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

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 ______ 

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

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

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

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 ______.

If z₁ = 2 – 4i and z₂ = 1 + 2i, then `bar"z"_1 + bar"z"_2` = ______.

Let f(x) be a non-negative continuous function such that the area bounded by the curve y = f(x), X-axis and the ordinates x = `pi/4` and x = `beta > pi/4` is `(beta sin beta + pi/4 cos beta + sqrt(2)beta)`. Then `"f"(pi/2)` is ______.

The general solution of the differential equation `y  "d"x - (1 + x^2) cot^-1 x  "d"y` = 0 is ______.

The solution of the differential equation `("d"y)/("d"x) + 2y tan x = 2x cos^2x` is ______.

If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.

Circle x² + y² – 4x = 0 touches ______.

The solution of the equation `1 + ("d"x)/("d"y) = (2y)/x` is ______.

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