Find the value of ${{\alpha }^{2}}+{{\beta }^{2}}$ if $\alpha +\beta =2$and the distance between the points $(1,\alpha \text{ )and (}\beta ,1)$is 3 units

In the diagram above, PQ = 4cm and TS = 6cm, if the area of parallelogram PQTU is 32 cm², Find the area of trapezium PQRU

PQRSTV is a regular of side 7cm inscribed in a circle. Find the circumference of the circle PQRSTV  [$\pi =\tfrac{22}{7}$] 

Find the value of x in the figure above

The shadow of a pole $5\sqrt{3}m$high is 5m. Find the angle of elevation of the sun

If $y=3\cos (\tfrac{x}{3})$find $\frac{dy}{dx}$when $x=\tfrac{3\pi }{2}$

What is the rate of change of the volume V of a hemisphere with respect to its radius when r =2

Some white balls were put in a basket containing twelve red balls and sixteen black balls. If the probability of picking a white ball from the basket is $\tfrac{3}{7}$, how many white balls were introduced.

Find the mean deviation of 1, 2, 3 and 4

The pie chart above the distribution of the crops harvested from a farmland in al year. If 3000 tonnes of millet is harvested, what amount of beans is harvested?

The mean age of a group of students is 15 years. When the age of a teacher is 45years old is added to the ages of the students, the mean of their ages becomes 18 years. Find the number of students in the group.

A committee of six is to be formed by a state governor from nine commissioner and three members of state house of assembly. In how many ways can the committee be chosen so as to include one member of the house of assembly?

I.    Rectangular bars of equal width
II.    The height of each rectangular bar is proportional to the frequency of the corresponding class interval
III.    Rectangular bar have common sides with no gaps in between
A histogram is described completely by

What are the integral values of x which satisfy the inequality $-1<3-2x\le 5$

Find the value of x where the curve $y={{x}^{3}}+2{{x}^{2}}-5x-6$cross the x – axis

The shaded area in the diagram above is represented by

Find the remainder when $3{{x}^{3}}+5{{x}^{2}}-11x+4$is divided by x + 3

if $P=\left( \begin{matrix}   1 & 0 & -1  \\   3 & 4 & 5  \\   -1 & 0 & 1  \\\end{matrix} \right)$, then $\left| P \right|$ is

Find the sum to infinity $\tfrac{1}{2},\tfrac{1}{6},\tfrac{1}{18}---$