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

Let `overlinea = 2hati + hatj + hatk, overlineb = hati + 2hatj - hatk` and a unit vector `overlinec` be coplanar. If `overlinec` is perpendicular to `overlinea`, then `overlinec` = ______ 

`int_-2^1 dx/(x^2 + 4x + 13)` = ______

`int_{pi/6}^{pi/3} sin^2x dx` = ______ 

A plane which passes through the point (3, 2, 0) and the line `(x - 3)/1 = (y - 6)/5, (z - 4)/4` is ______ 

`(sin8A + sin2A)/(cos2A - cos8A)` is equal to ______ 

`int_0^{1/sqrt2} (sin^-1x)/(1 - x^2)^{3/2} dx` = ______ 

The distance of the point (1, 0, 2) from the point of intersection of the line `(x - 2)/3 = (y + 1)/4 = (z - 2)/12` and the plane x - y + z = 16, is ______ 

If X denotes the number of ones in five consecutive throws of a dice, then P(X = 4) is ______ 

`int_0^1 "dx"/(sqrt(1 + x) - sqrtx)` = ?

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` = ______