Problem 1.

A small country has a very simple language. People there have only two letters and all their words have exactly seven letters. Calculate the number maximum of words people use in that country?

Problem 2

In the following figures, the larger circles are identical and so are the smaller ones. In $(i)$ the circles have a common center and the lines $AD$ and $BC$ divide both the circles in four equal halves. The larger circle has an area of $100$ square meters. Find the area of the shaded region in figure$(ii)$.
Problem 3.

A circus party has the same number of lions as tigers. You asked to the owner of the circus the number of lions and tigers. He gave you the following information:

(i) An elephant is enough to feed all the tigers and lions in the circus.

(ii) Eighteen deers produce the same amount of meat as an elephant does.

(iii) A lion eats twice as much as a tiger.

(iv) One buffalo is enough to feed a lion and a tiger.

(v) A tiger will eat exactly the same amount of meat a deer has.

Find the number of tigers and lions in that circus party.

Problem 4

In the following figure $BKLGNM$, $CMNHPO$ and $DOPIRQ$ are regular hexagons (all six sides of each hexagon are equal and so are the angles). $ BKLGNM$ has an area of $24$ square units. What is the area of the rectangle $AFJE$?
Problem 5

In a party, boys shake hands with girls but each girl shake hands with everyone else .If there are $40$ handshakes , find out the number of boys and girls in the party ?

Problem 6.

$ABCD$ is a parallelogram where $\angle{ACB}=80^{\circ} $ $\angle{ACD}=20^{\circ} $ ,$P$

is a point on $AC$ such that,$\angle{ABP}=20^{\circ} $ and $Q$ is a point on $AB$ such that $\angle{ACQ}=30^{\circ} $ .Find the magnitude of the angle determined by the lines $CD$ and $PQ$.