Evaluate \( \displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos x\,dx \)

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