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

`int_3^9 x^3/((12 - x)^3 + x^3)` dx = ______ 

Equation of the plane perpendicular to the line `x/1 = y/2 = z/3` and passing through the point (2, 3, 4) is ______

The p.m.f. of an r.v. X is ______ 

P(x) = `{{:(x^2/"k"";", x = - 4"," - 3"," - 2"," - 1),(0";", "otherwise"):}`

Then, E(X) = ______ 

A die is thrown nine times. If getting an odd number is considered as a success, then the probability of three successes is ______

The equation of the plane through the point (2, -1, -3) and parallel to the lines `(x - 1)/3 = (y + 2)/2 = z/(-4)` and `x/2 = (y - 1)/(-3) = (z - 2)/2` is ______

If A, B, C are the angles of ΔABC, then `tan  A/2 tan  B/2 + tan  B/2 tan  C/2 + tan  C/2 tan  A/2` = ______ 

If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______

The joint equation of the lines through the origin which forms two of the sides of the equilateral triangle having x = 2 as the third side is ______

In a trapezium, if the vector `overline(BC) = lambda   overline(AD)`, `overlinep = overline(AC) + overline(BD)` is collinear with `overline(AD)` and `overlinep = mu  overline(AD)`, then ______ 

The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is ______ 

The value of `int_1^3 dx/(x(1 + x^2))` is ______ 

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)` = ?