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

If α = ^mC₂, then ^αC₂ is equal to.

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

If a die is thrown at random, then the expectation of the number on it 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 angle between the pair of straight lines 2x² - 6xy + y² = 0 is tan^-1 (p), where p = ______

The angle between lines `(x - 2)/2 = (y - 3)/(- 2) = (z - 5)/1` and `(x - 2)/1 = (y - 3)/2 = (z - 5)/2` is ______.

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

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

Then, the variance of X is ______ 

If 4ab = 3h², then the ratio of slopes of the lines represented by the equation ax² +2hxy + by² = 0 will be ______

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

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 = ______.

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 = ______.

The length of the latusrectum of an ellipse is `18/5` and eccentncity is `4/5`, then equation of the ellipse is ______.

If `int 1/(1 - cot x)`dx = Ax + B log |sin x - cos x|  + c then A + B = ______.

The acute angle between lines x - 3 = 0 and x + y = 19 is ______.

The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______ 

If f = {(4, 1), (5, 2), (6, 3)} and g = { (3, 9), (1, 7), (2, 8)}, then gof is ______ 

A boy tosses a fair coin 3 times. If he gets ₹ 2x for x heads then his expected gain equals ₹ ______