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

`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 ______.

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 = ______.

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.

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 maximum value of Z = 5x + 4y, Subject to y ≤ 2x, x ≤ 2y, x + y ≤ 3, x ≥ 0, y ≥ 0 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 ₹ ______

In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?

Let F(x) = e^x, G(x) = e^-x and H(x) = G[F(x)], where x is a real variable. Then `"dH"/"dx"`at x = 0 is ______.

If `bar"a", bar"b", bar"c"` are the three non-coplanar vectors and `bar"p", bar"q", bar"r"` are defined by the relations `bar"p" = (bar"b" xx bar"c")/([(bar"a", bar"b", bar"c")]), bar"q" = (bar"c" xx bar"a")/([(bar"a", bar"b", bar"c")]), bar"r" = (bar"a" xx bar"b")/([(bar"a", bar"b", bar"c")])` then `(bar"a" + bar"b")* bar"p" + (bar"b" + bar"c") * bar"q" + (bar"c" + bar"a") * bar"r"` = ______.