JEE Main Practice Set 5
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 5: all 90 questions with answers
Try each question first, then open “Show answer” to check the correct option and explanation.
Q1.Solve for x: 8x + 7 = 31.
- A.4
- B.2
- C.5
- D.3
Show answer
Correct answer: D. 3
Subtract 7 from both sides: 8x = 24. Divide by 8: x = 3.
Q2.One root of x² − 16x + 63 = 0 is 7. The other root is:
- A.8
- B.16
- C.9
- D.10
Show answer
Correct answer: C. 9
Product of roots = 63. Other root = 63 ÷ 7 = 9.
Q3.The 8th term of an AP with first term 2 and common difference 8 is:
- A.61
- B.58
- C.50
- D.66
Show answer
Correct answer: B. 58
aₙ = a + (n−1)d = 2 + 7×8 = 58.
Q4.Slope of the line through (3, 8) and (6, 26) is:
- A.6
- B.7
- C.5
- D.8
Show answer
Correct answer: A. 6
Slope = (26−8) ÷ (6−3) = 18 ÷ 3 = 6.
Q5.Value of cos 270° is:
- A.1
- B.−1
- C.1/2
- D.0
Show answer
Correct answer: D. 0
cos 270° = 0.
Q6.A bag contains 7 red and 7 blue balls. Probability of drawing a red ball is:
- A.7/13
- B.8/15
- C.7/14
- D.7/15
Show answer
Correct answer: C. 7/14
P(red) = 7/14.
Q7.Determinant of matrix [[8, 1], [2, 7]] is:
- A.22
- B.54
- C.59
- D.51
Show answer
Correct answer: B. 54
det = ad − bc = 8×7 − 1×2 = 54.
Q8.Evaluate: log₂ₐₑₒₓ2(2^8) [log base 2].
- A.8
- B.9
- C.7
- D.16
Show answer
Correct answer: A. 8
logₐ(a^n) = n, so log_2(2^8) = 8.
Q9.Find 10P4.
- A.1260
- B.5048
- C.5032
- D.5040
Show answer
Correct answer: D. 5040
10P4 = 10!/(10−4)! = 10×9×8×7 = 5040.
Q10.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.
Q11.Simple interest on Rs 4500 at 6% p.a. for 2 years is:
- A.Rs 1080
- B.Rs 540
- C.Rs 660
- D.Rs 480
Show answer
Correct answer: B. Rs 540
SI = P×R×T/100 = 4500×6×2/100 = Rs 540.
Q12.Area of a triangle with base 6 cm and height 6 cm is:
- A.18 cm²
- B.36 cm²
- C.24 cm²
- D.12 cm²
Show answer
Correct answer: A. 18 cm²
Area = (1/2) × base × height = (1/2) × 6 × 6 = 18 cm².
Q13.Solve for x: 2x + 8 = 16.
- A.5
- B.3
- C.6
- D.4
Show answer
Correct answer: D. 4
Subtract 8 from both sides: 2x = 8. Divide by 2: x = 4.
Q14.One root of x² − 19x + 88 = 0 is 8. The other root is:
- A.10
- B.19
- C.11
- D.12
Show answer
Correct answer: C. 11
Product of roots = 88. Other root = 88 ÷ 8 = 11.
Q15.The 9th term of an AP with first term 3 and common difference 2 is:
- A.23
- B.19
- C.17
- D.21
Show answer
Correct answer: B. 19
aₙ = a + (n−1)d = 3 + 8×2 = 19.
Q16.Slope of the line through (4, 2) and (7, 23) is:
- A.7
- B.8
- C.6
- D.9
Show answer
Correct answer: A. 7
Slope = (23−2) ÷ (7−4) = 21 ÷ 3 = 7.
Q17.Value of tan 0° is:
- A.1
- B.undefined
- C.1/2
- D.0
Show answer
Correct answer: D. 0
tan 0° = 0.
Q18.A bag contains 8 red and 8 blue balls. Probability of drawing a red ball is:
- A.8/15
- B.9/17
- C.8/16
- D.8/17
Show answer
Correct answer: C. 8/16
P(red) = 8/16.
