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

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 = ?

P(x) = `{(1/"k" ((5),(x))"," (x=0,1,2,3,4,5); k > 0),(0 "," "otherwise"):},`

is p.m.f. of a r.v. X. Then `1/"k"` is equal to

The differential equation having y = (cos^-1 x)² + P (sin^-1 x) + Q as its general solution, where P and Q are arbitrary constants, is 

The maximum value of P = 7x + 6y subject to constraints x + 2y ≤ 24, 2x + y ≤ 30 and x ≥ 0, y ≥ 0 is ______.

The mean and variance of a binomial distribution are 2 and 1 respectively, then the probability of getting exactly three successes in this distribution is ______.

The family of curves y = `e^("a" sin x)`, where a is an arbitrary constant, is represented by the differential equation.

If z₁ and z₂ are z-coordinates of the points of trisection of the segment joining the points A (2, 1, 4), B (–1, 3, 6) then z₁ + z₂ = ______.

`(cos 25^circ + sin 25^circ)/(cos 25^circ - sin 25^circ)` = ?

(q v r) v (~ p v ~ q) is a ______.

The value of `tan^-1 (1/3) + tan^-1 (1/5) + tan^-1 (1/7) + tan^-1 (1/8)`is ______.