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

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 = ?

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 ______

If sin y = x sin(a + y), then `dy/dx` = ______ 

The point of intersection of lines given by the equation 2x² + 4xy - 2y² + 4x + 8y + 1 = 0 is ______

`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 proposition ∼(p ∧ ∼q) → p is a ______ 

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 ______

If cos y = x cos(a + y) with cos a ≠ ± 1, then `dy/dx` is equal to ______ 

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` = ______