Q19.Determinant of matrix [[2, 2], [3, 8]] is:
- A.18
- B.10
- C.15
- D.7
Show answer
Correct answer: B. 10
det = ad − bc = 2×8 − 2×3 = 10.
Q20.Evaluate: log₂ₐₑₒₓ3(3^2) [log base 3].
- A.2
- B.3
- C.1
- D.6
Show answer
Correct answer: A. 2
logₐ(a^n) = n, so log_3(3^2) = 2.
Q21.Find 11P2.
- A.55
- B.114
- C.106
- D.110
Show answer
Correct answer: D. 110
11P2 = 11!/(11−2)! = 11×10 = 110.
Q22.Find 10C2.
- A.48
- B.42
- C.45
- D.20
Show answer
Correct answer: C. 45
nC2 = n(n−1)/2 = 10×9/2 = 45.
Q23.Simple interest on Rs 4700 at 7% p.a. for 3 years is:
- A.Rs 1974
- B.Rs 987
- C.Rs 1197
- D.Rs 882
Show answer
Correct answer: B. Rs 987
SI = P×R×T/100 = 4700×7×3/100 = Rs 987.
Q24.Area of a triangle with base 7 cm and height 7 cm is:
- A.24.5 cm²
- B.49 cm²
- C.30.5 cm²
- D.18.5 cm²
Show answer
Correct answer: A. 24.5 cm²
Area = (1/2) × base × height = (1/2) × 7 × 7 = 24.5 cm².
Q25.Solve for x: 3x + 9 = 24.
- A.6
- B.4
- C.7
- D.5
Show answer
Correct answer: D. 5
Subtract 9 from both sides: 3x = 15. Divide by 3: x = 5.
Q26.One root of x² − 22x + 117 = 0 is 9. The other root is:
- A.12
- B.22
- C.13
- D.14
Show answer
Correct answer: C. 13
Product of roots = 117. Other root = 117 ÷ 9 = 13.
Q27.The 10th term of an AP with first term 4 and common difference 3 is:
- A.36
- B.31
- C.28
- D.34
Show answer
Correct answer: B. 31
aₙ = a + (n−1)d = 4 + 9×3 = 31.
Q28.Slope of the line through (5, 3) and (8, 27) is:
- A.8
- B.9
- C.7
- D.10
Show answer
Correct answer: A. 8
Slope = (27−3) ÷ (8−5) = 24 ÷ 3 = 8.
Q29.Value of sin(−30°) is:
- A.1/2
- B.√3/2
- C.−1
- D.−1/2
Show answer
Correct answer: D. −1/2
sin(−θ)=−sinθ, so −1/2.
Q30.A bag contains 9 red and 9 blue balls. Probability of drawing a red ball is:
- A.9/17
- B.10/19
- C.9/18
- D.9/19
Show answer
Correct answer: C. 9/18
P(red) = 9/18.
Q31.A body starts with velocity 6 m/s and has acceleration 8 m/s². Its velocity after 3 s is:
- A.22 m/s
- B.38 m/s
- C.9 m/s
- D.30 m/s
Show answer
Correct answer: D. 30 m/s
v = u + at = 6 + 8×3 = 30 m/s.
Q32.For u = 3 m/s, a = 2 m/s², t = 4 s, displacement is:
- A.36 m
- B.26 m
- C.28 m
- D.12 m
Show answer
Correct answer: C. 28 m
s = ut + ½At² = 3×4 + 0.5×2×4² = 28 m.
Q33.Net force needed to give 6 kg mass an acceleration of 9 m/s² is:
- A.15 N
- B.54 N
- C.63 N
- D.45 N
Show answer
Correct answer: B. 54 N
F = ma = 6×9 = 54 N.
Q34.Work done when force 50 N moves a body 7 m in its direction is:
- A.350 J
- B.400 J
- C.300 J
- D.57 J
Show answer
Correct answer: A. 350 J
W = F×d = 50×7 = 350 J.
Q35.A body does 1100 J of work in 7 s. Its power is:
- A.314.29 W
- B.164.14 W
- C.152.14 W
- D.157.14 W
Show answer
Correct answer: D. 157.14 W
P = W/t = 1100/7 = 157.14 W.
