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

Eight white chairs and four black chairs are randomly placed in a row. The probability that no two black chairs are placed adjacently equals.

The lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendicular to each other, if ______

The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n = 2t² + 3 and w = t² - t + 2, then the rate of change of W with respect to t at t = 1 is ______ 

If f(x) = `(3x + 1)/(5x - 4)` and t = `(5 + 3x)/(x - 4)`, then f(t) is ______ 

The equation of line is `(x - 1)/2 = (y + 1)/(-2) = (z + 1)/1`. The co-ordinates of the point on the line at a distance of 3 units from the point (1, -1, -1) is ______ 

The value of θ in (π, 2π) satisfying the equation sin²θ - cos²θ = 1 is ______ 

The measure of the angle between lines (sin²θ - 1)x² - 2xy cos²θ + cos²θy² = 0 is ______ 

Let p and q be the statements:

p: 3x³ + 8y³ ≥ 15, q: 5x + 2y < 11 

Then, which of the following is true?

Solution of the LPP minimize z = 7x + 2y subject to x + y ≥ 60, x - 2y ≥ 0, x + 2y ≤ 120, x, y ≥ 0 is ______ 

The general solution of sin 2x = cos 2x is ______ 

The joint equation of the lines through the origin which forms two of the sides of the equilateral triangle having x = 2 as the third side is ______

The equation of the circle which passes through the points (5, 1) and (7, -3) and the centre lies on the straight line 4x + 3y + 1 = 0, is ______ 

Find the number of integers greater than 7,000 that can be formed using the digits 4, 6, 7, 8, and 9, without repetition: ______

The general solution of the equation tan θ tan 2θ = 1 is given by ______ 

Which of the following is true in a triangle ABC?

The shaded region is represented by the in equations ______ 

If sin θ + cos θ = 1, then the general value of θ is ______.

The maximum value of z = 7x + 6y.
Subject to the constraints x ≤ 45, y ≤ 55 and x ≥ 0, y ≥ 0 is ______.

The equation of line equally inclined to co-ordinate axes and passing through (–3, 2, –5) is ______.

The general solution of cot θ + tan θ = 2 is ______.