51.Two resistors 10 Ω and 12 Ω connected in series. Total resistance is:
- A.120 Ω
- B.2 Ω
- C.24 Ω
- D.22 Ω
Show answer
Correct answer: D. 22 Ω
Series: R = R₁ + R₂ = 10 + 12 = 22 Ω.
Q52.Power of a lens with focal length 80 cm is:
- A.2.25 D
- B.0.8 D
- C.1.25 D
- D.80 D
Show answer
Correct answer: C. 1.25 D
P = 1/f = 1/0.8 m = 1.25 D.
Q53.Wave speed for frequency 170 Hz and wavelength 8 m is:
- A.178 m/s
- B.1360 m/s
- C.1530 m/s
- D.1280 m/s
Show answer
Correct answer: B. 1360 m/s
v = fλ = 170×8 = 1360 m/s.
Q54.Weight of a body in free fall is:
- A.zero (apparent weight)
- B.equal to mg
- C.doubled
- D.equal to mass
Show answer
Correct answer: A. zero (apparent weight)
In free fall, normal reaction = 0 → apparent weight = 0.
Q55.A body starts with velocity 9 m/s and has acceleration 2 m/s². Its velocity after 5 s is:
- A.17 m/s
- B.21 m/s
- C.14 m/s
- D.19 m/s
Show answer
Correct answer: D. 19 m/s
v = u + at = 9 + 2×5 = 19 m/s.
Q56.For u = 2 m/s, a = 4 m/s², t = 7 s, displacement is:
- A.140 m
- B.108 m
- C.112 m
- D.14 m
Show answer
Correct answer: C. 112 m
s = ut + ½At² = 2×7 + 0.5×4×7² = 112 m.
Q57.Net force needed to give 9 kg mass an acceleration of 3 m/s² is:
- A.12 N
- B.27 N
- C.30 N
- D.24 N
Show answer
Correct answer: B. 27 N
F = ma = 9×3 = 27 N.
Q58.Work done when force 45 N moves a body 10 m in its direction is:
- A.450 J
- B.495 J
- C.405 J
- D.55 J
Show answer
Correct answer: A. 450 J
W = F×d = 45×10 = 450 J.
Q59.A body does 450 J of work in 6 s. Its power is:
- A.150 W
- B.81 W
- C.70 W
- D.75 W
Show answer
Correct answer: D. 75 W
P = W/t = 450/6 = 75 W.
Q60.A body of mass 10 kg moves at 11 m/s. Its momentum is:
- A.99 kg·m/s
- B.21 kg·m/s
- C.110 kg·m/s
- D.120 kg·m/s
Show answer
Correct answer: C. 110 kg·m/s
p = mv = 10×11 = 110 kg·m/s.
Q61.If [H⁺] = 10⁻6 mol/L, the pH of the solution is:
- A.7
- B.8
- C.5
- D.6
Show answer
Correct answer: D. 6
pH = −log[H⁺] = −log(10⁻6) = 6.
Q62.Molar mass of HCl is:
- A.37 g/mol
- B.18 g/mol
- C.36.5 g/mol
- D.35.5 g/mol
Show answer
Correct answer: C. 36.5 g/mol
Add atomic masses: molar mass of HCl = 36.5 g/mol.
Q63.Oxidation state of oxygen in H₂O is:
- A.−1
- B.−2
- C.+2
- D.0
Show answer
Correct answer: B. −2
H is +1 (×2), so O = −2.
Q64.Formula of iron(III) chloride is:
- A.FeCl₃
- B.FeCl₂
- C.Fe₃Cl
- D.FeCl
Show answer
Correct answer: A. FeCl₃
Fe(+3) needs 3 Cl(−1).
Q65.Gas produced when Na reacts with water is:
- A.oxygen
- B.sodium oxide
- C.hydroxide gas
- D.hydrogen
Show answer
Correct answer: D. hydrogen
2Na + 2H₂O → 2NaOH + H₂↑.
Q66.Blue litmus paper turns red in:
- A.neutral salt solution
- B.distilled water
- C.acid
- D.base
Show answer
Correct answer: C. acid
Acids turn blue litmus red.
Q67.IUPAC name of CH₃OH is:
- A.methanal
- B.methanol
- C.ethanol
- D.propanol
Show answer
Correct answer: B. methanol
CH₃OH is methanol.
Q68.Which element has electronic configuration 2,8,7?
- A.Chlorine
- B.Fluorine
- C.Bromine
- D.Neon
Show answer
Correct answer: A. Chlorine
2+8+7=17 protons → Cl.
Q69.Number of moles in 40 g of NaOH (M = 40 g/mol) is:
- A.2
- B.3
- C.2.5
- D.1
Show answer
Correct answer: D. 1
n = mass/M = 40/40 = 1 mol.
Q70.Electron configuration of Na⁺ is:
- A.1s²2s²2p⁶ 3s²
- B.1s²2s²2p⁵
- C.1s²2s²2p⁶
- D.1s²2s²2p⁶ 3s¹
Show answer
Correct answer: C. 1s²2s²2p⁶
Na loses 1e⁻ → 10 electrons (Ne config).