Q36.A body of mass 7 kg moves at 6 m/s. Its momentum is:
- A.36 kg·m/s
- B.13 kg·m/s
- C.42 kg·m/s
- D.49 kg·m/s
Show answer
Correct answer: C. 42 kg·m/s
p = mv = 7×6 = 42 kg·m/s.
Q37.Kinetic energy of 8 kg body moving at 8 m/s is:
- A.248 J
- B.256 J
- C.64 J
- D.320 J
Show answer
Correct answer: B. 256 J
KE = ½mv² = 0.5×8×8² = 256 J.
Q38.Voltage across a 5 Ω resistor carrying 6 A current is:
- A.30 V
- B.35 V
- C.23 V
- D.13 V
Show answer
Correct answer: A. 30 V
V = IR = 6×5 = 30 V.
Q39.Two resistors 8 Ω and 8 Ω connected in series. Total resistance is:
- A.64 Ω
- B.0 Ω
- C.18 Ω
- D.16 Ω
Show answer
Correct answer: D. 16 Ω
Series: R = R₁ + R₂ = 8 + 8 = 16 Ω.
Q40.Power of a lens with focal length 60 cm is:
- A.2.67 D
- B.0.6 D
- C.1.67 D
- D.60 D
Show answer
Correct answer: C. 1.67 D
P = 1/f = 1/0.6 m = 1.67 D.
Q41.Wave speed for frequency 50 Hz and wavelength 8 m is:
- A.58 m/s
- B.400 m/s
- C.450 m/s
- D.320 m/s
Show answer
Correct answer: B. 400 m/s
v = fλ = 50×8 = 400 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 7 m/s and has acceleration 2 m/s². Its velocity after 4 s is:
- A.13 m/s
- B.17 m/s
- C.11 m/s
- D.15 m/s
Show answer
Correct answer: D. 15 m/s
v = u + at = 7 + 2×4 = 15 m/s.
Q44.For u = 4 m/s, a = 3 m/s², t = 5 s, displacement is:
- A.72.5 m
- B.54.5 m
- C.57.5 m
- D.20 m
Show answer
Correct answer: C. 57.5 m
s = ut + ½At² = 4×5 + 0.5×3×5² = 57.5 m.
Q45.Net force needed to give 7 kg mass an acceleration of 3 m/s² is:
- A.10 N
- B.21 N
- C.24 N
- D.18 N
Show answer
Correct answer: B. 21 N
F = ma = 7×3 = 21 N.
Q46.Work done when force 55 N moves a body 8 m in its direction is:
- A.440 J
- B.495 J
- C.385 J
- D.63 J
Show answer
Correct answer: A. 440 J
W = F×d = 55×8 = 440 J.
Q47.A body does 1150 J of work in 8 s. Its power is:
- A.287.5 W
- B.151.75 W
- C.138.75 W
- D.143.75 W
Show answer
Correct answer: D. 143.75 W
P = W/t = 1150/8 = 143.75 W.
Q48.A body of mass 8 kg moves at 7 m/s. Its momentum is:
- A.49 kg·m/s
- B.15 kg·m/s
- C.56 kg·m/s
- D.64 kg·m/s
Show answer
Correct answer: C. 56 kg·m/s
p = mv = 8×7 = 56 kg·m/s.
Q49.Kinetic energy of 2 kg body moving at 9 m/s is:
- A.79 J
- B.81 J
- C.18 J
- D.99 J
Show answer
Correct answer: B. 81 J
KE = ½mv² = 0.5×2×9² = 81 J.
Q50.Voltage across a 6 Ω resistor carrying 7 A current is:
- A.42 V
- B.48 V
- C.34 V
- D.15 V
Show answer
Correct answer: A. 42 V
V = IR = 7×6 = 42 V.
Q51.Two resistors 9 Ω and 9 Ω connected in series. Total resistance is:
- A.81 Ω
- B.0 Ω
- C.20 Ω
- D.18 Ω
Show answer
Correct answer: D. 18 Ω
Series: R = R₁ + R₂ = 9 + 9 = 18 Ω.
Q52.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.
