Mathematics questions
18011 published questions with worked solutions.
- 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...
- Consider the function f : R → R defined by f(x) = 2x 1 + 9x^2 . If the composition of f, (f∘f∘f∘…∘f)(x) (10 times) = 2^ 10 x 1 +...
- Let A be a 2 × 2 symmetric matrix such that A bmatrix 1 1 bmatrix = bmatrix 3 7 bmatrix and the determinant of A be 1. If A⁻¹ =...
- There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the...
- In a tournament, a team plays 10 matches with probabilities of winning and losing each match as 13 and 23 respectively. Let x be...
- Consider a line L passing through the points P(1, 2, 1) and Q(2, 1, −1). If the mirror image of the point A(2, 2, 2) in the line...
- Let y = y(x) be the solution of the differential equation (x + y + 2)² dx = dy, y(0) = −2. Let the maximum and minimum values of...