From a circular sheet of paper of radius $a$, a sector with a central angle is cut out and folded into the shape of a conical funnel. The volume of this funnel is maximum when $\mathrm{\theta }$ equals:

Find the equation of the graph shown below.

The graph of $\mathrm{y}-\mathrm{x}$ against $\mathrm{y}+\mathrm{x}$ is as shown below. (All graphs in this question are drawn to scale and the same scale has been used on each axis.)

Which of the following shows the graph of $\mathrm{y}$ against $\mathrm{x}?$

Directions for questions: Given below are three graphs made up of straight line segments shown as thick lines. In each case choose the answer as

Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as:

Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as:

What is the value of 

$\frac{1}{{\log }_2 n}+\frac{1}{{\log }_{3}n}+...+\frac{1}{{\log }_{40}n}?$