Evaluate $\frac{2.813\times {{10}^{-3}}\times 1.063}{5.637\times {{10}^{-2}}}$reducing each number to two significant figures and leaving your answer in two significant figures

If the population of a town was 240,000 in January 1998 and it increased by 2% each year, what will be the population of the town in January 2000

if $\frac{2\sqrt{3}-2}{\sqrt{3}+2\sqrt{2}}=m+n\sqrt{6}$. If the value of m and n respectively 

A man wishes to keep some money in a saving deposit at 25% compound interest, so that after 3 years he can buy a car for N150,000. How much does he need to deposit now?

In a youth club with 94 members, 60 like modern music and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?

If $\alpha \text{ and }\beta $are roots of the equation $3{{x}^{2}}+5x-2=0$. Find the value of $\tfrac{1}{\alpha }+\tfrac{1}{\beta }$.(A)  $-\tfrac{5}{2}$  (B)  $-\tfrac{3}{2}$  (C)  $\tfrac{1}{2}$  (D)$\tfrac{5}{2}$ 

The solution of the simultaneous inequality $2x-2\le y$ and $2y-x\le x$ represented by

The 3^rd term of an A.P is 4x – 2y and the 9^th is 10x – 8y. Find the common difference. 

Find the inverse of P under the binary operation defined by $p*q=p+q-pq$where p and q are real numbers and zero is the identity

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

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

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

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.

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 $\angle UST$

$3y=4x-1$and $ky=x+3$are equation of two straight lines. If the two lines are perpendicular to each other, find k 

A ship sails a distance of 50km in the direction S50^oE and then sails a distance of 50km N40^oE. Find the bearing of the ship from its original position.

The expression of $a{{x}^{2}}+bx+c$equals 5 at x =1. If its derivative is 2x + 1, what are the value of a, b,  respectively.

Find the value of $\int_{0}^{\pi }{\frac{{{\cos }^{2}}\theta -1}{{{\sin }^{2}}\theta }d\theta }$ 

A bowl is designed by resolving completely the area enclosed by y = x² – 1, y = 0, y = 3 and x ≥ 0 around the y –axis. What is the volume of this bowl?