A predator moves in a circle of radius $\sqrt{2}$centre (0,0), while a prey moves along  y = x. If $0\le x\le 2$, at which point will they meet

P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight ST is on the locus of P and $\angle VUS={{50}^{o}}$ find $\angle UST$

If P and Q are fixed and X is a point which moves so that XP = XQ. The locus of X is

A frustum of pyramid with square base has its upper and lower section as squares of sizes 2m and 5m respectively and the distance between them 6m. Find the height of the pyramid from which the frustum was obtained.

In the diagram above , EFGH is a circle, centre O, FH is a diameter and GE is a chord, which meets FH at right angle at point N. If NH is 8cm and EG= 24cm. Calculate FH

An equilateral triangle of sides $\sqrt{3}$is inscribed in a circle. Find the radius of the circle.

In the diagram above, $\angle RPS={{50}^{o}}$, $\angle RPQ={{30}^{o}}$and PQ = QR . Find the value of $\angle PRS$

In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon.

Find the value of t for which the determinant of   the matrix$\left( \begin{matrix}   t-4 & 0 & 0  \\   -1 & t+1 & 1  \\   3 & 4 & t-2  \\\end{matrix} \right)$is zero

A matrix $P=\left( \begin{matrix}   a & b  \\   c & d  \\\end{matrix} \right)$is such that P^T = -P. P^T is the transpose of P. If b = 1, then P is