Which of the following matchstick patterns is the correct representation of $\frac{4}{3}$?

Check whether the following expression is with numbers only:

$5(31-6)-6\times 3+11$

Check whether the following expression is with numbers only:

$2z-13$

The diameter of a circle is a line which joins two points on the circle and also passes through the centre of the circle. (In the below figure $\mathrm{AB}$ is a diameter of the circle; $\mathrm{C}$ is its centre). Express the diameter of the circle ($d$) in terms of its radius ($r$).

Check whether the following expression is with numbers only:

$7-11+13$

The difference between the ages of two sisters Leela and Yamini is a variable.

The following patterns of huts are made using matchsticks.

How many huts will be involved in a pattern having $111$ matchsticks?

Check whether the following expression is with numbers only:

$5+5x$

Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares.

(a)

(b)

(c)

(d)

(Hint: If you remove the vertical stick at the end, you will get a pattern of Cs.)

 The following patterns of huts are made using matchsticks.

 Write down the rule to find the number of matchsticks in a pattern involving $n$ huts.