JEE Mathematics Practice Questions

Real exam: 90 questions · 180 minutes · +4 / −1 marking

22 free Mathematics MCQs written in the JEE exam pattern, each with a step-by-step solution. Tap an option for instant feedback — no sign-up, no ads.

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✍️ These are original practice questions written in the JEE pattern for the JEE Main engineering entrance exam — not questions from any official past paper.

Practice questions with solutions

Score: 0 / 22
Calculus

Q1. The derivative of sin x with respect to x is:

  1. cos x
  2. −cos x
  3. −sin x
  4. tan x
Show answer

A. cos x — d/dx (sin x) = cos x. (For reference, d/dx (cos x) = −sin x.)

Trigonometry

Q2. The value of sin 90° is:

  1. 0
  2. 1/2
  3. 1
  4. √3/2
Show answer

C. 1 — sin 90° = 1, its maximum value. (sin 0° = 0, sin 30° = 1/2, sin 60° = √3/2.)

Algebra

Q3. How many real roots does the equation x² + 1 = 0 have?

  1. 2
  2. 1
  3. 0
  4. Infinitely many
Show answer

C. 0 — x² + 1 = 0 gives x² = −1, which has no real solution (a real square is never negative). Its two roots are imaginary: x = ±i.

Calculus

Q4. The derivative of a constant (for example, of the number 7) is:

  1. 0
  2. 1
  3. 7
  4. x
Show answer

A. 0 — The derivative of any constant is 0, because a constant does not change as x changes (its graph is a flat horizontal line with zero slope).

Coordinate Geometry

Q5. The slope of the straight line y = 2x + 3 is:

  1. 3
  2. 2
  3. 5
  4. 2/3
Show answer

B. 2 — For a line in the form y = mx + c, the slope is m. Here m = 2, so the slope is 2 (and 3 is the y-intercept).

Algebra

Q6. The sum of the first n natural numbers (1 + 2 + … + n) is:

  1. n(n+1)/2
  2. n(n−1)/2
  3. n²
  4. n(n+1)
Show answer

A. n(n+1)/2 — The sum 1 + 2 + … + n equals n(n+1)/2. For example, 1+2+3+4 = 4·5/2 = 10.

Quadratic Equations

Q7. For the quadratic equation 2x^2 - 5x + 3 = 0, the sum of its roots is:

  1. -5/2
  2. 3/2
  3. 5/2
  4. -3/2
Show answer

C. 5/2 — For ax^2 + bx + c = 0, the sum of roots is -b/a = -(-5)/2 = 5/2. (Note: 3/2 is the product of the roots.)

Coordinate Geometry

Q8. The distance between the points (1, 2) and (4, 6) in the coordinate plane is:

  1. sqrt(7)
  2. 7
  3. 5
  4. 25
Show answer

C. 5 — Distance = sqrt((4-1)^2 + (6-2)^2) = sqrt(9 + 16) = sqrt(25) = 5.

Differentiation

Q9. If f(x) = x^3, then the value of f'(x) at x = 2 is:

  1. 6
  2. 8
  3. 24
  4. 12
Show answer

D. 12 — f'(x) = 3x^2, so f'(2) = 3(2)^2 = 3 x 4 = 12. (8 = 2^3 mistakenly uses the original function.)

Limits

Q10. The value of the limit as x -> 0 of sin(3x)/x is:

  1. 0
  2. 1/3
  3. 1
  4. 3
Show answer

D. 3 — sin(3x)/x = 3 * sin(3x)/(3x), and sin(3x)/(3x) -> 1 as x -> 0, so the limit is 3.

Probability

Q11. Two fair dice are rolled together. The probability that the sum of the numbers shown is 7 is:

  1. 1/6
  2. 1/9
  3. 5/36
  4. 1/12
Show answer

A. 1/6 — There are 6 favourable outcomes (1-6, 2-5, 3-4, 4-3, 5-2, 6-1) out of 36 equally likely outcomes, giving 6/36 = 1/6.

Binomial Theorem

Q12. In the binomial expansion of (1 + x)^4, the coefficient of x^2 is:

  1. 6
  2. 4
  3. 8
  4. 12
Show answer

A. 6 — The coefficient of x^2 is C(4,2) = 4!/(2!2!) = 6.

Sequences And Series

Q13. The 10th term of the arithmetic progression 3, 7, 11, 15, ... is:

  1. 36
  2. 39
  3. 43
  4. 40
Show answer

B. 39 — First term a = 3, common difference d = 4. The 10th term = a + 9d = 3 + 9(4) = 39.

Geometric Progression

Q14. The sum to infinity of the geometric series 1 + 1/2 + 1/4 + 1/8 + ... is:

  1. 3/2
  2. 2
  3. 1
  4. infinite (does not exist)
Show answer

B. 2 — With first term a = 1 and ratio r = 1/2 (|r| < 1), the sum is a/(1 - r) = 1/(1 - 1/2) = 2.

Complex Numbers

Q15. The modulus of the complex number 3 + 4i is:

  1. 5
  2. 7
  3. sqrt(7)
  4. 25
Show answer

A. 5 — |a + bi| = sqrt(a^2 + b^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.

Vectors

Q16. The magnitude of the vector 2i + 3j + 6k is:

  1. 6
  2. 11
  3. 7
  4. 49
Show answer

C. 7 — Magnitude = sqrt(2^2 + 3^2 + 6^2) = sqrt(4 + 9 + 36) = sqrt(49) = 7.

Permutations And Combinations

Q17. The number of distinct arrangements of all the letters of the word MATH is:

  1. 12
  2. 16
  3. 256
  4. 24
Show answer

D. 24 — All four letters are distinct, so the number of arrangements is 4! = 24. (256 = 4^4 wrongly allows repetition.)

Logarithms

Q18. The value of log base 2 of 32 is:

  1. 4
  2. 6
  3. 5
  4. 16
Show answer

C. 5 — log_2(32) asks for the power of 2 that gives 32. Since 2^5 = 32, the value is 5.

Matrices And Determinants

Q19. The determinant of the matrix [[2, 1], [3, 4]] is:

  1. 8
  2. 11
  3. 5
  4. 14
Show answer

C. 5 — For [[a, b], [c, d]] the determinant is ad - bc = (2)(4) - (1)(3) = 8 - 3 = 5.

Trigonometry

Q20. The value of sin 30 degrees + cos 60 degrees is:

  1. 1
  2. 1/2
  3. sqrt(3)/2
  4. 0
Show answer

A. 1 — sin 30 = 1/2 and cos 60 = 1/2, so their sum is 1/2 + 1/2 = 1.

Sets

Q21. If a set A has exactly 3 elements, the total number of subsets of A is:

  1. 6
  2. 8
  3. 3
  4. 9
Show answer

B. 8 — A set with n elements has 2^n subsets. Here n = 3, so 2^3 = 8 subsets (including the empty set and A itself).

Straight Lines

Q22. The slope of any line perpendicular to the line y = 3x + 2 is:

  1. 3
  2. -1/3
  3. -3
  4. 1/3
Show answer

B. -1/3 — The given line has slope 3. A perpendicular line has slope equal to the negative reciprocal, which is -1/3 (since 3 x -1/3 = -1).

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