$A$ boy goes to school from his home at a speed of $x$ km/hour and comes back at a speed of $y$ km/hour,then the average speed is given by

If every term of a $G.P.$ with positive terms is the sum of its two previous terms,then the common ratio of the series is

Three numbers are selected from the set ${3^1, 3^2, 3^3, \dots, 3^{20}}$. Find the number of ways these selected numbers can form an increasing Geometric Progression $(G.P.)$.

If $a, b, c$ are in $A$.$P$.,then the straight line $ax + by + c = 0$ will always pass through the point

Let the sequence $a_1, a_2, a_3, \dots, a_{2n}$ form an $A.P.$ Then $a_1^2 - a_2^2 + a_3^2 - a_4^2 + \dots + a_{2n - 1}^2 - a_{2n}^2 = $

The sum of $(n + 1)$ terms of $\frac{1}{1} + \frac{1}{1 + 2} + \frac{1}{1 + 2 + 3} + \dots$ is: