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

`int 1/(x^2 + 1)^2 dx` = ______.

If `int dx/sqrt(16 - 9x^2)` = A sin^–1 (Bx) + C then A + B = ______.

If planes `vecr.(phati - hatj + 2hatk) + 3` = 0 and `vecr.(2hati - phatj - hatk) - 5` = 0 include angle `π/3` then the value of p is ______.

If `int 1/((x^2 + 4)(x^2 + 9))dx = A tan^-1  x/2 + B tan^-1(x/3) + C`, then A – B = ______.

If `intsqrt((x - 5)/(x - 7))dx = Asqrt(x^2 - 12x + 35) + log|x| - 6 + sqrt(x^2 - 12x + 35) + C|`, then A = ______.

lf Rolle's theorem for f(x) = e^x (sin x – cos x) is verified on `[π/4, (5π)/4]`, then the value of c is ______.

The internal angles of a convex polygon are in A.P. The smallest angle is 120° and the common difference is 5°. The number to sides of the polygon is ______.

The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is ______.

The three straight lines ax + by = c, bx + cy = a and cx + ay = b are collinear, if ______.

If the line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then the equation of the line in new position is ______.

Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find 

1. P (A and B)
2. P(A and not B)
3. P(A or B)
4. P(neither A nor B)

The inverse of the function y = `(16^x - 16^-x)/(16^x + 16^-x)` is

If α = ^mC₂, then ^αC₂ is equal to.

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 ______.