Solve the following for x; $\frac{1}{2a+b+2x} =\frac{1}{2a} +\frac{1}{b} +\frac{1}{2x}$.

Sum of the areas of two squares is 400 cm$^{2}$. If the difference of their perimeter is 16 cm, Find the sides of the two squares.

In figure below, $DE\ ||\ BC$.

If $DE\ =\ 4\ m$, $BC\ =\ 6\ cm$ and $Area\ (ΔADE)\ =\ 16\ cm^2$, find the $Area\ of\ ΔABC$.

In fig, l and m are two parallel tangents to a circle with center O, touching the circle at A and B respectively. Another tangent at C intersects the line l at D and m at E. prove that$\angle DOE=90^{o}$

A bucket is open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs. 10 per $100\ cm^{2}$. [use $\pi =3.14$].

A group consists of 12 persons, of which 3 are extremely patients, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is $( 1)$.extremely patient, $( 2)$.extremely kind or honest. which of the above value you prefer more?

Water is flowing through a cylinderical pipe, of internal diameter 2 cm, into a cylinderical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour.

Show that the points$( -2,\ 3) ,\ ( 8,\ 3)$ and $( 6,\ 7)$ are the vertices of a right triangle.

$ABC$ is a triangle in which $∠\ A\ =\ 90^o$, $AN\ ⊥\ BC$, $BC\ =\ 12\ cm$ and $AC\ =\ 5\ cm$. Find the ratio of the areas of $ΔANC$ and $ΔABC$.

Construct a tangent of a circle of radius 4cm from a point on the concentric circle of radius 6 cm.

We are really eager to clarify your doubts