JEE Main Practice Set 3
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 3: all 90 questions with answers
Try each question first, then open “Show answer” to check the correct option and explanation.
Q1.Solve for x: 5x + 6 = 21.
- A.4
- B.2
- C.5
- D.3
Show answer
Correct answer: D. 3
Subtract 6 from both sides: 5x = 15. Divide by 5: x = 3.
Q2.One root of x² − 12x + 35 = 0 is 5. The other root is:
- A.6
- B.12
- C.7
- D.8
Show answer
Correct answer: C. 7
Product of roots = 35. Other root = 35 ÷ 5 = 7.
Q3.The 8th term of an AP with first term 2 and common difference 5 is:
- A.40
- B.37
- C.32
- D.42
Show answer
Correct answer: B. 37
aₙ = a + (n−1)d = 2 + 7×5 = 37.
Q4.Slope of the line through (5, 5) and (8, 17) is:
- A.4
- B.5
- C.3
- D.6
Show answer
Correct answer: A. 4
Slope = (17−5) ÷ (8−5) = 12 ÷ 3 = 4.
Q5.Value of sin 60° is:
- A.1/2
- B.1
- C.1/√2
- D.√3/2
Show answer
Correct answer: D. √3/2
sin 60° = √3/2.
Q6.A bag contains 5 red and 6 blue balls. Probability of drawing a red ball is:
- A.5/10
- B.7/12
- C.5/11
- D.6/12
Show answer
Correct answer: C. 5/11
P(red) = 5/11.
Q7.Determinant of matrix [[5, 1], [4, 5]] is:
- A.19
- B.21
- C.26
- D.18
Show answer
Correct answer: B. 21
det = ad − bc = 5×5 − 1×4 = 21.
Q8.Evaluate: log₂ₐₑₒₓ5(5^5) [log base 5].
- A.5
- B.6
- C.4
- D.25
Show answer
Correct answer: A. 5
logₐ(a^n) = n, so log_5(5^5) = 5.
Q9.Find 8P3.
- A.112
- B.342
- C.330
- D.336
Show answer
Correct answer: D. 336
8P3 = 8!/(8−3)! = 8×7×6 = 336.
Q10.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.
Q11.Simple interest on Rs 2500 at 5% p.a. for 4 years is:
- A.Rs 1000
- B.Rs 500
- C.Rs 700
- D.Rs 400
Show answer
Correct answer: B. Rs 500
SI = P×R×T/100 = 2500×5×4/100 = Rs 500.
Q12.Area of a triangle with base 6 cm and height 5 cm is:
- A.15 cm²
- B.30 cm²
- C.21 cm²
- D.9 cm²
Show answer
Correct answer: A. 15 cm²
Area = (1/2) × base × height = (1/2) × 6 × 5 = 15 cm².
Q13.Solve for x: 6x + 7 = 31.
- A.5
- B.3
- C.6
- D.4
Show answer
Correct answer: D. 4
Subtract 7 from both sides: 6x = 24. Divide by 6: x = 4.
Q14.One root of x² − 15x + 54 = 0 is 6. The other root is:
- A.8
- B.15
- C.9
- D.10
Show answer
Correct answer: C. 9
Product of roots = 54. Other root = 54 ÷ 6 = 9.
Q15.The 9th term of an AP with first term 3 and common difference 6 is:
- A.55
- B.51
- C.45
- D.57
Show answer
Correct answer: B. 51
aₙ = a + (n−1)d = 3 + 8×6 = 51.
Q16.Slope of the line through (6, 6) and (9, 21) is:
- A.5
- B.6
- C.4
- D.7
Show answer
Correct answer: A. 5
Slope = (21−6) ÷ (9−6) = 15 ÷ 3 = 5.
Q17.Value of tan 30° is:
- A.√3
- B.1
- C.1/2
- D.1/√3
Show answer
Correct answer: D. 1/√3
tan 30° = 1/√3.
Q18.A bag contains 6 red and 7 blue balls. Probability of drawing a red ball is:
- A.6/12
- B.8/14
- C.6/13
- D.7/14
Show answer
Correct answer: C. 6/13
P(red) = 6/13.
Q19.Determinant of matrix [[6, 2], [5, 6]] is:
- A.22
- B.26
- C.31
- D.23
Show answer
Correct answer: B. 26
det = ad − bc = 6×6 − 2×5 = 26.
