JEE Main Maths Chapter-wise Quiz: 30 MCQs with Solutions

This JEE Main maths chapter-wise quiz gives you 30 MCQs, five per chapter set, with a full answer key and step-by-step working. Every chapter comes from the official JEE Main 2026 maths syllabus, which is still the base for 2027 preparation.

Use one set at the end of each chapter block in your 100-day JEE Main 2027 study plan, then retake weak sets in the revision weeks. The same format is available for the other two subjects in our JEE Main physics chapter-wise quiz and JEE Main chemistry chapter-wise quiz.

Notation: powers are written with ^, so x^2 means x squared and e^(x^2) means e to the power x squared. A matrix is written row by row, so [[2, 1], [5, 3]] has first row 2, 1 and second row 5, 3. |A| means the determinant of A, and i, j, k are unit vectors along the axes (except in Set A, where i is the square root of −1).

Which chapters does this JEE Main maths quiz cover?

The quiz covers six chapter sets that span 10 of the 14 maths units in the official NTA syllabus. Each set has five single-answer MCQs. Sets, relations and functions, permutations and combinations, statistics and probability, and trigonometry are not tested here, so revise them separately.

For the full unit list and the topics removed in 2024, such as mathematical reasoning, mathematical induction and planes in 3D, see our JEE Main 2027 syllabus guide. NTA has not released a separate 2027 syllabus yet, so recheck when the 2027 bulletin comes out.

Set A: Can you solve these quadratic equations and complex numbers MCQs?

This set tests roots, the discriminant, modulus, powers of i and the principal argument. Plot the point first in question 5.

1. If α and β are the roots of x^2 − 5x + 6 = 0, then α^2 + β^2 equals: (a) 25 (b) 13 (c) 37 (d) 11
2. The equation x^2 + kx + 9 = 0 has equal roots when k equals: (a) ±3 (b) 6 only (c) ±9 (d) ±6
3. The modulus of (3 + 4i)/(1 − i) is: (a) 5/√2 (b) 5√2 (c) 5 (d) 7/√2
4. The value of i^103 is: (a) 1 (b) −1 (c) −i (d) i
5. The principal argument of −1 + i√3 is: (a) π/3 (b) −π/3 (c) 5π/6 (d) 2π/3

Also readJEE Main Chemistry Chapter-wise Quiz: Physical and Organic

Set B: How well do you know sequences, series and the binomial theorem?

Here you need AP and GP sums, AM-GM and the binomial general term T(r + 1).

6. The sum of the first 20 terms of the AP 3, 7, 11, ... is: (a) 800 (b) 820 (c) 840 (d) 780
7. The sum to infinity of the GP 6 + 2 + 2/3 + ... is: (a) 9 (b) 8 (c) 12 (d) 18
8. For x > 0, the minimum value of x + 9/x is: (a) 3 (b) 9 (c) 6 (d) 10
9. The coefficient of x^3 in the expansion of (1 + 2x)^5 is: (a) 40 (b) 160 (c) 10 (d) 80
10. The term independent of x in the expansion of (x^2 + 1/x)^6 is: (a) 20 (b) 15 (c) 6 (d) 30

Set C: Can you crack matrices and determinants MCQs?

This set checks adjoint and determinant properties, a 2 × 2 inverse, consistency and area. Note the order n of each matrix.

11. A is a 3 × 3 matrix with |A| = 4. The value of |adj A| is: (a) 4 (b) 64 (c) 16 (d) 8
12. A is a 3 × 3 matrix with |A| = 3. The value of |2A| is: (a) 24 (b) 6 (c) 12 (d) 54
13. The inverse of A = [[2, 1], [5, 3]] is: (a) [[3, 1], [5, 2]] (b) [[−3, 1], [5, −2]] (c) [[2, −1], [−5, 3]] (d) [[3, −1], [−5, 2]]
14. The system x + y = 2 and 2x + ky = 4 has infinitely many solutions when k equals: (a) 1 (b) 4 (c) 2 (d) every real number
15. The area of the triangle with vertices (1, 0), (6, 0) and (4, 3) is: (a) 15 sq units (b) 7.5 sq units (c) 5 sq units (d) 10 sq units

Set D: How strong are you in limits, continuity and differentiation?

This set covers standard limits, 0/0 forms, continuity, the product rule and local maxima.

16. The value of lim (x → 0) sin 5x / x is: (a) 0 (b) 1 (c) 1/5 (d) 5
17. The value of lim (x → 2) (x^2 − 4)/(x − 2) is: (a) 4 (b) 0 (c) 2 (d) the limit does not exist
18. f(x) = kx + 1 for x ≤ 2 and f(x) = 3x − 1 for x > 2. If f is continuous at x = 2, then k equals: (a) 1 (b) 2 (c) 3 (d) 5/2
19. If y = x^2 e^x, the value of dy/dx at x = 1 is: (a) e (b) 2e (c) 4e (d) 3e
20. The function f(x) = x^3 − 3x has a local maximum at: (a) x = 1 (b) x = 0 (c) x = −1 (d) x = 3

Also readJEE Mains 2027 Registration & Notification: Status on 11 Oct 2026

Set E: Can you answer these integration and differential equations MCQs?

