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

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 ______.

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 ₹ ______

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"` = ______.

The p.m.f. of a r.v. X is
P(x) = `{:(= 1/13","  "for"  x = 1","  2","  ......","  14","  13),(= 0","  "otherwise."):}`
Then, E(X) is equal to ______.

The minimum value of z = 2x + 9y subject to constraints x + y ≥ 1, 2x + 3y ≤ 6, x ≥ 0, y ≥ 0 is ______.

For the function z = 19x + 9y to be maximum under the constraints 2x + 3y ≤ 134, x + 5y ≤ 200, x ≥ 0, y ≥ 0; the values of x and y are ______.

A pair of dice is thrown and X denotes the absolute difference of the numbers on uppermost faces. Then the expected value of X is ______

`int "e"^x ((cos x - sin x)/(sin^2x)) "d"x` = ______.

The feasible region of an LPP is shown in the figure. If z = 3x + 9y, then the minimum value of z occurs at ______.

If f(x) = `sin^2x + sin^2(x + pi/3) + cosx cos(x + pi/3) and g(5/4) = 1`, then (gof)(x) is equal to: ______ 

The region XOY - plane which is represented by the inequalities -5 ≤ x ≤ 5, -5 ≤ y ≤ 5 is ______ 

The co-ordinates of a point on the line x = 4y + 5, z = 3y – 6 at a distance `3sqrt(26)` from the point (5, 0, –6) are ______.

The p.m.f. of a r.v. X is 

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is ______.

If P₁ and P₂ are the lengths of the perpendiculars from the points (2, 3, 4) and (1, 1, 4) respectively from the plane 3x – 6y + 2z + 11 = 0, then P₁ and P₂ are the roots of the equation ______.

If f(x) =bx - 7 and f(-1) = 4, then b = ______.