Question : Find the area of a triangle whose length of two sides are 4 cm and 5 cm and the angle between them is 45°.

Option 1: $4 \sqrt{2} \mathrm{~cm}^2$

Option 2: $7 \sqrt{2} \mathrm{~cm}^2$

Option 3: $5 \sqrt{2} \mathrm{~cm}^2$

Option 4: $6 \sqrt{2} \mathrm{~cm}^2$

Question : Out of two concentric circles, the radius of the outer circle is 6 cm and the chord PQ of the length 10 cm is a tangent to the inner circle. Find the radius (in cm) of the inner circle.

Option 1: $4$

Option 2: $\sqrt{7}$

Option 3: $\sqrt{13}$

Option 4: $\sqrt{11}$

Question : $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are two triangles such that $\triangle \mathrm{ABC} \cong \triangle \mathrm{FDE}$. If AB = 5 cm, $\angle$B = 40° and $\angle$A = 80°, then which of the following options is true?

Option 1: DF = 5 cm, $\angle$E = 60°

Option 2: DE = 5 cm, $\angle$F = 60°

Option 3:  DE = 5 cm, $\angle$D = 60°

Option 4: DE = 5 cm, $\angle$E = 60°

Question : Two identical circles each of radius $2\;\mathrm{cm}$ intersect each other such that the circumference of each one passes through the centre of the other. What is the area (in $\mathrm{cm^2}$) of the intersecting region?

Option 1: $\frac{8\pi }{3}-2\sqrt{3}$

Option 2: $\frac{8\pi }{3}-\sqrt{3}$

Option 3: $\frac{4\pi }{3}-\sqrt{3}$

Option 4: $\frac{4\pi }{3}-2\sqrt{3}$

Question : In a circle with centre O, AD is a diameter and AC is a chord. Point B is on AC such that OB = 7 cm and $\angle OBA=60^{\circ}$. If $\angle \mathrm{DOC}=60^{\circ}$, then what is the length of BC?

Option 1: $3 \sqrt{7} \mathrm{~cm}$

Option 2: $3.5 \mathrm{~cm}$

Option 3: $7 \mathrm{~cm}$

Option 4: $5 \sqrt{7} \mathrm{~cm}$