If x - 3 is directly proportional to the square of y and x = 5 when y =2, find x when y = 6.

Find the values of x and y respectively if ⎛⎜⎝10−1−122⎞⎟⎠ ( 1 0 − 1 − 1 2 2 ) + ⎛⎜⎝x1−10y−2⎞⎟⎠ ( x 1 − 1 0 y − 2 ) = ⎛⎜⎝−21−2−1−300⎞⎟⎠

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

(−2123) ( − 2 1 2 3 ) + (pqrs) ( p q r s ) = (1001) ( 1 0 0 1 ) . What is the value of r?

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 logX12 l o g X 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 38÷12−1318×23+13