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

If x ∈ R – {0}, then `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2)))`

The value of cos (2cos^–1 x + sin^–1 x) at x = `1/5` is ______.

Which of the following is logically equivalent to `∼(∼p \implies q)`?

The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x-axis is ______.

`int sqrt(x^2 - a^2)/x dx` = ______.

`int 1/(sinx.cos^2x)dx` = ______.

The area of the region bounded by x² = 4y, y = 1, y = 4 and the y-axis lying in the first quadrant is square units.

If tan^–1 (2x) + tan^–1 (3x) = `π/4`, then x = ______.

If X∼B (n, p) with n = 10, p = 0.4 then E(X²) = ______.

The general solution of differential equation `dx/dy` = cos (x + y) is ______.

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

If slopes of lines represented by kx² + 5xy + y² = 0 differ by 1, then k = ______.

The area of the region bounded by the lines y = 2x + 1, y = 3x + 1 and x = 4 is ______.

The value of `cos^-1(cos(π/2)) + cos^-1(sin((2π)/2))` is ______.

The particular solution of the differential equation x dy + 2y dx = 0, when x = 2,y = 1 is ______.

Derivative of `tan^-1(x/sqrt(1 - x^2))` with respect sin^–1(3x – 4x³) is ______.

If 2 tan^–1 (cosx) = tan^–1 (2 cosec x), then sin x + cos x is equal to ______.

`(tan^-1 (sqrt(3)) - sec^-1(-2))/("cosec"^-1(-sqrt(2)) + cos^-1(-1/2))` is equal to ______.

The area of the region bounded by the curve y = 2x – x² and X-axis is ______.

If a = `veca = hati + hatj - 2hatk, vecb = 2hati - hatj + hatk` and `vecc = 3hati - hatk` and `vecc = mveca + nvecb`, then m + n is equal to ______.