JEE Main Practice Set 4
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 4: all 90 questions with answers
Try each question first, then open “Show answer” to check the correct option and explanation.
Q1.Solve for x: 3x + 11 = 35.
- A.9
- B.7
- C.10
- D.8
Show answer
Correct answer: D. 8
Subtract 11 from both sides: 3x = 24. Divide by 3: x = 8.
Q2.One root of x² − 22x + 120 = 0 is 10. The other root is:
- A.11
- B.22
- C.12
- D.13
Show answer
Correct answer: C. 12
Product of roots = 120. Other root = 120 ÷ 10 = 12.
Q3.The 8th term of an AP with first term 7 and common difference 3 is:
- A.36
- B.28
- C.25
- D.31
Show answer
Correct answer: B. 28
aₙ = a + (n−1)d = 7 + 7×3 = 28.
Q4.Slope of the line through (4, 3) and (7, 30) is:
- A.9
- B.10
- C.8
- D.11
Show answer
Correct answer: A. 9
Slope = (30−3) ÷ (7−4) = 27 ÷ 3 = 9.
Q5.Value of sin 150° is:
- A.−1/2
- B.√3/2
- C.0
- D.1/2
Show answer
Correct answer: D. 1/2
sin 150° = sin 30° = 1/2.
Q6.A bag contains 10 red and 11 blue balls. Probability of drawing a red ball is:
- A.10/20
- B.12/22
- C.10/21
- D.11/22
Show answer
Correct answer: C. 10/21
P(red) = 10/21.
Q7.Determinant of matrix [[3, 1], [5, 10]] is:
- A.23
- B.25
- C.30
- D.22
Show answer
Correct answer: B. 25
det = ad − bc = 3×10 − 1×5 = 25.
Q8.Evaluate: log₂ₐₑₒₓ10(10^3) [log base 10].
- A.3
- B.4
- C.2
- D.30
Show answer
Correct answer: A. 3
logₐ(a^n) = n, so log_10(10^3) = 3.
Q9.Find 13P2.
- A.78
- B.160
- C.152
- D.156
Show answer
Correct answer: D. 156
13P2 = 13!/(13−2)! = 13×12 = 156.
Q10.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.
Q11.Simple interest on Rs 3500 at 10% p.a. for 5 years is:
- A.Rs 3500
- B.Rs 1750
- C.Rs 2250
- D.Rs 1500
Show answer
Correct answer: B. Rs 1750
SI = P×R×T/100 = 3500×10×5/100 = Rs 1750.
Q12.Area of a triangle with base 11 cm and height 10 cm is:
- A.55 cm²
- B.110 cm²
- C.61 cm²
- D.49 cm²
Show answer
Correct answer: A. 55 cm²
Area = (1/2) × base × height = (1/2) × 11 × 10 = 55 cm².
Q13.Solve for x: 4x + 12 = 48.
- A.10
- B.8
- C.11
- D.9
Show answer
Correct answer: D. 9
Subtract 12 from both sides: 4x = 36. Divide by 4: x = 9.
Q14.One root of x² − 9x + 18 = 0 is 3. The other root is:
- A.5
- B.9
- C.6
- D.7
Show answer
Correct answer: C. 6
Product of roots = 18. Other root = 18 ÷ 3 = 6.
Q15.The 9th term of an AP with first term 8 and common difference 4 is:
- A.49
- B.40
- C.36
- D.44
Show answer
Correct answer: B. 40
aₙ = a + (n−1)d = 8 + 8×4 = 40.
Q16.Slope of the line through (5, 4) and (8, 10) is:
- A.2
- B.3
- C.1
- D.4
Show answer
Correct answer: A. 2
Slope = (10−4) ÷ (8−5) = 6 ÷ 3 = 2.
Q17.Value of cos 150° is:
- A.√3/2
- B.−1/2
- C.0
- D.−√3/2
Show answer
Correct answer: D. −√3/2
cos 150° = −√3/2.
Q18.A bag contains 3 red and 12 blue balls. Probability of drawing a red ball is:
- A.3/14
- B.13/16
- C.3/15
- D.12/16
Show answer
Correct answer: C. 3/15
P(red) = 3/15.
Q19.Determinant of matrix [[4, 2], [2, 3]] is:
- A.14
- B.8
- C.13
- D.5
Show answer
Correct answer: B. 8
det = ad − bc = 4×3 − 2×2 = 8.
Q20.Evaluate: log₂ₐₑₒₓ2(2^4) [log base 2].
- A.4
- B.5
- C.3
- D.8
Show answer
Correct answer: A. 4
logₐ(a^n) = n, so log_2(2^4) = 4.
Q21.Find 6P3.
- A.40
- B.126
- C.114
- D.120
Show answer
Correct answer: D. 120
6P3 = 6!/(6−3)! = 6×5×4 = 120.
Q22.Find 14C2.
- A.94
- B.88
- C.91
- D.28
Show answer
Correct answer: C. 91
nC2 = n(n−1)/2 = 14×13/2 = 91.
Q23.Simple interest on Rs 3700 at 11% p.a. for 2 years is:
- A.Rs 1628
- B.Rs 814
- C.Rs 1034
- D.Rs 704
Show answer
Correct answer: B. Rs 814
SI = P×R×T/100 = 3700×11×2/100 = Rs 814.
Q24.Area of a triangle with base 12 cm and height 11 cm is:
- A.66 cm²
- B.132 cm²
- C.72 cm²
- D.60 cm²
Show answer
Correct answer: A. 66 cm²
Area = (1/2) × base × height = (1/2) × 12 × 11 = 66 cm².
Q25.Solve for x: 5x + 13 = 63.
- A.11
- B.9
- C.12
- D.10
Show answer
Correct answer: D. 10
Subtract 13 from both sides: 5x = 50. Divide by 5: x = 10.
Q26.One root of x² − 12x + 32 = 0 is 4. The other root is:
- A.7
- B.12
- C.8
- D.9
Show answer
Correct answer: C. 8
Product of roots = 32. Other root = 32 ÷ 4 = 8.
Q27.The 10th term of an AP with first term 9 and common difference 5 is:
- A.64
- B.54
- C.49
- D.59
Show answer
Correct answer: B. 54
aₙ = a + (n−1)d = 9 + 9×5 = 54.
Q28.Slope of the line through (6, 5) and (9, 14) is:
- A.3
- B.4
- C.2
- D.5
Show answer
Correct answer: A. 3
Slope = (14−5) ÷ (9−6) = 9 ÷ 3 = 3.
Q29.Value of sin 180° is:
- A.1
- B.−1
- C.1/2
- D.0
Show answer
Correct answer: D. 0
sin 180° = 0.
Q30.A bag contains 4 red and 13 blue balls. Probability of drawing a red ball is:
- A.4/16
- B.14/18
- C.4/17
- D.13/18
Show answer
Correct answer: C. 4/17
P(red) = 4/17.
Q31.A body starts with velocity 9 m/s and has acceleration 3 m/s². Its velocity after 3 s is:
- A.15 m/s
- B.21 m/s
- C.12 m/s
- D.18 m/s
Show answer
Correct answer: D. 18 m/s
v = u + at = 9 + 3×3 = 18 m/s.
Q32.For u = 4 m/s, a = 2 m/s², t = 7 s, displacement is:
- A.91 m
- B.75 m
- C.77 m
- D.28 m
Show answer
Correct answer: C. 77 m
s = ut + ½At² = 4×7 + 0.5×2×7² = 77 m.
Q33.Net force needed to give 9 kg mass an acceleration of 4 m/s² is:
- A.13 N
- B.36 N
- C.40 N
- D.32 N
Show answer
Correct answer: B. 36 N
F = ma = 9×4 = 36 N.
Q34.Work done when force 25 N moves a body 10 m in its direction is:
- A.250 J
- B.275 J
- C.225 J
- D.35 J
Show answer
Correct answer: A. 250 J
W = F×d = 25×10 = 250 J.
Q35.A body does 850 J of work in 8 s. Its power is:
- A.212.5 W
- B.114.25 W
- C.101.25 W
- D.106.25 W
Show answer
Correct answer: D. 106.25 W
P = W/t = 850/8 = 106.25 W.
Q36.A body of mass 10 kg moves at 10 m/s. Its momentum is:
- A.90 kg·m/s
- B.20 kg·m/s
- C.100 kg·m/s
- D.110 kg·m/s
Show answer
Correct answer: C. 100 kg·m/s
p = mv = 10×10 = 100 kg·m/s.
