Mathematics questions
18011 published questions with worked solutions.
- An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that...
- If the area of the region (x, y) : 0 ≤ y ≤ min 2x, 6x – x² is A, then 12 A is equal to ____
- Let f(x) = _0^xg(t) _e ( 1-t 1+t )dt, where g is a continuous odd function. If _ - /2 ^ /2 (f(x) + x^2 x 1 + e^x )dx = ( )^2 - ,...
- Let the complex number α and 1 lie on the circles |z – z₀|² = 4 and |z – z₀|² = 16 respectively, where z₀ = 1 + i. Then, the...
- If the sum of squares of all real values of α, for which the lines 2x – y + 3 = 0, 6x + 3y + 1 = 0 and αx + 2y – 2 = 0 do not...
- The coefficient of x²⁰¹² in the expansion of (1 – x)²⁰⁰⁸(1 + x + x²)²⁰⁰⁷ is equal to ____.
- The lines x-2 2 = y -2 = z-7 16 and x+3 4 = y+2 3 = z+2 1 intersect at the point P. If the distance of P from the line x+1 2 =...
- The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an...
- Let A be a 2 × 2 real matrix and I be the identity matrix of order 2. If the roots of the equation |A – xI| = 0 be –1 and 3, then...
- Consider a circle (x – α)² + (y – β)² = 50, where α, β > 0. If the circle touches the line y + x = 0 at the point P, whose...
- If the solution curve, of the differential equation dy dx = x + y - 2 x - y passing through the point (2, 1) is ^ -1 ( y-1 x-1 )...
- The function f : N – 1 → N; defined by f(n) = the highest prime factor of n, is:
- Let x = x(t) and y = y(t) be solutions of the differential equations dx dt + ax = 0 and dy dt + by = 0 respectively, a, b ∈ R....
- Let S = 1, 2, 3, …, 10 . Suppose M is the set of all the subsets of S, then the relation R = (A, B) : A ∩ B ≠ φ ; A, B ∈ M is:
- If a = _ x 0 1+ 1+x^4 - 2 x^4 and b = _ x 0 ^2x 2- 1+ x , then the value of ab³ is :
- The length of the chord of the ellipse x^2 25 + y^2 16 = 1, whose mid point is (1, 25 ), is equal to :
- If S = z ∈ C : |z – i| = |z + i| = |z – 1| , then n(S) is:
- Consider the matrix f(x) = bmatrix x & - x & 0 x & x & 0 0 & 0 & 1 bmatrix Given below are two statements : Statement I : f(–x)...
- ^ n-1 C_r = (k^2 - 8) , ^nC_ r+1 if and only if :
- The distance of the point (7, –2, 11) from the line x-6 1 = y-4 0 = z-8 3 along the line x-5 2 = y-1 -3 = z-5 6 is :