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

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)

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 ______.

`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 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)` = ?

The derivative of `sqrt(x^2 + 1)` is

Maximum value of 4x + 13y subject to constraints x ≥ 0, y ≥ 0, x + y ≤ 5 and 3x + y ≤ 9 is ______. 

The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.

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

The negation of the statement 'He is poor but happy' is ______.

`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?

tan A +2 tan 2A + 4 tan 4A + 8 cot 8A = ?

cos (36° - A) cos (36° + A) + cos(54° + A) cos (54° - A) = ?