These test a definite integral, integration by parts, area between curves, order and degree, and an integrating factor.

21. The value of the integral of sin^2 x from 0 to π/2 is: (a) π/2 (b) π/4 (c) 1 (d) 1/2
22. The indefinite integral of x e^x with respect to x is: (a) x e^x + C (b) (x + 1)e^x + C (c) (x − 1)e^x + C (d) x^2 e^x/2 + C
23. The area enclosed between the curves y = x^2 and y = x is: (a) 1/6 sq unit (b) 1/3 sq unit (c) 1/2 sq unit (d) 2/3 sq unit
24. The order and degree of the differential equation (d^2y/dx^2)^3 + (dy/dx)^4 + y = 0 are: (a) order 3, degree 2 (b) order 2, degree 4 (c) order 2, degree 3 (d) order 4, degree 3
25. The integrating factor of dy/dx + (2/x)y = x, for x > 0, is: (a) 2 ln x (b) x^2 (c) e^x (d) 1/x^2

Set F: How well do you know coordinate geometry, vectors and 3D?

The last set mixes lines, circles, the parabola, the dot product and direction cosines.

26. The distance of the point (3, 4) from the line 3x + 4y − 5 = 0 is: (a) 5 (b) 20 (c) 4 (d) 3
27. The centre and radius of the circle x^2 + y^2 − 4x + 6y − 12 = 0 are: (a) (2, −3) and 5 (b) (−2, 3) and 5 (c) (2, −3) and 25 (d) (4, −6) and 5
28. The focus of the parabola y^2 = 12x is: (a) (0, 3) (b) (12, 0) (c) (−3, 0) (d) (3, 0)
29. The vectors 2i + λj + k and i − 2j + 4k are perpendicular when λ equals: (a) 3 (b) −3 (c) 2 (d) 1
30. The direction cosines of the vector 2i − j + 2k are: (a) (2, −1, 2) (b) (2/3, −1/3, 2/3) (c) (2/9, −1/9, 2/9) (d) (2/√5, −1/√5, 2/√5)

Answer key with explanations

The working is shown for every question. Count a guessed answer as wrong even if it matched.

Set A answers

1. (b) 13. α + β = 5 and αβ = 6. α^2 + β^2 = (α + β)^2 − 2αβ = 25 − 12 = 13. Check: the roots are 2 and 3, and 4 + 9 = 13.
2. (d) ±6. Equal roots need discriminant zero: k^2 − 4 × 1 × 9 = 0, so k^2 = 36 and k = 6 or −6.
3. (a) 5/√2. |z1/z2| = |z1|/|z2|. |3 + 4i| = √(9 + 16) = 5 and |1 − i| = √2, so the modulus is 5/√2.
4. (c) −i. Powers of i repeat every 4. 103 = 4 × 25 + 3, so i^103 = i^3 = −i.
5. (d) 2π/3. The point (−1, √3) lies in the second quadrant. tan α = √3/1 gives α = π/3, so the argument is π − π/3 = 2π/3.

Set B answers

6. (b) 820. a = 3, d = 4, n = 20. S = n/2 × [2a + (n − 1)d] = 10 × [6 + 76] = 10 × 82 = 820.
7. (a) 9. a = 6, r = 2/6 = 1/3, and |r| < 1. S = a/(1 − r) = 6/(2/3) = 9.
8. (c) 6. By AM ≥ GM, (x + 9/x)/2 ≥ √(x × 9/x) = 3, so x + 9/x ≥ 6. Equality holds when x = 9/x, that is x = 3.
9. (d) 80. T(r + 1) = C(5, r)(2x)^r. For x^3, r = 3: C(5, 3) × 2^3 = 10 × 8 = 80.
10. (b) 15. T(r + 1) = C(6, r)(x^2)^(6 − r)(1/x)^r = C(6, r) x^(12 − 3r). For no x, 12 − 3r = 0, so r = 4. The term is C(6, 4) = 15.

Set C answers

11. (c) 16. For an n × n matrix, |adj A| = |A|^(n − 1). Here n = 3, so |adj A| = 4^2 = 16.
12. (a) 24. For an n × n matrix, |kA| = k^n |A|. So |2A| = 2^3 × 3 = 24.
13. (d) [[3, −1], [−5, 2]]. |A| = 2 × 3 − 1 × 5 = 1. For [[a, b], [c, d]], the inverse is (1/|A|) × [[d, −b], [−c, a]] = [[3, −1], [−5, 2]]. Check: the first row of A times the columns gives 6 − 5 = 1 and −2 + 2 = 0; the second row gives 15 − 15 = 0 and −5 + 6 = 1.
14. (c) 2. The coefficient determinant is 1 × k − 1 × 2 = k − 2. For k ≠ 2 there is a unique solution. For k = 2, the second equation becomes 2x + 2y = 4, which is just twice the first, so there are infinitely many solutions.
15. (b) 7.5 sq units. Area = 1/2 |x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)| = 1/2 |1(0 − 3) + 6(3 − 0) + 4(0 − 0)| = 1/2 |−3 + 18| = 7.5. Check: base 5 on the x-axis, height 3, so 1/2 × 5 × 3 = 7.5.

