A student sitting on a tower 68 metres high observes his principal's car at the angle of depression of 20o. How far is the car from the bottom of the tower ...

Find the values of x and y respectively if \[ \begin{pmatrix} 1 & 0\\ -1 & -1\\ 2 & 2 \end{pmatrix} + \begin{pmatrix} x & 1\\ -1 & 0\\ y & -2 \end{pmatrix} =...

A binary operation on the set of real numbers excluding -1 is such that sor all \(m, n \in R\), \(m \Delta n = m + n + mn\). Find the identity element of the...

\[ \begin{pmatrix} -2 & 1 \\ 2 & 3 \end{pmatrix} + \begin{pmatrix} p & q \\ r & s \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}. \] What is th...

Find the angle subtended at the centre of a circle by a chord which is equal in length to the radius of the circle

If p varies inverse as the square of q and p = 8 when q =4, find q when p = 32

If \( \log X^{\frac{1}{2}} \) 64 = 3, find the value of x.

if X = {n2 + 1 : n = 0, 2, 3} and y = {n + 1 : n = 2, 3, 4, 5}, find x ∩ y

Evaluate \( \frac{\frac{3}{8} \div \frac{1}{2} - \frac{1}{3}}{\frac{1}{8} \times \frac{2}{3} + \frac{1}{3}} \)