Mathematics questions
18011 published questions with worked solutions.
- The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12...
- The plane passing through the line L : x - y + 3(1 - )z = 1, x + 2y − z = 2 and perpendicular to the plane 3x + 2y + z = 6 is 3x...
- Suppose y = y(x) be the solution curve to the differential equation dy/dx − y = 2 - e^ -x such that _ x y(x) is finite. If a and...
- Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the...
- The number of matrices A = bmatrix a & b c & d bmatrix , where a, b, c, d −1, 0, 1, 2, 3, _____, 10 , such that A = A^ -1 , is...
- Let O be the origin and A be the point z_ 1 = 1 + 2i. If B is the point z_ 2 , Re(z_ 2 ) < 0, such that OAB is a right angled...
- If the system of linear equations 8x + y + 4z = −2 x + y + z = 0 x - 3y = has infinitely many solutions, then the distance of the...
- Let A be a 2 2 matrix with det(A) = −1 and det((A + I)(Adj(A) + I)) = 4. Then the sum of the diagonal elements of A can be
- The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = y^ a is 364/3, is equal to
- Consider two G.P.s 2, 2^ 2 , 2^ 3 , .... and 4, 4^ 2 , 4^ 3 , ... of 60 and n terms respectively. If the geometric mean of all...
- If the function f(x) = [log_e(1 − x + x^ 2 ) + log_e(1 + x + x^ 2 )]/( x − cos x), x (- /2, /2) − 0 , and f(0) = k, is continuous...
- If f(x) = x + a for x 0 and |x − 4| for x > 0, and g(x) = x + 1 for x < 0 and (x - 4)^ 2 + b for x 0, are continuous on R, then...
- Let f(x) = x^ 3 - x^ 2 + 10x - 7 for x 1 and f(x) = −2x + _ 2 (b^ 2 - 4) for x > 1. Then the set of all values of b, for which...
- If a = _ n _ k=1 ^ n 2n/(n^ 2 + k^ 2 ) and f(x) = (1 − cos x)/(1 + cos x)), x (0, 1), then
- If dy/dx + 2y tan x = sin x, 0 < x < /2 and y( /3) = 0, then the maximum value of y(x) is :
- Let the tangent drawn to the parabola y^ 2 = 24x at the point ( , ) is perpendicular to the line 2x + 2y = 5. Then the normal to...
- The length of the perpendicular from the point (1, −2, 5) on the line passing through (1, 2, 4) and parallel to the line x + y −...
- Let a = i + j - k and b = 2 i + j - k , > 0. If the projection of a b on the vector - i + 2 j - 2 k is 30, then is equal to
- The mean and variance of a binomial distribution are and /3 respectively. If P(X = 1) = 4/243, then P(X = 4 or 5) is equal to :
- Let E_ 1 , E_ 2 , E_ 3 be three mutually exclusive events such that P(E_ 1 ) = (2 + 3p)/6, P(E_ 2 ) = (2 − p)/8 and P(E_ 3 ) = (1...