Practice questions
88551 published questions with worked solutions.
- The solution of the differential equation x dy dx + 2y = x^2 (x 0) with y(1) = 1, is:
- If a tangent to the circle x^2 + y^2 = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the...
- Slope of a line passing through P(2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P, is:
- If f(x) is a non-zero polynomial of degree four, having local extreme points at x = −1, 0, 1; then the set S = x R : f(x) = f(0)...
- A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at...
- The integral ^ 2/3 x , cosec ^ 4/3 x ,dx is equal to: (Here C is a constant of integration)
- Let p, q ∈ R. If 2 - 3 is a root of the quadratic equation, x^2 + px + q = 0, then:
- Let f(x) = 15 − |x − 10|; x ∈ R. Then the set of all values of x, at which the function, g(x) = f(f(x)) is not differentiable, is:
- Let _ k=1 ^ 10 f(a + k) = 16(2^ 10 - 1), where the function f satisfies f(x + y) = f(x)f(y) for all natural numbers x, y and f(1)...
- If the standard deviation of the numbers −1, 0, 1, k is 5 where k > 0, then k is equal to:
- If the line y = mx + 7 3 is normal to the hyperbola x^2 24 - y^2 18 = 1, then a value of m is:
- If bmatrix 1&1 0&1 bmatrix bmatrix 1&2 0&1 bmatrix bmatrix 1&3 0&1 bmatrix bmatrix 1&n-1 0&1 bmatrix = bmatrix 1&78 0&1 bmatrix ,...
- If the function f defined on ( 6 , 3 ) by f(x) = cases 2 x - 1 x - 1 , & x 4 k, & x = 4 cases is continuous, then k is equal to:
- Four persons can hit a target correctly with probabilities 12, 13, 14 and 18 respectively. If all hit at the target...
- If one end of a focal chord of the parabola, y^2 = 16x is at (1, 4), then the length of this focal chord is:
- Let α and β be the roots of the equation x^2 + x + 1 = 0. Then for y ≠ 0 in R, vmatrix y+1 & & & y+ & 1 & 1 & y+ vmatrix is equal...
- All the points in the set S = + i - i : R (i = -1 ) lie on a:
- The value of _0^ /2 ^3x x + x dx is:
- The value of ^210° - 10° 50° + ^250° is:
- Let the sum of the first n terms of a non-constant A.P., a_1, a_2, a_3, be 50n + n(n-7) 2 A, where A is a constant. If d is the...