Set D answers

16. (d) 5. sin 5x / x = 5 × (sin 5x)/(5x). As x → 0, (sin 5x)/(5x) → 1, so the limit is 5.
17. (a) 4. For x ≠ 2, (x^2 − 4)/(x − 2) = x + 2. The limit as x → 2 is 2 + 2 = 4. The function is undefined at x = 2, but the limit exists.
18. (b) 2. Left value at x = 2: 2k + 1. Right-hand limit: 3 × 2 − 1 = 5. Continuity needs 2k + 1 = 5, so k = 2.
19. (d) 3e. By the product rule, dy/dx = 2x e^x + x^2 e^x = e^x(x^2 + 2x). At x = 1: e(1 + 2) = 3e.
20. (c) x = −1. f'(x) = 3x^2 − 3 = 0 gives x = ±1. f''(x) = 6x. At x = −1, f'' = −6 < 0, so it is a local maximum (value f(−1) = −1 + 3 = 2). At x = 1, f'' = 6 > 0, a local minimum.

Set E answers

21. (b) π/4. sin^2 x = (1 − cos 2x)/2. The integral from 0 to π/2 is [x/2 − sin 2x/4] from 0 to π/2 = π/4 − 0 = π/4.
22. (c) (x − 1)e^x + C. By parts with u = x and dv = e^x dx: ∫x e^x dx = x e^x − ∫e^x dx = x e^x − e^x + C = (x − 1)e^x + C. Check: differentiating gives e^x + (x − 1)e^x = x e^x.
23. (a) 1/6 sq unit. The curves meet where x^2 = x, at x = 0 and x = 1. Between them y = x lies above y = x^2. Area = integral of (x − x^2) from 0 to 1 = 1/2 − 1/3 = 1/6.
24. (c) order 2, degree 3. The highest derivative present is d^2y/dx^2, so the order is 2. The equation is a polynomial in the derivatives, and that highest derivative is raised to the power 3, so the degree is 3.
25. (b) x^2. For dy/dx + P(x)y = Q(x), IF = e^(∫P dx). Here P = 2/x, so ∫P dx = 2 ln x = ln(x^2), and IF = e^(ln x^2) = x^2.

Set F answers

26. (c) 4. Distance = |ax1 + by1 + c|/√(a^2 + b^2) = |9 + 16 − 5|/√(9 + 16) = 20/5 = 4.
27. (a) (2, −3) and 5. Compare with x^2 + y^2 + 2gx + 2fy + c = 0: g = −2, f = 3, c = −12. Centre = (−g, −f) = (2, −3). Radius = √(g^2 + f^2 − c) = √(4 + 9 + 12) = √25 = 5.
28. (d) (3, 0). Compare y^2 = 12x with y^2 = 4ax: 4a = 12, so a = 3. The focus is (a, 0) = (3, 0).
29. (a) 3. Perpendicular vectors have zero dot product: 2 × 1 + λ × (−2) + 1 × 4 = 0, so 6 − 2λ = 0 and λ = 3.
30. (b) (2/3, −1/3, 2/3). Magnitude = √(4 + 1 + 4) = 3. Direction cosines = components divided by magnitude: 2/3, −1/3, 2/3. Check: 4/9 + 1/9 + 4/9 = 1. Option (a) gives direction ratios, not cosines.

How should you score and use this maths quiz?

Give yourself one mark per correct answer and judge each set separately. Also note whether each mistake was conceptual or an algebra slip, because the fixes differ.

Do not just read the solution for a question you got wrong. Close the answer key, solve it again from a blank page, and only then compare. Reading a solution feels like learning, but solving it yourself is what sticks on exam day.

How does this quiz fit into the 100-day plan for JEE Main 2027?

Take each set when you finish its chapters in the 100-day plan, retake low-scoring sets during the revision weeks, and shift to full-length timed papers in the final phase. Chapter quizzes show weak topics; mock tests build speed and the skill of skipping long questions.

Once most of your maths sets score 4 or 5, start the official NTA mocks; our guide to JEE Main 2027 free mock tests explains where to find them and how to review each attempt. JEE Main 2027 Session 1 dates have been announced in NTA's official calendar (tentative), and registration is not open yet.

Maths is often where scores vary the most between students, so a few extra correct answers here can move your percentile noticeably. Our pillar guide on colleges for low JEE Main rank shows which colleges open up in each percentile band.

Final Word: make this JEE Main maths chapter-wise quiz a habit

This JEE Main maths chapter-wise quiz is most useful when you repeat it: take each set after its chapters and retake weak sets after a week.

• Attempt each set in about 8 minutes without notes or a calculator.
• Redo every wrong question from a blank page before reading the working.
• Keep a formula sheet for standard results like AP sums, T(r + 1) and standard integrals.
• Revise units not covered here: functions, permutations and combinations, statistics and probability, and trigonometry.
• Move to NTA mock tests once most sets score 4 or 5.