Q20.Evaluate: log₂ₐₑₒₓ10(10^6) [log base 10].
- A.6
- B.7
- C.5
- D.60
Show answer
Correct answer: A. 6
logₐ(a^n) = n, so log_10(10^6) = 6.
Q21.Find 9P4.
- A.756
- B.3032
- C.3016
- D.3024
Show answer
Correct answer: D. 3024
9P4 = 9!/(9−4)! = 9×8×7×6 = 3024.
Q22.Find 9C2.
- A.39
- B.33
- C.36
- D.18
Show answer
Correct answer: C. 36
nC2 = n(n−1)/2 = 9×8/2 = 36.
Q23.Simple interest on Rs 2700 at 6% p.a. for 5 years is:
- A.Rs 1620
- B.Rs 810
- C.Rs 1110
- D.Rs 660
Show answer
Correct answer: B. Rs 810
SI = P×R×T/100 = 2700×6×5/100 = Rs 810.
Q24.Area of a triangle with base 7 cm and height 6 cm is:
- A.21 cm²
- B.42 cm²
- C.27 cm²
- D.15 cm²
Show answer
Correct answer: A. 21 cm²
Area = (1/2) × base × height = (1/2) × 7 × 6 = 21 cm².
Q25.Solve for x: 7x + 8 = 43.
- A.6
- B.4
- C.7
- D.5
Show answer
Correct answer: D. 5
Subtract 8 from both sides: 7x = 35. Divide by 7: x = 5.
Q26.One root of x² − 18x + 77 = 0 is 7. The other root is:
- A.10
- B.18
- C.11
- D.12
Show answer
Correct answer: C. 11
Product of roots = 77. Other root = 77 ÷ 7 = 11.
Q27.The 10th term of an AP with first term 4 and common difference 7 is:
- A.72
- B.67
- C.60
- D.74
Show answer
Correct answer: B. 67
aₙ = a + (n−1)d = 4 + 9×7 = 67.
Q28.Slope of the line through (1, 7) and (4, 25) is:
- A.6
- B.7
- C.5
- D.8
Show answer
Correct answer: A. 6
Slope = (25−7) ÷ (4−1) = 18 ÷ 3 = 6.
Q29.Value of tan 60° is:
- A.1
- B.1/√3
- C.2
- D.√3
Show answer
Correct answer: D. √3
tan 60° = √3.
Q30.A bag contains 7 red and 8 blue balls. Probability of drawing a red ball is:
- A.7/14
- B.9/16
- C.7/15
- D.8/16
Show answer
Correct answer: C. 7/15
P(red) = 7/15.
Q31.A body starts with velocity 4 m/s and has acceleration 5 m/s². Its velocity after 3 s is:
- A.14 m/s
- B.24 m/s
- C.7 m/s
- D.19 m/s
Show answer
Correct answer: D. 19 m/s
v = u + at = 4 + 5×3 = 19 m/s.
Q32.For u = 5 m/s, a = 2 m/s², t = 6 s, displacement is:
- A.78 m
- B.64 m
- C.66 m
- D.30 m
Show answer
Correct answer: C. 66 m
s = ut + ½At² = 5×6 + 0.5×2×6² = 66 m.
Q33.Net force needed to give 4 kg mass an acceleration of 6 m/s² is:
- A.10 N
- B.24 N
- C.30 N
- D.18 N
Show answer
Correct answer: B. 24 N
F = ma = 4×6 = 24 N.
Q34.Work done when force 60 N moves a body 5 m in its direction is:
- A.300 J
- B.360 J
- C.240 J
- D.65 J
Show answer
Correct answer: A. 300 J
W = F×d = 60×5 = 300 J.
Q35.A body does 600 J of work in 9 s. Its power is:
- A.133.33 W
- B.75.67 W
- C.61.67 W
- D.66.67 W
Show answer
Correct answer: D. 66.67 W
P = W/t = 600/9 = 66.67 W.
Q36.A body of mass 5 kg moves at 5 m/s. Its momentum is:
- A.20 kg·m/s
- B.10 kg·m/s
- C.25 kg·m/s
- D.30 kg·m/s
Show answer
Correct answer: C. 25 kg·m/s
p = mv = 5×5 = 25 kg·m/s.
