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

Maximum value of 4x + 13y subject to constraints x ≥ 0, y ≥ 0, x + y ≤ 5 and 3x + y ≤ 9 is ______. 

For f(x) = [x] , where [x] is the greatest integer function, which of the following is true, for every x ∈ R.

The negation of the statement 'He is poor but happy' is ______.

If a die is thrown at random, then the expectation of the number on it is ______.

The negation of the statement pattern ~ p v(q → ~ r) is ______.

If `a + pi/2 < 2tan^-1x + 3cot^-1x < b`, then a and b are respectively.

It is observed that 25% of the cases related to child labour reported to the police station are solved. If 6 new cases are reported, then the probability that atleast 5 of them will be solved is ______.

`int (cos x + x sin x)/(x^2 + x cos x)`dx = ______.

The co-ordinates of the foot of perpendicular drawn from origin to the plane 2x - y + 5z - 3 = 0 are ______.

The minimum value of z = 10x + 25y subject to 0 ≤ x ≤ 3, 0 ≤ y ≤ 3, x + y ≥ 5 is ______.

A group of 5 men and 4 women are arranged at random, one after the other. The probability that women and men occupy alternate seats is ______

If X is a random variable with probability distribution as given below:

Then, the variance of X is ______ 

Negation of the statement 'A is rich but silly' is ______

`int_0^4 x[x]  dx`, where [.] denotes the greatest integer function, equals ______

The maximum value of z = 6x + 8y subject to x - y ≥ 0, x + 3y ≤ 12, x ≥ 0, y ≥ 0 is ______.

If `int (cos x - sin x)/(8 - sin 2x) "dx" = 1/"p" log [(3 + sin x + cos x)/(3 - sin x - cos x)] + "c"` then p = ______.

The number of ways in which 51 books can be distributed among three students, each receiving 17 books, is ______

For L.P.P. maximize z = 4x₁ + 2x₂ subject to 3x₁ + 2x₂ ≥ 9, x₁ - x₂ ≤ 3, x₁ ≥ 0, x₂ ≥ 0 has ______.

If ∫ tan (x - α) tan (x + α) · tan 2x dx
= p log |sec 2x| + q log |log (x - α)| + r log |sec (x - α)| + c then p + q + r = ______.

Area of the region bounded by y = cos x, x = 0, x = π and X-axis is ______ sq.units.