JEE Main questions
34568 published questions with worked solutions.
- Suppose f(x) = (2^x + 2^ -x ) x ^ -1 (x^2 - x + 1) (7x^2 + 3x + 1)^3 . Then the value of f′(0) is equal to-
- Let A be a square matrix such that AAᵀ = I. Then 12A [(A + A^T)^2 + (A - A^T)^2 ] is equal to-
- Let (5, a/4) be the circumcentre of a triangle with vertices A(a, –2), B(a, 6) and C(a/4, –2). Let α denote the circumradius, β...
- Let R be a relation on Z × Z defined by (a, b) R (c, d) if and only if ad – bc is divisible by 5. Then R is
- A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is-
- If ^ 11 C_1 2 + ^ 11 C_2 3 + + ^ 11 C_9 10 = nm with gcd(n, m) = 1, then n + m is equal to ________.
- Let α, β be the roots of the equation x² – x + 2 = 0 with Im(α) > Im(β). Then α⁶ + α⁴ + β⁴ – 5α² is equal to ______.
- A line with direction ratios 2, 1, 2 meets the lines x = y + 2 = z and x + 2 = 2y = 2z respectively at the points P and Q. If the...
- All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in...
- The area (in sq. units) of the part of the circle x² + y² = 169 which is below the line 5x – y = 13 is 2 - 65 2 + ^ -1 ( 12 13 ),...
- If the mean and variance of the data 65, 68, 58, 44, 48, 45, 60, α, β, 60 where α > β are 56 and 66.2 respectively, then α² + β²...
- If the solution curve y = y(x) of the differential equation (1 + y²)(1 + log_e x)dx + x dy = 0, x > 0 passes through the point...
- Equations of two diameters of a circle are 2x – 3y = 5 and 3x – 4y = 7. The line joining the points (–22/7, –4) and (–1/7, 3)...
- Let f(x) = 2ˣ – x², x ∈ ℝ. If m and n are respectively the number of points at which the curves y = f(x) and y = f ′(x) intersect...
- If mass is written as m = kc^P G^ −1/2 h^ 1/2 then the value of P will be : (Constants have their usual meanings with k a...
- A particle of charge '–q' and mass 'm' moves in a circle of radius 'r' around an infinitely long line charge of linear charge...
- Match List I with List II List I: A. Gauss's law of magnetostatics, B. Faraday's law of electro magnetic induction, C. Ampere's...
- A beam of unpolarised light of intensity I₀ is passed through a Polaroid A and then through another Polaroid B which is oriented...
- An electron revolving in nᵗʰ Bohr orbit has magnetic moment μₙ. If μₙ ∝ nˣ, the value of x is
- In a nuclear fission reaction of an isotope of mass M, three similar daughter nuclei of same mass are formed. The speed of a...