Q37.Kinetic energy of 5 kg body moving at 6 m/s is:
- A.85 J
- B.90 J
- C.30 J
- D.120 J
Show answer
Correct answer: B. 90 J
KE = ½mv² = 0.5×5×6² = 90 J.
Q38.Voltage across a 4 Ω resistor carrying 4 A current is:
- A.16 V
- B.20 V
- C.11 V
- D.10 V
Show answer
Correct answer: A. 16 V
V = IR = 4×4 = 16 V.
Q39.Two resistors 6 Ω and 7 Ω connected in series. Total resistance is:
- A.42 Ω
- B.1 Ω
- C.15 Ω
- D.13 Ω
Show answer
Correct answer: D. 13 Ω
Series: R = R₁ + R₂ = 6 + 7 = 13 Ω.
Q40.Power of a lens with focal length 40 cm is:
- A.3.5 D
- B.0.4 D
- C.2.5 D
- D.40 D
Show answer
Correct answer: C. 2.5 D
P = 1/f = 1/0.4 m = 2.5 D.
Q41.Wave speed for frequency 50 Hz and wavelength 5 m is:
- A.55 m/s
- B.250 m/s
- C.300 m/s
- D.200 m/s
Show answer
Correct answer: B. 250 m/s
v = fλ = 50×5 = 250 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 5 m/s and has acceleration 6 m/s². Its velocity after 4 s is:
- A.23 m/s
- B.35 m/s
- C.9 m/s
- D.29 m/s
Show answer
Correct answer: D. 29 m/s
v = u + at = 5 + 6×4 = 29 m/s.
Q44.For u = 6 m/s, a = 3 m/s², t = 7 s, displacement is:
- A.136.5 m
- B.112.5 m
- C.115.5 m
- D.42 m
Show answer
Correct answer: C. 115.5 m
s = ut + ½At² = 6×7 + 0.5×3×7² = 115.5 m.
Q45.Net force needed to give 5 kg mass an acceleration of 7 m/s² is:
- A.12 N
- B.35 N
- C.42 N
- D.28 N
Show answer
Correct answer: B. 35 N
F = ma = 5×7 = 35 N.
Q46.Work done when force 65 N moves a body 6 m in its direction is:
- A.390 J
- B.455 J
- C.325 J
- D.71 J
Show answer
Correct answer: A. 390 J
W = F×d = 65×6 = 390 J.
Q47.A body does 650 J of work in 10 s. Its power is:
- A.130 W
- B.75 W
- C.60 W
- D.65 W
Show answer
Correct answer: D. 65 W
P = W/t = 650/10 = 65 W.
Q48.A body of mass 6 kg moves at 6 m/s. Its momentum is:
- A.30 kg·m/s
- B.12 kg·m/s
- C.36 kg·m/s
- D.42 kg·m/s
Show answer
Correct answer: C. 36 kg·m/s
p = mv = 6×6 = 36 kg·m/s.
Q49.Kinetic energy of 6 kg body moving at 7 m/s is:
- A.141 J
- B.147 J
- C.42 J
- D.189 J
Show answer
Correct answer: B. 147 J
KE = ½mv² = 0.5×6×7² = 147 J.
Q50.Voltage across a 5 Ω resistor carrying 5 A current is:
- A.25 V
- B.30 V
- C.19 V
- D.12 V
Show answer
Correct answer: A. 25 V
V = IR = 5×5 = 25 V.
Q51.Two resistors 7 Ω and 8 Ω connected in series. Total resistance is:
- A.56 Ω
- B.1 Ω
- C.17 Ω
- D.15 Ω
Show answer
Correct answer: D. 15 Ω
Series: R = R₁ + R₂ = 7 + 8 = 15 Ω.
Q52.Power of a lens with focal length 50 cm is:
- A.3 D
- B.0.5 D
- C.2 D
- D.50 D
Show answer
Correct answer: C. 2 D
P = 1/f = 1/0.5 m = 2 D.
Q53.Wave speed for frequency 70 Hz and wavelength 6 m is:
- A.76 m/s
- B.420 m/s
- C.490 m/s
- D.360 m/s
Show answer
Correct answer: B. 420 m/s
v = fλ = 70×6 = 420 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 6 m/s and has acceleration 7 m/s². Its velocity after 5 s is:
- A.34 m/s
- B.48 m/s
- C.11 m/s
- D.41 m/s
Show answer
Correct answer: D. 41 m/s
v = u + at = 6 + 7×5 = 41 m/s.
