Mathematics questions
18011 published questions with worked solutions.
- The direction ratios of normal to the plane through the points (0, −1, 0) and (0, 0, 1) and making an angle 4 with the plane y −...
- Let A = pmatrix 0 & 2q & r p & q & -r p & -q & r pmatrix . If AA^T = I_3, then |p| is:
- If tangents are drawn to the ellipse x^2 + 2y^2 = 2 at all points on the ellipse other than its four vertices then the mid points...
- If x _e( _ex) - x^2 + y^2 = 4 (y > 0), then dy dx at x = e is equal to:
- The area (in sq. units) of the region bounded by the curve x^2 = 4y and the straight line x = 4y − 2 is:
- Let f: R → R be defined by f(x) = x 1 + x^2 , x ∈ R. Then the range of f is:
- Let (-2 - 13i )^3 = x + iy 27 (i = -1 ), where x and y are real numbers, then y − x equals:
- Two integers are selected at random from the set 1, 2, …., 11 . Given that the sum of selected numbers is even, the conditional...
- Two circles with equal radii are intersecting at the points (0, 1) and (0, −1). The tangent at the point (0, 1) to one of the...
- The length of the chord of the parabola x^2 = 4y having equation x - 2y + 4 2 = 0 is:
- Let N be the set of natural numbers and two functions f and g be defined as f, g: N → N such that f(n) = cases n+1 2 ; & if n is...
- If mean and standard deviation of 5 observations x_1, x_2, x_3, x_4, x_5 are 10 and 3, respectively, then the variance of 6...
- The value of ( _ n=1 ^ 19 ^ -1 (1 + _ p=1 ^ n 2p ) ) is:
- The value of 2^2 2^3 2^ 10 2^ 10 is:
- If _ r=0 ^ 25 , ^ 50 C_r ^ 50-r C_ 25-r = K ( ^ 50 C_ 25 ), then K is equal to:
- Let a_1, a_2, a_3, , a_ 10 be in G.P. with a_i > 0 for i = 1, 2, …, 10 and S be the set of pairs (r, k), r, k ∈ N (the set of...
- Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin, then its third vertex lies in which...
- The tangent to the curve, y = xe^ x^2 passing through the point (1, e) also passes through the point:
- The value of _ - /2 ^ /2 dx [x] + [ x] + 4 , where [t] denotes the greatest integer less than or equal to t, is:
- Let S = (x, y) R ^2 : y^2 1 + r - x^2 1 - r = 1 ; r ≠ ±1. Then S represents: