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

`int_(pi/18)^((4pi)/9) (2 sqrt(sin x))/(sqrt (sin x) + sqrt(cos x))` dx = ?

The maximum value of Z = 5x + 4y, Subject to y ≤ 2x, x ≤ 2y, x + y ≤ 3, x ≥ 0, y ≥ 0 is ______.

XY-plane divides the line joining the points A(2, 3, -5) and B(1, -2, -3) in the ratio ______ 

f(x) =  `{:{(x^3/k;       0 ≤ x ≤ 2), (0;     "otherwise"):}` is a p.d.f. of X. The value of k is ______

The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______

`int_0^{pi/2} cos^2x  dx` = ______ 

The equation of the plane through (1, 2, -3) and (2, -2, 1) and parallel to the X-axis is ______ 

`(tanA + secA - 1)/(tanA - secA + 1)` = ______ 

`int_0^1 x tan^-1x  dx` = ______ 

`int_3^9 x^3/((12 - x)^3 + x^3)` dx = ______ 

Equation of the plane perpendicular to the line `x/1 = y/2 = z/3` and passing through the point (2, 3, 4) is ______

The p.m.f. of an r.v. X is ______ 

P(x) = `{{:(x^2/"k"";", x = - 4"," - 3"," - 2"," - 1),(0";", "otherwise"):}`

Then, E(X) = ______ 

A die is thrown nine times. If getting an odd number is considered as a success, then the probability of three successes is ______

The equation of the plane through the point (2, -1, -3) and parallel to the lines `(x - 1)/3 = (y + 2)/2 = z/(-4)` and `x/2 = (y - 1)/(-3) = (z - 2)/2` is ______

If A, B, C are the angles of ΔABC, then `tan  A/2 tan  B/2 + tan  B/2 tan  C/2 + tan  C/2 tan  A/2` = ______ 

If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______

The joint equation of the lines through the origin which forms two of the sides of the equilateral triangle having x = 2 as the third side is ______

In a trapezium, if the vector `overline(BC) = lambda   overline(AD)`, `overlinep = overline(AC) + overline(BD)` is collinear with `overline(AD)` and `overlinep = mu  overline(AD)`, then ______ 

The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is ______ 

The value of `int_1^3 dx/(x(1 + x^2))` is ______