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

Let I be the purchase value of equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by the differential equation `(dV)/dt` = -k(T - t), where k > 0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is ______ 

A point is in a motion along a hyperbola `y = 10/x` so that its abscissa x increases uniformly at a rate of 1 unit per second. Then the rate of change of its ordinate, when the point passes through (5, 2) ______ 

If cartesian co-ordinates of a point are `(1, -sqrt3)`, then its polar co-ordinates are ______ 

`int "e"^x ((sqrt(1 - x^2) * sin^-1 x + 1)/sqrt(1 - x^2))`dx = ________.

The probability distribution of a random variable X is given below.

The variance of X is ______

If P(X ∩ Y) = `1/3` and P(X' ∩ Y') = `1/2`, P(X) = 2a and P(Y) = a, then the value of a is ______ 

The line x - 2y = 0 is perpenrucular to one of the lines given by ax² + 2hxy + by² = 0, when ______.

A card is chosen from a well-shuffled pack of cards. The probability of getting an ace of spade or a jack of diamond is ______.

The degree of the differential equation `1/2 ("d"^3"y")/"dx"^3 = {1 + (("d"^2"y")/"dx"^2)}^(5/3)` is ______.

If the sum of the slopes of the lines represented by x² + kxy + y² = 0 is four times their product, the value of k is ______.

Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.

In ΔABC, a = 7cm, b = 3cm and c = 8 cm, then angle A is ______ 

In any triangle ABC, the simplified form of `(cos2A)/a^2 - (cos2B)/b^2` is ______

The smallest angle of the ΔABC, when a = 7, b = `4sqrt(3)` and c = `sqrt(13)` is ______.

Area enclosed between the curve y²(4 - x) = x³ and line x = 4 above X-axis is ______.

If polar co-ordinates of a point are `(1/2, pi/2)`, then its cartesian co-ordinates are ______.

The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.

If in Δ ABC, 3a = b + c, then `cot ("B"/2) cot ("C"/2)` = ______.

Area under the curve `y=sqrt(4x+1)` between x = 0 and x = 2 is ______.

The differential equation of the family of curves y = e^x (A cos x + B sin x). Where A and B are arbitary constants is ______.