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

The length of the latusrectum of an ellipse is `18/5` and eccentncity is `4/5`, then equation of the ellipse is ______.

`int log x * [log ("e"x)]^-2` dx = ?

If y = log `[(x + sqrt(x^2 + 25))/(sqrt(x^2 + 25) - x)]` then `"dy"/"dx"` = ______.

`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.

If `hati - 2hatj + hatk`, `2hati + phatj + 3hatk` and `5hati - 9hatj + 4hatk` are coplanar, then the value of p is equal to ______

Equation of plane parallel to ZX-plane and passing through the point (0, 5, 0) is ______

`sqrt3 sin15^circ + cos15^circ` = ______

`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________

`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________

In a multiple-choice question, there are three options out of which only one is correct. A person is guessing the answer at random. If there are 7 such questions, then the probability that he will get exactly 4 correct answers is ______ 

If line `(2x - 4)/lambda = ("y" - 1)/2 = ("z" - 3)/1` and `(x - 1)/1 = (3"y" - 1)/lambda = ("z" - 2)/1` are perpendicular to each other then λ = ______.

`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` = ______