A club has a fund of $₹195$. Each member of the club gives the amount of money which is same as the number of members and the total amount of money is divided equally among the members and each gets $₹28$. Find the number of members of the club.

Simplify: $\frac{3\sqrt{7}}{\sqrt{2}+\sqrt{5}}-\frac{5\sqrt{5}}{\sqrt{2}+\sqrt{7}}+\frac{\sqrt{8}}{\sqrt{5}+\sqrt{7}}$

$15$ farmers can plough $18$ bighas of land in $5$ days. By the principle of variation find in how many days $10$ farmers can plough $12$ bighas of land.

Prove that in a circle on the same arc, the angle at the centre is twice the angle on the circumference.

Prove that in a right-angled triangle, the area of the square on the hypotenuse is equal to the sum of the areas of two squares on other two sides.

ln $△ABC$, the bisectors of $\angle A, \angle B$ and $\angle C$ intersect the circumcircle of the triangle in $P, Q$ and $R$. Prove that the angles of the triangles $PQR$ are $90°-\frac{1}{2}\angle A, 90°-\frac{1}{2}\angle B$ and $90°-\frac{1}{2}\angle C$.

In a circle $APB$, the foot of the perpendicular from $P$ (on the circle) upon the diameter $AB$ is $N$. Prove that, $P{B}^2=AB.NB$.

Draw a triangle of sides $5 \mathrm{cm}, 6 \mathrm{cm}$ and $7 \mathrm{cm}$ and draw the incircle of the triangle.

Find the value of $x$: 

$x{\tan }^2 60°-{\sin }^2 60°-\frac{1}{2}{\cot }^2 30°+\frac{1}{8}{\sec }^2 45°=1$