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

If the plane x - 3y + 5z = d passes through the point (1, 2, 4), then the lengths of intercepts cut by it on the axes of X, Y, Z are respectively ______ 

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 ______ 

Area of the ellipse `x^2/9 + y^2/4` = 1 is ______.

If x = cos t sin 2t and y = sin t cos 2t, then at t = `pi/4`, the value of `dy/dx` is equal to ______ 

`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.

The negation of the statement "If you don't work bard you will not become successful." is ______ 

The d.r.s of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle `pi/4` with plane x + y = 3, are ______.

The differential equation representing the family of parabolas having vertex at origin and axis along positive direction of X-axis is ______.

If 4x + 5y ≤ 20, x + y ≥ 3, x ≥ 0, y ≥ 0, maximum 2x + 3y is ______.

`int_0^(pi/2) 1/(1 + cos^3x) "d"x` = ______.

The area of the curve xy² =  4(2 – x) bounded by Y-axis is ______.

The equation of the plane passing through the points (1, –2, 1), (2, –1, –3) and (0, 1, 5) is ______.

The combined equation of the lines which pass through the origin and each of which makes an angle of 30° with the line 3x + 2y – 11 = 0 is ______.

If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to ______.

The equation of the plane passing through a point having position vector`-2hat"i" + 7hat"j" + 5hat"k"` and parallel to the vectors `4hat"i" - hat"j" + 3hat"k"` and `hat"i" + hat"j" + hat"k"` is ______.

The maximum of z = 5x + 2y, subject to the constraints x + y ≤ 7, x + 2y ≤ 10, x, y ≥ 0 is ______.

If m and n are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and X-axis as its axis, then mn - m + n = ______.

Negation of (∼p → q) is ______.

`int_0^1 "e"^(5logx) "d"x` = ______.