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

If 2sin²θ = 3cosθ, where 0 ≤ θ ≤ 2π, then θ = ______ 

`int(sin2x)/(5sin^2x+3cos^2x)  dx=` ______.

The solution of the differential equation (x + 1) sin y dy = [(x + 1 )e^x log(x + 1) + e^x]dx is ______.

The area of the region is bounded by the curve y = sinx, X-axis and the lines x = 0, x = `(2pi)/3` is ______ 

If `3sin^-1((2x)/(1 + x^2)) - 4cos^-1((1 - x^2)/(1 + x^2)) + 2tan^-1((2x)/(1 - x^2)) = pi/3`, then x is equal to ______ 

Let f: (–1, 1) → R be a differentiable function with f(0) = –1 and f'(0) = 1. If g(x) = [f(2f(x) + 2)]², then g'(0) = ______.

The area of the region lying above X-axis, and included between the circle x² + y² = 2ax and the parabola y² = ax, a > 0 is ______ 

`int sec^6 x tan x   "d"x` = ______.

Solution of `sinx dy/dx + y cosx = 1` is ______ 

If z₁ = 5 + 3i and z₂ = 2 - 4i, then z₁ + z₂ = ______.

`int ("d"x)/(x(x^4 + 1))` = ______.

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: ______