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

If y = `tan^-1  (sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))`, then `dy/dx` is equal to ______.

The value of `sqrt(2) int (sinx  dx)/(sin(x - π/4))` is ______.

If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.

The solution of the differential equation `(1 + y^2) + (x - e^(tan^-1 y)) dy/dx` = 0 is ______.

If `|(6i, -3i, 1),(4, 3i, -1),(20, 3, i)|` = x + iy, then ______.

Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals to ______.

The position vectors of vertices of ΔABC are `4hati - 2hatj; hati + 4hatj - 3hatk` and `-hati + 5hatj + hatk` respectively, then ∠ABC = ______.

`int x/sqrt(1 - 2x^4) dx` = ______.

(where c is a constant of integration)

The particular solution of the differential equation (2x – 2y + 3) dx – (x – y + 1) dy = when x = 0, y = 1 is ______.

If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.

The distance between the lines `x/2 = y/(-1) = z/2` and `(x - 1)/2 = (y - 1)/(-1) = (z - 1)/2` is ______.

In a binomial distribution, n = 4 and 2P(X = 3) = 3P(X = 2), then q = ______.

`int dx/(2 + cos x)` = ______.

(where C is a constant of integration)

If cos^–1 x > sin^–1 x, then ______.

Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.

The solution of the differential equation e^–x (y + 1) dy + (cos² x – sin 2x)ydx = 0 subjected to the condition that y = 1, when x = 0 is ______.

If a = `3hati - 2hatj + hatk` and b = `2hati - 4hatj - 3hatk`, then | a – 2b | will be ______.

`int (logx)^2/x dx` = ______.

`int (cos x + x sin x)/(x(x + cos x))`dx = ?

`int_0^(pi/4) (sec^2 x)/((1 + tan x)(2 + tan x))`dx = ?