Question : In the given figure ABCD, is a square whose side is 4 cm. P is a point on the side AD. What is the minimum value (in cm) of BP + CP?

Option 1: $4\sqrt5$

Option 2: $4\sqrt4$

Option 3: $6\sqrt3$

Option 4: $4\sqrt6$

Question : What is the value of $\left[\frac{12}{(\sqrt5+\sqrt3)}+\frac{18}{(\sqrt{5}-\sqrt3)}\right]$?

Option 1: $15(\sqrt5–\sqrt3)$

Option 2: $3(5\sqrt5+\sqrt3)$

Option 3: $15(\sqrt5+\sqrt3)$

Option 4: $3(3\sqrt5+\sqrt3)$

Question : In the given figure, ABCD is a square. EFGH is a square formed by joining mid-points of sides of ABCD. LMNO is a square formed by joining mid-points of sides of EFGH. A circle is inscribed inside LMNO. If the area of a circle is 38.5 cm² then what is the area (in cm²) of square ABCD?

Option 1: 98

Option 2: 196

Option 3: 122.5

Option 4: 171.5

Question :
In the figure, AB = AD = 9 cm, AC = AE = 13 cm, and BC = 15 cm. Find ED.

Option 1: 18 cm

Option 2: 16 cm

Option 3: 14 cm

Option 4: 15 cm

Question :
In the figure, O is the centre of the circle. Its two chords AB and CD intersect each other at the point P within the circle. If AB = 20 cm, PB = 12 cm, and CP = 8 cm, then find the measure of PD.

Option 1: 12 cm

Option 2: 11 cm

Option 3: 22 cm

Option 4: 14 cm

Question : In the given figure, ABCD is a square of side 14 cm. E and F are mid-points of sides AB and DC respectively. EPF is a semi-circle whose diameter is EF. LMNO is square. What is the area (in cm²) of the shaded region?

Option 1: 108.5

Option 2: 94.5

Option 3: 70

Option 4: 120