Q56.For u = 1 m/s, a = 4 m/s², t = 4 s, displacement is:
- A.52 m
- B.32 m
- C.36 m
- D.4 m
Show answer
Correct answer: C. 36 m
s = ut + ½At² = 1×4 + 0.5×4×4² = 36 m.
Q57.Net force needed to give 6 kg mass an acceleration of 8 m/s² is:
- A.14 N
- B.48 N
- C.56 N
- D.40 N
Show answer
Correct answer: B. 48 N
F = ma = 6×8 = 48 N.
Q58.Work done when force 10 N moves a body 7 m in its direction is:
- A.70 J
- B.80 J
- C.60 J
- D.17 J
Show answer
Correct answer: A. 70 J
W = F×d = 10×7 = 70 J.
Q59.A body does 700 J of work in 5 s. Its power is:
- A.280 W
- B.145 W
- C.135 W
- D.140 W
Show answer
Correct answer: D. 140 W
P = W/t = 700/5 = 140 W.
Q60.A body of mass 7 kg moves at 7 m/s. Its momentum is:
- A.42 kg·m/s
- B.14 kg·m/s
- C.49 kg·m/s
- D.56 kg·m/s
Show answer
Correct answer: C. 49 kg·m/s
p = mv = 7×7 = 49 kg·m/s.
Q61.If [H⁺] = 10⁻11 mol/L, the pH of the solution is:
- A.12
- B.3
- C.10
- D.11
Show answer
Correct answer: D. 11
pH = −log[H⁺] = −log(10⁻11) = 11.
Q62.Molar mass of MgO is:
- A.32 g/mol
- B.44 g/mol
- C.40 g/mol
- D.24 g/mol
Show answer
Correct answer: C. 40 g/mol
Add atomic masses: molar mass of MgO = 40 g/mol.
Q63.Oxidation state of sulfur in SO₂ is:
- A.−2
- B.+4
- C.+6
- D.+2
Show answer
Correct answer: B. +4
2O(−2)+S=0 → S=+4.
Q64.Formula of iron(II) sulfate is:
- A.FeSO₄
- B.Fe₂SO₄
- C.Fe(SO₄)₂
- D.FeSO₃
Show answer
Correct answer: A. FeSO₄
Fe(+2) and SO₄²⁻: FeSO₄.
Q65.Gas produced when CaC₂ reacts with water is:
- A.methane
- B.ethane
- C.propane
- D.acetylene (ethyne)
Show answer
Correct answer: D. acetylene (ethyne)
CaC₂ + 2H₂O → Ca(OH)₂ + C₂H₂↑.
Q66.pH of 0.1 M HCl solution is:
- A.7
- B.0
- C.1
- D.3
Show answer
Correct answer: C. 1
[H⁺]=0.1=10⁻¹; pH=1.
Q67.General formula of alkynes is:
- A.CₙHₙ
- B.CₙH₂ₙ₋₂
- C.CₙH₂ₙ₊₂
- D.CₙH₂ₙ
Show answer
Correct answer: B. CₙH₂ₙ₋₂
Alkynes: CₙH₂ₙ₋₂ (one triple bond).
Q68.Which is a metalloid?
- A.Silicon
- B.Sulphur
- C.Phosphorus
- D.Selenium
Show answer
Correct answer: A. Silicon
Silicon is a common metalloid.
Q69.Number of moles in 56 g of CaO (M = 56 g/mol) is:
- A.2
- B.3
- C.2.5
- D.1
Show answer
Correct answer: D. 1
n = mass/M = 56/56 = 1 mol.
Q70.Isotopes are atoms with same:
- A.same neutrons
- B.same A and Z
- C.atomic number but different mass number
- D.mass number but different Z
Show answer
Correct answer: C. atomic number but different mass number
Isotopes: same Z, different A.
Q71.Electronegativity order: F, O, N, C is:
- A.N > O > C > F
- B.F > O > N > C
- C.C > N > O > F
- D.O > F > N > C
Show answer
Correct answer: B. F > O > N > C
Electronegativity: F > O > N > C.
Q72.Colour of anhydrous copper sulfate (CuSO₄) is:
- A.white
- B.blue
- C.green
- D.yellow
Show answer
Correct answer: A. white
Anhydrous CuSO₄ is white; turns blue on absorbing water.