Q37.Kinetic energy of 3 kg body moving at 11 m/s is:
- A.178.5 J
- B.181.5 J
- C.33 J
- D.214.5 J
Show answer
Correct answer: B. 181.5 J
KE = ½mv² = 0.5×3×11² = 181.5 J.
Q38.Voltage across a 9 Ω resistor carrying 9 A current is:
- A.81 V
- B.90 V
- C.71 V
- D.20 V
Show answer
Correct answer: A. 81 V
V = IR = 9×9 = 81 V.
Q39.Two resistors 11 Ω and 12 Ω connected in series. Total resistance is:
- A.132 Ω
- B.1 Ω
- C.25 Ω
- D.23 Ω
Show answer
Correct answer: D. 23 Ω
Series: R = R₁ + R₂ = 11 + 12 = 23 Ω.
Q40.Power of a lens with focal length 90 cm is:
- A.2.11 D
- B.0.9 D
- C.1.11 D
- D.90 D
Show answer
Correct answer: C. 1.11 D
P = 1/f = 1/0.9 m = 1.11 D.
Q41.Wave speed for frequency 150 Hz and wavelength 3 m is:
- A.153 m/s
- B.450 m/s
- C.600 m/s
- D.420 m/s
Show answer
Correct answer: B. 450 m/s
v = fλ = 150×3 = 450 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 2 m/s and has acceleration 4 m/s². Its velocity after 4 s is:
- A.14 m/s
- B.22 m/s
- C.6 m/s
- D.18 m/s
Show answer
Correct answer: D. 18 m/s
v = u + at = 2 + 4×4 = 18 m/s.
Q44.For u = 5 m/s, a = 3 m/s², t = 4 s, displacement is:
- A.56 m
- B.41 m
- C.44 m
- D.20 m
Show answer
Correct answer: C. 44 m
s = ut + ½At² = 5×4 + 0.5×3×4² = 44 m.
Q45.Net force needed to give 2 kg mass an acceleration of 5 m/s² is:
- A.7 N
- B.10 N
- C.15 N
- D.5 N
Show answer
Correct answer: B. 10 N
F = ma = 2×5 = 10 N.
Q46.Work done when force 30 N moves a body 3 m in its direction is:
- A.90 J
- B.120 J
- C.60 J
- D.33 J
Show answer
Correct answer: A. 90 J
W = F×d = 30×3 = 90 J.
Q47.A body does 900 J of work in 9 s. Its power is:
- A.200 W
- B.109 W
- C.95 W
- D.100 W
Show answer
Correct answer: D. 100 W
P = W/t = 900/9 = 100 W.
Q48.A body of mass 3 kg moves at 11 m/s. Its momentum is:
- A.22 kg·m/s
- B.14 kg·m/s
- C.33 kg·m/s
- D.36 kg·m/s
Show answer
Correct answer: C. 33 kg·m/s
p = mv = 3×11 = 33 kg·m/s.
Q49.Kinetic energy of 4 kg body moving at 4 m/s is:
- A.28 J
- B.32 J
- C.16 J
- D.48 J
Show answer
Correct answer: B. 32 J
KE = ½mv² = 0.5×4×4² = 32 J.
Q50.Voltage across a 10 Ω resistor carrying 2 A current is:
- A.20 V
- B.30 V
- C.17 V
- D.14 V
Show answer
Correct answer: A. 20 V
V = IR = 2×10 = 20 V.
Q51.Two resistors 4 Ω and 13 Ω connected in series. Total resistance is:
- A.52 Ω
- B.9 Ω
- C.19 Ω
- D.17 Ω
Show answer
Correct answer: D. 17 Ω
Series: R = R₁ + R₂ = 4 + 13 = 17 Ω.
Q52.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.
Q53.Wave speed for frequency 170 Hz and wavelength 4 m is:
- A.174 m/s
- B.680 m/s
- C.850 m/s
- D.640 m/s
Show answer
Correct answer: B. 680 m/s
v = fλ = 170×4 = 680 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 3 m/s and has acceleration 5 m/s². Its velocity after 5 s is:
- A.23 m/s
- B.33 m/s
- C.8 m/s
- D.28 m/s
Show answer
Correct answer: D. 28 m/s
v = u + at = 3 + 5×5 = 28 m/s.
