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

`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.

The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is ______.

`int_-1^1x^2/(1+x^2)  dx=` ______.

Let the line `(x - 2)/3 = (y - 1)/(-5) = (z + 2)/2` lie in the plane x + 3y - αz + β = 0. Then, (α, β) equals ______ 

Two dice are thrown. Find the probability that the sum of numbers appearing is more than 11, is ______.

Which of the following statement is contradiction?

Which of the following statement is a contingency?

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ______ 

If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.

`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.

Which of the following statements is a tautology?

`int_0^pi x*sin x*cos^4x  "d"x` = ______.

The proposition (∼p → p) ∨ (p → ∼p) is a ______ 

If the mean and variance of a binomial variate X are 14 and 10 respectively, then the probability that X takes a value greater than or equal to 1 is ______

The value of `int_2^7 (sqrtx)/(sqrt(9 - x) + sqrtx)dx` is ______ 

`int_0^pi x sin^2x dx` = ______ 

The elimination of the arbitrary constant m from the equation y = e^mx gives the differential equation ______.

The joint equation of pair of straight lines passing through the origin and having slopes `1 + sqrt2` and `1/(1 + sqrt2)` is ______ 

`(sec8A - 1)/(sec4A - 1)` = ______ 

`int_0^9 1/(1 + sqrtx)` dx = ______