The value of $1^2 + 3^2 + 5^2 + ....... + 25^2$ is

If $x_1, x_2, \dots, x_n$ and $\frac{1}{h_1}, \frac{1}{h_2}, \dots, \frac{1}{h_n}$ are two $A.P.s$ such that $x_3 = h_2 = 8$ and $x_8 = h_7 = 20$,then $x_5 \cdot h_{10}$ equals

If $A = 1 + r^z + r^{2z} + r^{3z} + .......\infty$,then the value of $r$ will be

Find the $n^{th}$ term of the $H.P.$ whose first two terms are $6$ and $3,$ respectively.

The sum $11^{2} + 12^{2} + \cdots + 20^{2} + 21^{2} = ?$

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball,the second row consists of two balls and so on. If $99$ more identical balls are added to the total number of balls used in forming the equilateral triangle,then all these balls can be arranged in a square whose each side contains exactly $2$ balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is