Mathematics questions
18011 published questions with worked solutions.
- If α and β are the roots of the equation 375x^2 - 25x - 2 = 0, then _ n _ r=1 ^n ^r + _ n _ r=1 ^n ^r is equal to:
- The number of solutions of the equation 1 + ^4x = ^23x, x [- 5 2 , 5 2 ] is:Not in JEE Main syllabus
- The equation |z − i| = |z − 1|, i = -1 , represents:
- If e^y + xy = e, the ordered pair ( dy dx , d^2y dx^2 ) at x = 0 is equal to:
- The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:
- If m is the minimum value of k for which the function f(x) = x kx - x^2 is increasing in the interval [0, 3] and M is the maximum...
- If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm)...
- The coefficient of x^ 18 in the product (1 + x)(1 - x)^ 10 (1 + x + x^2)^9 is:
- Consider the differential equation, y^2dx + (x - 1y )dy = 0. If value of y is 1 when x = 1, then the value of x for which y = 2,...
- If the area (in sq. units) of the region (x, y) : y^2 4x, x + y ≤ 1, x ≥ 0, y ≥ 0 is a 2 + b, then a − b is equal to:
- If the data x_1, x_2, , x_ 10 is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum...
- If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = bmatrix 2 & 3 5 & -1 bmatrix , then AB is equal to:
- If the normal to the ellipse 3x^2 + 4y^2 = 12 at a point P on it is parallel to the line, 2x + y = 4 and the tangent to the...
- Let a = 3 i + 2 j + 2 k and b = i + 2 j - 2 k be two vectors. If a vector perpendicular to both the vectors a + b and a - b has...
- If B = bmatrix 5 & 2 & 1 0 & 2 & 1 & 3 & -1 bmatrix is the inverse of a 3 × 3 matrix A, then the sum of all values of α for which...
- The equation y = sin x sin(x + 2) − sin^2(x + 1) represents a straight line lying in:
- If the truth value of the statement p → (~q ∨ r) is false (F), then the truth values of the statements p, q, r are respectively:Not in JEE syllabus
- Let a random variable X have a binomial distribution with mean 8 and variance 4. If P(X 2) = k 2^ 16 , then k is equal to:
- Let S_n denote the sum of the first n terms of an A.P. If S_4 = 16 and S_6 = -48, then S_ 10 is equal to:
- Let f: R → R be a continuously differentiable function such that f(2) = 6 and f'(2) = 1 48 . If _6^ f(x) 4t^3dt = (x - 2)g(x),...