Q53.Wave speed for frequency 70 Hz and wavelength 2 m is:
- A.72 m/s
- B.140 m/s
- C.210 m/s
- D.120 m/s
Show answer
Correct answer: B. 140 m/s
v = fλ = 70×2 = 140 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 8 m/s and has acceleration 3 m/s². Its velocity after 5 s is:
- A.20 m/s
- B.26 m/s
- C.13 m/s
- D.23 m/s
Show answer
Correct answer: D. 23 m/s
v = u + at = 8 + 3×5 = 23 m/s.
Q56.For u = 5 m/s, a = 4 m/s², t = 6 s, displacement is:
- A.126 m
- B.98 m
- C.102 m
- D.30 m
Show answer
Correct answer: C. 102 m
s = ut + ½At² = 5×6 + 0.5×4×6² = 102 m.
Q57.Net force needed to give 8 kg mass an acceleration of 4 m/s² is:
- A.12 N
- B.32 N
- C.36 N
- D.28 N
Show answer
Correct answer: B. 32 N
F = ma = 8×4 = 32 N.
Q58.Work done when force 60 N moves a body 9 m in its direction is:
- A.540 J
- B.600 J
- C.480 J
- D.69 J
Show answer
Correct answer: A. 540 J
W = F×d = 60×9 = 540 J.
Q59.A body does 1200 J of work in 9 s. Its power is:
- A.266.67 W
- B.142.33 W
- C.128.33 W
- D.133.33 W
Show answer
Correct answer: D. 133.33 W
P = W/t = 1200/9 = 133.33 W.
Q60.A body of mass 9 kg moves at 8 m/s. Its momentum is:
- A.64 kg·m/s
- B.17 kg·m/s
- C.72 kg·m/s
- D.81 kg·m/s
Show answer
Correct answer: C. 72 kg·m/s
p = mv = 9×8 = 72 kg·m/s.
Q61.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.
Q62.Molar mass of Cl₂ is:
- A.70 g/mol
- B.72 g/mol
- C.71 g/mol
- D.35.5 g/mol
Show answer
Correct answer: C. 71 g/mol
Add atomic masses: molar mass of Cl₂ = 71 g/mol.
Q63.Oxidation state of Zn in ZnSO₄ is:
- A.+3
- B.+2
- C.+1
- D.0
Show answer
Correct answer: B. +2
SO₄=−2, Zn=+2.
Q64.Formula of manganese(II) oxide is:
- A.MnO
- B.Mn₂O₃
- C.MnO₂
- D.Mn₃O₄
Show answer
Correct answer: A. MnO
Mn(+2) and O(−2): MnO.
Q65.Colour of copper sulfate solution is:
- A.green
- B.colourless
- C.pink
- D.blue
Show answer
Correct answer: D. blue
CuSO₄ solution is blue due to [Cu(H₂O)₄]²⁺.
Q66.Formula of bleaching powder is:
- A.CaCl₂
- B.Ca(ClO₃)₂
- C.Ca(OCl)Cl
- D.CaO
Show answer
Correct answer: C. Ca(OCl)Cl
Bleaching powder = Ca(OCl)Cl.
Q67.Functional group in nitrobenzene is:
- A.−COOH
- B.−NO₂ (nitro)
- C.−NH₂ (amine)
- D.−OH
Show answer
Correct answer: B. −NO₂ (nitro)
C₆H₅NO₂ has a nitro group.
Q68.Which element in Period 2 has 2 valence electrons?
- A.Beryllium
- B.Magnesium
- C.Lithium
- D.Boron
Show answer
Correct answer: A. Beryllium
Be (Z=4): config 2,2 → Period 2, Group 2.
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.Heisenberg uncertainty principle:
- A.energy is conserved
- B.photons have mass
- C.position and momentum cannot both be measured precisely simultaneously
- D.electrons move in fixed orbits
Show answer
Correct answer: C. position and momentum cannot both be measured precisely simultaneously
Δx·Δp ≥ h/(4π).
Q71.London dispersion forces are present in:
- A.metals only
- B.all molecules
- C.polar molecules only
- D.ionic compounds only
Show answer
Correct answer: B. all molecules
London forces arise from temporary dipoles in all molecules.
Q72.Greenhouse gas produced mainly from fossil fuel combustion is:
- A.CO₂
- B.O₂
- C.N₂
- D.H₂
Show answer
Correct answer: A. CO₂
CO₂ is the primary greenhouse gas from human activity.
