Assertion (A): According to the information in the given figure, the length of BC = 10 cm.

Reason (R):

$\text{BC} = \sqrt{13^2 - 12^2}\text{ cm} = 5\text{ cm}$
$\text{AC} = \sqrt{20^2 - 12^2}\text{ cm} = 16\text{ cm}$
∴ AB = AC - BC = 11 cm

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): In a regular polygon, sum of its interior angles : sum of its external angles is 3 : 1. The number of sides (n) in it is 8.

Reason (R): $\dfrac{(2n - 4)\times 90°}{360°}=\dfrac{3}{1}$

⇒ $\dfrac{2n - 4}{4} = 3 \text{ and } n = 8$

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): ABCD is a parallelogram. AX is bisector of ∠A, CY is bisector of ∠C. Then quadrilateral AXCY is also a parallelogram.

Reason (R): If any one pair of opposite sides of a quadrilateral are equal and parallel then the quadrilateral is a parallelogram.

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): In the given figure, if the area of the parallelogram ABEF is 120 cm², then area of rectangle ABCD is 120 cm².

Reason (R): Parallelogram and rectangle on the same base and between the same parallels are equal in area.

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.