MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions for Mathematics

`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.

The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is ______.

`int_-1^1x^2/(1+x^2)  dx=` ______.

Let the line `(x - 2)/3 = (y - 1)/(-5) = (z + 2)/2` lie in the plane x + 3y - αz + β = 0. Then, (α, β) equals ______ 

The minimum value of z = 2x + 9y subject to constraints x + y ≥ 1, 2x + 3y ≤ 6, x ≥ 0, y ≥ 0 is ______.

For the function z = 19x + 9y to be maximum under the constraints 2x + 3y ≤ 134, x + 5y ≤ 200, x ≥ 0, y ≥ 0; the values of x and y are ______.

Let f: (–1, 1) → R be a differentiable function with f(0) = –1 and f'(0) = 1. If g(x) = [f(2f(x) + 2)]², then g'(0) = ______.

The equation of line passing through the midpoint of the line joining the points (-1, 3, -2) and (-5, 3, -6) and equally inclined to the axes is ______.

Two dice are thrown. Find the probability that the sum of numbers appearing is more than 11, is ______.

The joint equation of pair of lines having slopes `1+sqrt2` and `1-sqrt2` and passing through the origin is ______.

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ______ 

The feasible region of an LPP is shown in the figure. If z = 3x + 9y, then the minimum value of z occurs at ______.

If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.

`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.

`int_0^pi x*sin x*cos^4x  "d"x` = ______.

The region XOY - plane which is represented by the inequalities -5 ≤ x ≤ 5, -5 ≤ y ≤ 5 is ______ 

How many words can be formed with the letters of the word MANAGEMENT by rearranging them?

If the mean and variance of a binomial variate X are 14 and 10 respectively, then the probability that X takes a value greater than or equal to 1 is ______

For the LPP, maximize z = x + 4y subject to the constraints x + 2y ≤ 2, x + 2y ≥ 8, x, y ≥ 0 ______.

The value of `int_2^7 (sqrtx)/(sqrt(9 - x) + sqrtx)dx` is ______