Question : In $\triangle$ ABC, $\angle$ C = 90$^{\circ}$. M and N are the midpoints of sides AB and AC, respectively. CM and BN intersect each other at D and $\angle$ BDC = 90$^{\circ}$. If BC = 8 cm, then the length of BN is:

Option 1: $6 \sqrt{3} {~cm}$

Option 2: $6 \sqrt{6} {~cm}$

Option 3: $4 \sqrt{6} {~cm}$

Option 4: $8 \sqrt{3} {~cm}$

Question : Let ABC and PQR be two congruent triangles such that $\angle A = \angle P = 90^{\circ}$. If BC = 17 cm, PR = 8 cm, find AB (in cm).

Option 1: 12

Option 2: 15

Option 3: 14

Option 4: 9

Question : The value of $\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ is:

Option 1: $\frac{29}{6}$

Option 2: $\frac{17}{9}$

Option 3: $\frac{14}{3}$

Option 4: $\frac{49}{12}$

Question : The value of $\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}-\frac{3}{4}+\frac{3}{4} \div \frac{1}{2}$ is:

Option 1: $\frac{25}{6}$

Option 2: $\frac{14}{3}$

Option 3: $\frac{17}{9}$

Option 4: $\frac{49}{12}$

Question : Two circles of radii 5 cm and 3 cm intersect each other at A and B, and the distance between their centres is 6 cm. The length (in cm) of the common chord AB is:

Option 1: $\frac{4 \sqrt{13}}{3}$

Option 2: $\frac{2 \sqrt{14}}{3}$

Option 3: $\frac{2 \sqrt{13}}{3}$

Option 4: $\frac{4 \sqrt{14}}{3}$