If the binary operation \( \ast \) is defined by \( m \ast n = mn + m + n \) for any real number m and n, find the identity of the elements under this opera...

In how many ways can 2 students be selected from a group of 5 students in a debating competition?

determine the maximum value of \(y=3x^2+5x-3\)

What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2?

Solve the following equation: \( \frac{2}{(2r-1)} - \frac{5}{3} = \frac{1}{(r+2)} \)

A trapezium has two parallel sides of lengths 5cm and 9cm. If the area is 91cm\(^{2}\), find the distance between the parallel sides

find the value of p if the line which passes through (-1, -p) and (-2,2) is parallel to the line 2y+8x-17=0?

Find the derivative of the function \(y = 2x^2(2x - 1)\) at the point \(x = -1\)?

The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is \(351\text{cm}^3\), then the volume of the other blo...