Q56.For u = 6 m/s, a = 4 m/s², t = 5 s, displacement is:
- A.100 m
- B.76 m
- C.80 m
- D.30 m
Show answer
Correct answer: C. 80 m
s = ut + ½At² = 6×5 + 0.5×4×5² = 80 m.
Q57.Net force needed to give 3 kg mass an acceleration of 6 m/s² is:
- A.9 N
- B.18 N
- C.24 N
- D.12 N
Show answer
Correct answer: B. 18 N
F = ma = 3×6 = 18 N.
Q58.Work done when force 35 N moves a body 4 m in its direction is:
- A.140 J
- B.175 J
- C.105 J
- D.39 J
Show answer
Correct answer: A. 140 J
W = F×d = 35×4 = 140 J.
Q59.A body does 950 J of work in 10 s. Its power is:
- A.190 W
- B.105 W
- C.90 W
- D.95 W
Show answer
Correct answer: D. 95 W
P = W/t = 950/10 = 95 W.
Q60.A body of mass 4 kg moves at 12 m/s. Its momentum is:
- A.36 kg·m/s
- B.16 kg·m/s
- C.48 kg·m/s
- D.52 kg·m/s
Show answer
Correct answer: C. 48 kg·m/s
p = mv = 4×12 = 48 kg·m/s.
Q61.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.
Q62.Molar mass of CaCl₂ is:
- A.95 g/mol
- B.113 g/mol
- C.111 g/mol
- D.75 g/mol
Show answer
Correct answer: C. 111 g/mol
Add atomic masses: molar mass of CaCl₂ = 111 g/mol.
Q63.Oxidation state of sulfur in Na₂S is:
- A.+6
- B.−2
- C.+2
- D.0
Show answer
Correct answer: B. −2
Na=+1 each, so S=−2.
Q64.Formula of lithium oxide is:
- A.Li₂O
- B.LiO
- C.Li₃O₂
- D.LiO₂
Show answer
Correct answer: A. Li₂O
Li(+1) and O(−2): Li₂O.
Q65.Product when P₂O₅ reacts with water is:
- A.H₃PO₃
- B.HPO₃
- C.H₄P₂O₇
- D.H₃PO₄
Show answer
Correct answer: D. H₃PO₄
P₂O₅ + 3H₂O → 2H₃PO₄.
Q66.Which salt hydrolyses to give acidic solution?
- A.Na₂CO₃
- B.CH₃COONa
- C.NH₄Cl
- D.NaCl
Show answer
Correct answer: C. NH₄Cl
NH₄⁺ hydrolyses: NH₄⁺+H₂O ⇌ NH₃+H₃O⁺.
Q67.Tollens’ reagent (silver mirror test) is given by:
- A.esters
- B.aldehydes
- C.ketones
- D.alcohols
Show answer
Correct answer: B. aldehydes
Aldehydes reduce [Ag(NH₃)₂]⁺ to silver mirror.
Q68.Which metal is liquid at room temperature?
- A.Mercury
- B.Tin
- C.Lead
- D.Bismuth
Show answer
Correct answer: A. Mercury
Mercury (Hg) is liquid at room temperature.
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.De Broglie wavelength is:
- A.h·mv
- B.m/hv
- C.h/mv
- D.mv/h
Show answer
Correct answer: C. h/mv
λ = h/p = h/(mv).
Q71.Bond angle in methane (CH₄) is:
- A.180°
- B.109.5°
- C.90°
- D.120°
Show answer
Correct answer: B. 109.5°
Tetrahedral CH₄: 109.5°.
Q72.Hypo (sodium thiosulfate) is used in photography to:
- A.fix the image (remove unexposed AgBr)
- B.develop the image
- C.wash the film
- D.sensitise the film
Show answer
Correct answer: A. fix the image (remove unexposed AgBr)
Na₂S₂O₃ dissolves unreacted AgBr (fixing).
Q73.If [H⁺] = 10⁻4 mol/L, the pH of the solution is:
- A.5
- B.10
- C.3
- D.4
Show answer
Correct answer: D. 4
pH = −log[H⁺] = −log(10⁻4) = 4.
