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

If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals ______.

The solution of the differential equation x(e^y - 1)dy + (x³ - 1)e^y dx = 0 is ______.

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set is ______ 

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

The solution of the differential equation `dy/dx - cos^2y = 0` is ______ 

`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.

Solution of the differential equation `dy/dx = ((tanx - y))/(cos^2x)` is ______ 

`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = ______.

The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______ 

`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.

The value of `sin^-1(cos  (53pi)/5)` is ______ 

`sin{tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))}` is equal to ______ 

The value of `cos(pi/4 + x) - cos(pi/4 - x)` is ______.

The area (in sq. units) enclosed between the curves y = x² and y = |x| is ______ 

`cos^-1  4/5 + tan^-1  3/5` = ______.

If x = cos t sin 2t and y = sin t cos 2t, then at t = `pi/4`, the value of `dy/dx` is equal to ______ 

The solution of the differential equation `dy/dx = x^3 + cos4x` is ______ 

`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.

If X follows a binomial distribution with parameters n = 10 and p. If 4P(X = 6) = P(X = 4), then p = ______ 

The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.