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

`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`

If x² + (2h - 1)xy + y² - 24x - 8y + k = 0 is the equation of the circle and 12 is the radius of the circle, then ______.

`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.

If the value of `lim_(x -> 1) (1 - (1 - x))^"m"/x` is 99, then n = ______.

The equation of the circle with centre (4, 5) which passes through (7, 3) is ______.

The equation of circle whose diameter is the line joining the points (–5, 3) and (13, –3) is ______.

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

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

`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 ______ 

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 ______ 

If P(α, β) be a point on the line 3x + y = 0 such that the point P and the point Q(1, 1) lie on either side of the line 3x = 4y + 8, then _______.

`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))` = ______.

The solution of the differential equation x(e^y - 1)dy + (x³ - 1)e^y dx = 0 is ______.