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

`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.

Which of the following statements is a tautology?

`int_0^pi x*sin x*cos^4x  "d"x` = ______.

The proposition (∼p → p) ∨ (p → ∼p) is a ______ 

If the mean and variance of a binomial variate X are 14 and 10 respectively, then the probability that X takes a value greater than or equal to 1 is ______

The value of `int_2^7 (sqrtx)/(sqrt(9 - x) + sqrtx)dx` is ______ 

`int_0^pi x sin^2x dx` = ______ 

The elimination of the arbitrary constant m from the equation y = e^mx gives the differential equation ______.

The joint equation of pair of straight lines passing through the origin and having slopes `1 + sqrt2` and `1/(1 + sqrt2)` is ______ 

`(sec8A - 1)/(sec4A - 1)` = ______ 

`int_0^9 1/(1 + sqrtx)` dx = ______ 

If the points `P(overlinea+2overlineb+overlinec)`, `Q(2overlinea+3overlineb), R(overlineb+ t overlinec)` are collinear, where `overlinea, overlineb, overlinec` are three non-coplanar vectors, the value of t is ______ 

Which of the following is true?

If the plane x - 3y + 5z = d passes through the point (1, 2, 4), then the lengths of intercepts cut by it on the axes of X, Y, Z are respectively ______ 

Area of the ellipse `x^2/9 + y^2/4` = 1 is ______.

Let L be the line joining the origin to the point of intersection of the lines represented by 2x² – 3xy – 2y² + 10x + 5y = 0. lf L is perpendicular to the line kx + y + 3 = 0, then k = ______.

`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.

How many numbers greater than 200 and divisible by 2 can be made from the digits 4, 5, 6, and 7 if no digit is repeated. 

The d.r.s of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle `pi/4` with plane x + y = 3, are ______.

The differential equation representing the family of parabolas having vertex at origin and axis along positive direction of X-axis is ______.