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

`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 ______.

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

The acute angle between the curve x = 2y² and y = 2x² at `(1/2, 1/2)` is ______.

If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.

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 ______.

The value of `sin^-1[cos(pi/3)] + sin^-1[tan((5pi)/4)]` 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 ______.