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

`int (cos x)/(1 - sin x) "dx" =` ______.

If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.

The value of cot (- 1110°) is equal to ______.

General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)

`int[ tan (log x) + sec^2 (log x)] dx= ` ______

If `overline (a) =10hat("i") + lambda hat("j") + 2hat("k")` is perpendicular to `overline (b)= hat ("i")+hat("j")-hat("k")`, then λ is equal to ______.

If the line `x/(3) = y/(4)` = z is perpendicular to the line `(x - 1)/k = (y + 2)/(3) = (z - 3)/(k - 1)`, then the value of k is ______.

In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.

`cos(2sin^-1  3/4+cos^-1  3/4)=` ______.

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))` = ______.