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

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 ______.

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

Which one of the following statements is not a tautology?

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 = ______.

9x² + hxy + y² = 0 represents pair of parallel straight lines, if h is ______.

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

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