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

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 = ______.

For the LPP, maximize z = x + 4y subject to the constraints x + 2y ≤ 2, x + 2y ≥ 8, x, y ≥ 0 ______.

The maximum value of z = 3x + 10y subjected to the conditions 5x + 2y ≤ 10, 3x + 5y ≤ 15, x, y ≥ 0 is ______.

If the origin and the points P(2, -7, 5), Q(2, 3, - 5) and R(x, y, z) are co-planar, then ______ 

`int "e"^x [2"cosec"  2x + log(tanx)] "d"x` = ______.

The constraints of an LPP are 7 ≤ x ≤ 12, 8 ≤ y ≤ 13. Determine the vertices of the feasible region formed by them.

The point which provides the solution to the linear programming problem: Max P = 2x + 3y subject to constraints: x ≥ 0, y ≥ 0, 2x + 2y ≤ 9, 2x + y ≤ 7, x + 2y ≤ 8, is ______ 

`int("I" - cosx)"cosec"^2x"d"x` = ______.