Q71.Hybridisation of carbon in methane (CH₄) is:
- A.dsp²
- B.sp³
- C.sp²
- D.sp
Show answer
Correct answer: B. sp³
CH₄ is tetrahedral; C is sp³ hybridised.
Q72.Rust is chemically:
- A.Fe₂O₃·xH₂O
- B.FeO
- C.Fe₃O₄
- D.FeSO₄
Show answer
Correct answer: A. Fe₂O₃·xH₂O
Rust = hydrated iron(III) oxide.
Q73.If [H⁺] = 10⁻7 mol/L, the pH of the solution is:
- A.8
- B.9
- C.6
- D.7
Show answer
Correct answer: D. 7
pH = −log[H⁺] = −log(10⁻7) = 7.
Q74.Molar mass of NaOH is:
- A.39 g/mol
- B.42 g/mol
- C.40 g/mol
- D.23 g/mol
Show answer
Correct answer: C. 40 g/mol
Add atomic masses: molar mass of NaOH = 40 g/mol.
Q75.Oxidation state of nitrogen in HNO₃ is:
- A.+4
- B.+5
- C.+3
- D.−3
Show answer
Correct answer: B. +5
H=+1, O=−2(×3), so N=+5.
Q76.Formula of silver nitrate is:
- A.AgNO₃
- B.Ag₂NO₃
- C.AgNO₂
- D.AgNO₄
Show answer
Correct answer: A. AgNO₃
Ag(+1) and NO₃⁻: AgNO₃.
Q77.Gas evolved when limestone reacts with dilute HCl is:
- A.hydrogen
- B.sulfur dioxide
- C.chlorine
- D.carbon dioxide
Show answer
Correct answer: D. carbon dioxide
CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂↑.
Q78.Common name of NaHCO₃ is:
- A.common salt
- B.lime water
- C.baking soda
- D.washing soda
Show answer
Correct answer: C. baking soda
NaHCO₃ = baking soda.
Q79.IUPAC name of CH₃CHO is:
- A.methanol
- B.ethanal
- C.ethanol
- D.propanone
Show answer
Correct answer: B. ethanal
CH₃CHO is ethanal (acetaldehyde).
Q80.First element of the periodic table is:
- A.Hydrogen
- B.Helium
- C.Lithium
- D.Carbon
Show answer
Correct answer: A. Hydrogen
Hydrogen has atomic number 1.
Q81.Number of moles in 117 g of NaCl (M = 58.5 g/mol) is:
- A.3
- B.1
- C.3.5
- D.2
Show answer
Correct answer: D. 2
n = mass/M = 117/58.5 = 2 mol.
Q82.Maximum electrons in shell n=3 is:
- A.6
- B.32
- C.18
- D.8
Show answer
Correct answer: C. 18
Max = 2n² = 18.
Q83.Shape of BF₃ is:
- A.pyramidal
- B.trigonal planar
- C.tetrahedral
- D.linear
Show answer
Correct answer: B. trigonal planar
3 bond pairs, no lone pairs → trigonal planar.
Q84.Dry ice is:
- A.solid CO₂
- B.solid N₂
- C.solid H₂O (below 0°C)
- D.solid SO₂
Show answer
Correct answer: A. solid CO₂
Dry ice = solid carbon dioxide.
Q85.If [H⁺] = 10⁻8 mol/L, the pH of the solution is:
- A.9
- B.6
- C.7
- D.8
Show answer
Correct answer: D. 8
pH = −log[H⁺] = −log(10⁻8) = 8.
Q86.Molar mass of CH₄ is:
- A.12 g/mol
- B.18 g/mol
- C.16 g/mol
- D.14 g/mol
Show answer
Correct answer: C. 16 g/mol
Add atomic masses: molar mass of CH₄ = 16 g/mol.
Q87.Oxidation state of Mn in KMnO₄ is:
- A.+6
- B.+7
- C.+2
- D.+4
Show answer
Correct answer: B. +7
K=+1, O=−2(×4), Mn=+7.
Q88.Formula of barium sulfate is:
- A.BaSO₄
- B.Ba₂SO₄
- C.BaSO₃
- D.Ba(SO₄)₂
Show answer
Correct answer: A. BaSO₄
Ba(+2) and SO₄²⁻: BaSO₄.
Q89.Product when CaO (quicklime) reacts with water is:
- A.CaCO₃
- B.CaCl₂
- C.Ca(HCO₃)₂
- D.Ca(OH)₂
Show answer
Correct answer: D. Ca(OH)₂
CaO + H₂O → Ca(OH)₂ (slaked lime).
Q90.Chemical formula of washing soda is:
- A.NaOH
- B.Na₂SO₄
- C.Na₂CO₃·10H₂O
- D.NaHCO₃
Show answer
Correct answer: C. Na₂CO₃·10H₂O
Washing soda = Na₂CO₃·10H₂O.