Q74.Molar mass of O₂ is:
- A.48 g/mol
- B.30 g/mol
- C.32 g/mol
- D.16 g/mol
Show answer
Correct answer: C. 32 g/mol
Add atomic masses: molar mass of O₂ = 32 g/mol.
Q75.Oxidation state of iron in FeCl₃ is:
- A.+4
- B.+3
- C.+2
- D.0
Show answer
Correct answer: B. +3
Cl=−1 (×3), Fe=+3.
Q76.Formula of copper(I) chloride is:
- A.CuCl
- B.CuCl₂
- C.Cu₂Cl
- D.CuCl₃
Show answer
Correct answer: A. CuCl
Cu(+1) and Cl(−1): CuCl.
Q77.White precipitate formed when AgNO₃ reacts with HCl is:
- A.AgBr
- B.Ag₂O
- C.Ag₂S
- D.AgCl
Show answer
Correct answer: D. AgCl
AgNO₃ + HCl → AgCl↓(white) + HNO₃.
Q78.Concentrated H₂SO₄ acts as:
- A.bleaching agent alone
- B.weak acid
- C.dehydrating agent
- D.reducing agent
Show answer
Correct answer: C. dehydrating agent
Conc. H₂SO₄ is a powerful dehydrating agent.
Q79.Reagent that converts alkene to alkane is:
- A.HBr alone
- B.H₂/Ni (hydrogenation)
- C.Cl₂/hν
- D.KMnO₄/H⁺
Show answer
Correct answer: B. H₂/Ni (hydrogenation)
Catalytic hydrogenation: alkene + H₂ → alkane.
Q80.The most abundant element in Earth’s crust is:
- A.Oxygen
- B.Silicon
- C.Aluminium
- D.Iron
Show answer
Correct answer: A. Oxygen
Oxygen (∼46%) is most abundant in Earth’s crust.
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.Photoelectric effect proves light has:
- A.both wave and particle simultaneously
- B.no mass
- C.particle nature (photons)
- D.wave nature only
Show answer
Correct answer: C. particle nature (photons)
Photoelectric effect demonstrated photon (particle) nature.
Q83.Ionic bond typically forms between:
- A.metal and metalloid
- B.metal and non-metal
- C.two non-metals
- D.two metals
Show answer
Correct answer: B. metal and non-metal
Ionic bonds form between metals (+) and non-metals (−).
Q84.Philosopher’s wool is:
- A.ZnO (white powder)
- B.MgO
- C.Al₂O₃
- D.CaO
Show answer
Correct answer: A. ZnO (white powder)
Zinc oxide forms white fluffy powder = philosopher’s wool.
Q85.If [H⁺] = 10⁻5 mol/L, the pH of the solution is:
- A.6
- B.9
- C.4
- D.5
Show answer
Correct answer: D. 5
pH = −log[H⁺] = −log(10⁻5) = 5.
Q86.Molar mass of N₂ is:
- A.21 g/mol
- B.30 g/mol
- C.28 g/mol
- D.14 g/mol
Show answer
Correct answer: C. 28 g/mol
Add atomic masses: molar mass of N₂ = 28 g/mol.
Q87.Oxidation state of carbon in CH₄ is:
- A.+2
- B.−4
- C.+4
- D.0
Show answer
Correct answer: B. −4
H=+1 (×4), C=−4.
Q88.Formula of nickel(II) sulfate is:
- A.NiSO₄
- B.Ni₂SO₄
- C.Ni(SO₄)₂
- D.NiSO₃
Show answer
Correct answer: A. NiSO₄
Ni(+2) and SO₄²⁻: NiSO₄.
Q89.Brown gas formed when Cu reacts with dil. HNO₃ is:
- A.NO₂
- B.N₂O
- C.N₂
- D.NO
Show answer
Correct answer: D. NO
3Cu + 8HNO₃(dil.) → 3Cu(NO₃)₂ + 2NO↑ + 4H₂O.
Q90.Which acid is used in car batteries?
- A.HNO₃
- B.H₃PO₄
- C.H₂SO₄
- D.HCl
Show answer
Correct answer: C. H₂SO₄
Lead-acid batteries use dilute H₂SO₄.