Q73.If [H⁺] = 10⁻12 mol/L, the pH of the solution is:
- A.13
- B.2
- C.11
- D.12
Show answer
Correct answer: D. 12
pH = −log[H⁺] = −log(10⁻12) = 12.
Q74.Molar mass of C₂H₄ is:
- A.24 g/mol
- B.30 g/mol
- C.28 g/mol
- D.26 g/mol
Show answer
Correct answer: C. 28 g/mol
Add atomic masses: molar mass of C₂H₄ = 28 g/mol.
Q75.Oxidation state of nitrogen in N₂ gas is:
- A.+5
- B.0
- C.+3
- D.−3
Show answer
Correct answer: B. 0
Elemental N₂ has oxidation state 0.
Q76.Formula of copper(II) oxide is:
- A.CuO
- B.Cu₂O
- C.Cu₂O₃
- D.CuO₂
Show answer
Correct answer: A. CuO
Cu(+2) and O(−2): CuO.
Q77.When excess CO₂ is passed through Ca(OH)₂, precipitate:
- A.remains unchanged
- B.turns yellow
- C.turns red
- D.dissolves (Ca(HCO₃)₂ forms)
Show answer
Correct answer: D. dissolves (Ca(HCO₃)₂ forms)
CaCO₃ + CO₂ + H₂O → Ca(HCO₃)₂ (soluble).
Q78.Acid that cannot be stored in glass bottles is:
- A.H₂SO₄
- B.HNO₃
- C.HF
- D.HCl
Show answer
Correct answer: C. HF
HF etches glass (SiO₂ + 4HF → SiF₄ + 2H₂O).
Q79.Product of fermentation of glucose is:
- A.methanol and CO
- B.ethanol and CO₂
- C.acetic acid and H₂
- D.lactic acid
Show answer
Correct answer: B. ethanol and CO₂
C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂ (yeast).
Q80.Halogens belong to which group?
- A.Group 17
- B.Group 1
- C.Group 16
- D.Group 18
Show answer
Correct answer: A. Group 17
Halogens are Group 17 elements.
Q81.Number of moles in 32 g of CH₄ (M = 16 g/mol) is:
- A.3
- B.1
- C.3.5
- D.2
Show answer
Correct answer: D. 2
n = mass/M = 32/16 = 2 mol.
Q82.Shape of s-orbital is:
- A.clover-leaf
- B.linear
- C.spherical
- D.dumbbell
Show answer
Correct answer: C. spherical
s-orbital is spherically symmetric.
Q83.Bond order in O₂ is:
- A.1.5
- B.2
- C.1
- D.3
Show answer
Correct answer: B. 2
O=O double bond; bond order = 2.
Q84.Laughing gas is:
- A.N₂O
- B.NO
- C.NO₂
- D.N₂
Show answer
Correct answer: A. N₂O
Laughing gas = nitrous oxide (N₂O).
Q85.If [H⁺] = 10⁻13 mol/L, the pH of the solution is:
- A.14
- B.1
- C.12
- D.13
Show answer
Correct answer: D. 13
pH = −log[H⁺] = −log(10⁻13) = 13.
Q86.Molar mass of C₂H₆ is:
- A.26 g/mol
- B.32 g/mol
- C.30 g/mol
- D.28 g/mol
Show answer
Correct answer: C. 30 g/mol
Add atomic masses: molar mass of C₂H₆ = 30 g/mol.
Q87.Oxidation state of copper in CuO is:
- A.+3
- B.+2
- C.+1
- D.0
Show answer
Correct answer: B. +2
O=−2, so Cu=+2.
Q88.Formula of magnesium nitrate is:
- A.Mg(NO₃)₂
- B.MgNO₃
- C.Mg₂NO₃
- D.Mg(NO₂)₂
Show answer
Correct answer: A. Mg(NO₃)₂
Mg(+2) and NO₃⁻: need 2 NO₃⁻.
Q89.Reaction of K with water produces:
- A.K₂O and H₂O
- B.K₂O₂ and H₂
- C.KH and O₂
- D.KOH and H₂
Show answer
Correct answer: D. KOH and H₂
2K + 2H₂O → 2KOH + H₂↑.
Q90.Common name of Ca(OH)₂ is:
- A.limestone
- B.marble
- C.slaked lime
- D.quicklime
Show answer
Correct answer: C. slaked lime
Ca(OH)₂ = slaked lime.