Q73.If [H⁺] = 10⁻9 mol/L, the pH of the solution is:
- A.10
- B.5
- C.8
- D.9
Show answer
Correct answer: D. 9
pH = −log[H⁺] = −log(10⁻9) = 9.
Q74.Molar mass of SO₂ is:
- A.80 g/mol
- B.66 g/mol
- C.64 g/mol
- D.48 g/mol
Show answer
Correct answer: C. 64 g/mol
Add atomic masses: molar mass of SO₂ = 64 g/mol.
Q75.Oxidation state of Na in Na₂O₂ is:
- A.−1
- B.+1
- C.+2
- D.0
Show answer
Correct answer: B. +1
Na=+1; peroxide O=−1.
Q76.Formula of cobalt(II) chloride is:
- A.CoCl₂
- B.CoCl
- C.CoCl₃
- D.Co₂Cl₃
Show answer
Correct answer: A. CoCl₂
Co(+2) and Cl(−1): CoCl₂.
Q77.PbS precipitate colour with H₂S in lead acetate solution is:
- A.white
- B.yellow
- C.red
- D.black
Show answer
Correct answer: D. black
Pb(CH₃COO)₂ + H₂S → PbS↓(black).
Q78.Neutralisation of acid with base always produces:
- A.only water
- B.H₂ gas
- C.salt and water
- D.only salt
Show answer
Correct answer: C. salt and water
Acid + Base → Salt + Water.
Q79.Saponification reaction: ester + alkali gives:
- A.alkene + H₂O
- B.alcohol + soap (salt of fatty acid)
- C.ester + acid → alcohol
- D.alcohol + acid → ester
Show answer
Correct answer: B. alcohol + soap (salt of fatty acid)
RCOOR’ + NaOH → RCOONa + R’OH.
Q80.Which pair is in the same group of the periodic table?
- A.Na and K
- B.Na and Mg
- C.K and Ca
- D.Li and Be
Show answer
Correct answer: A. Na and K
Na and K are both in Group 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.
Q82.3d subshell electrons of Fe²⁺ (Z=26) is:
- A.8
- B.5
- C.6
- D.4
Show answer
Correct answer: C. 6
Fe: [Ar]3d⁶ 4s²; Fe²⁺: [Ar]3d⁶.
Q83.Which has the shortest bond length?
- A.ionic bond
- B.triple bond
- C.single bond
- D.double bond
Show answer
Correct answer: B. triple bond
Bond order ↑ → bond length ↓.
Q84.Formula of washing soda is:
- A.Na₂CO₃·10H₂O
- B.NaHCO₃
- C.Na₂CO₃ (anhydrous)
- D.NaOH·10H₂O
Show answer
Correct answer: A. Na₂CO₃·10H₂O
Washing soda = Na₂CO₃·10H₂O.
Q85.If [H⁺] = 10⁻10 mol/L, the pH of the solution is:
- A.11
- B.4
- C.9
- D.10
Show answer
Correct answer: D. 10
pH = −log[H⁺] = −log(10⁻10) = 10.
Q86.Molar mass of NO₂ is:
- A.44 g/mol
- B.48 g/mol
- C.46 g/mol
- D.30 g/mol
Show answer
Correct answer: C. 46 g/mol
Add atomic masses: molar mass of NO₂ = 46 g/mol.
Q87.Oxidation state of carbon in CO is:
- A.0
- B.+2
- C.+4
- D.−2
Show answer
Correct answer: B. +2
O=−2, C=+2.
Q88.Formula of chromium(III) chloride is:
- A.CrCl₃
- B.CrCl₂
- C.Cr₂Cl₃
- D.CrCl
Show answer
Correct answer: A. CrCl₃
Cr(+3) needs 3 Cl(−1).
Q89.Gas used to test for presence of unsaturation in organic compound:
- A.H₂S
- B.NH₃
- C.Cl₂
- D.Br₂ water (bromine water)
Show answer
Correct answer: D. Br₂ water (bromine water)
Bromine water decolourises with alkenes/alkynes.
Q90.A buffer solution resists change in:
- A.colour
- B.volume
- C.pH
- D.temperature
Show answer
Correct answer: C. pH
Buffers maintain nearly constant pH.