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

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

If the slope of one of the lines given by ax² + 2hxy + by² = 0 is two times the other, then ______ 

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` = ______ 

If (a + 3b)(3a + b) = 4h², then the angle between the lines represented by ax² + 2hxy + by² = 0 is ______ 

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 ______.

The maximum value of P = 3x + 4y subject to the constraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is ______ 

The dual of '(~ q ∧ t) ∨ (~ p ∧ c)' where t is a tautology and c is a contradiction, is ______.

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

If the equation `lambdax^2 + 2y^2 - 5xy + 5x - 7y + 3 = 0` represents two straight lines, then the value of λ will be ______.