JEE Main questions
34495 published questions with worked solutions.
- Let a relation R on N × N be defined as: (x_1, y_1) R (x_2, y_2) if and only if x_1 ≤ x_2 or y_1 ≤ y_2. Consider the two...
- Let three real numbers a, b, c be in arithmetic progression and a + 1, b, c + 3 be in geometric progression. If a > 10 and the...
- Let A = bmatrix 1 & 2 0 & 1 bmatrix and B = I + adj(A) + (adj A)² + … + (adj A)^ 10 . Then, the sum of all the elements of the...
- The value of 1 2^2 + 2 3^2 + + 100 (101)^2 1^2 2 + 2^2 3 + + 100^2 101 is
- Let f(x) = _0^x(t + (1 - e^t))dt, x ∈ R. Then _ x 0 f(x) x^3 is equal to
- The area (in sq. units) of the region described by (x, y) : y² ≤ 2x, and y ≥ 4x − 1 is
- The area (in sq. units) of the region S = z ∈ C; |z − 1| ≤ 2; (z + z) + i(z − z) ≤ 2, Im(z) ≥ 0 is
- If the value of the integral _ -1 ^ 1 x 1 + 3^x dx is 2 . Then, a value of α is
- Let f(x) = 3 x - 2 + 4 - x be a real valued function. If α and β are respectively the minimum and the maximum values of f, then...
- If the coefficients of x⁴, x⁵ and x⁶ in the expansion of (1 + x)^n are in the arithmetic progression, then the maximum value of n...
- Consider a hyperbola H having centre at the origin and foci on the x-axis. Let C_1 be the circle touching the hyperbola H and...
- If the mean of the following probability distribution of a random variable X: | X | 0 | 2 | 4 | 6 | 8 | |---|---|---|---|---|---|...
- Let PQ be a chord of the parabola y² = 12x and the midpoint of PQ be at (4, 1). Then, which of the following point lies on the...
- Given the inverse trigonometric function assumes principal values only. Let x, y be any two real numbers in [−1, 1] such that...
- Let y = y(x) be the solution of the differential equation (x² + 4)² dy + (2x³y + 8xy − 2)dx = 0. If y(0) = 0, then y(2) is equal...
- Let a = i + j + k, b = 2 i + 4 j - 5 k and c = x i + 2 j + 3 k, x ∈ R. If d is the unit vector in the direction of b + c such...
- Let P the point of intersection of the lines x - 2 1 = y - 4 5 = z - 2 1 and x - 3 2 = y - 2 3 = z - 3 2 . Then, the shortest...
- Let S = sin²2θ : (sin⁴θ + cos⁴θ)x² + (sin 2θ)x + (sin⁶θ + cos⁶θ) = 0 has real roots . If α and β be the smallest and largest...
- If ^5x ,dx = x x ( ^2x + 32 ) + _e | x2 | + C where α, β ∈ R and C is constant of integration, then the value of 8(α + β) equals...
- Let f : R → R be a thrice differentiable function such that f(0) = 0, f(1) = 1, f(2) = –1, f(3) = 2 and f(4) = –2. Then, the...