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

The joint equation of pair of lines having slopes `1+sqrt2` and `1-sqrt2` and passing through the origin is ______.

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ______ 

The feasible region of an LPP is shown in the figure. If z = 3x + 9y, then the minimum value of z occurs at ______.

If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.

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

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

The region XOY - plane which is represented by the inequalities -5 ≤ x ≤ 5, -5 ≤ y ≤ 5 is ______ 

How many words can be formed with the letters of the word MANAGEMENT by rearranging them?

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 ______

For the LPP, maximize z = x + 4y subject to the constraints x + 2y ≤ 2, x + 2y ≥ 8, x, y ≥ 0 ______.

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 maximum value of z = 3x + 10y subjected to the conditions 5x + 2y ≤ 10, 3x + 5y ≤ 15, x, y ≥ 0 is ______.

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 = ______ 

The joint equation of pair of lines having slopes 2 and 5 and passing through the origin is ______.

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?