## Question 30

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

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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