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

If `int_0^"k" "dx"/(2 + 32x^2) = pi/32,` then the value of k is ______.

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 3y + 5 = 0.

`int_0^pi sin^2x.cos^2x  dx` = ______ 

At any point on a curve, the slope of the tangent is equal to the sum of abscissa and the product of ordinate and abscissa of that point. If the curve passes through (0, 1), then the equation of the curve is ______.

The value of `int "e"^(5x) (1/x - 1/(5x^2))  "d"x` is ______.

`int_(-1)^1 log ((2 - x)/(2 + x)) "dx" = ?`

`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.

`int_0^1 log(1/x - 1) "dx"` = ______.

If the plane passing through the points (1, 2, 3), (2, 3, 1) and (3, 1, 2) is ax + by + cz = d then a + 2b + 3c = ______.

`int_(pi/4)^(pi/2) sqrt(1-sin 2x)  dx =` ______.

`int_0^{pi/2} (cos2x)/(cosx + sinx)dx` = ______

`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.

The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is ______.

`int_-1^1x^2/(1+x^2)  dx=` ______.

Let the line `(x - 2)/3 = (y - 1)/(-5) = (z + 2)/2` lie in the plane x + 3y - αz + β = 0. Then, (α, β) equals ______ 

The minimum value of z = 2x + 9y subject to constraints x + y ≥ 1, 2x + 3y ≤ 6, x ≥ 0, y ≥ 0 is ______.

For the function z = 19x + 9y to be maximum under the constraints 2x + 3y ≤ 134, x + 5y ≤ 200, x ≥ 0, y ≥ 0; the values of x and y are ______.

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 equation of line passing through the midpoint of the line joining the points (-1, 3, -2) and (-5, 3, -6) and equally inclined to the axes is ______.

Two dice are thrown. Find the probability that the sum of numbers appearing is more than 11, is ______.