Assertion (A): Using the information in the given figure, we get CE : EA = 5:3.

Reason (R): Since, ∠ADE = ∠ABC = 90°

so, $\dfrac{CE}{EA} = \dfrac{BD}{AD} = \dfrac{8-5}{5} = \dfrac{3}{5}$

⇒ CE : EA = 3 : 5

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): Using the information in the given figure, we have PQ = 10 cm.

Reason (R): In right-triangle DAB, DB = 20 cm.

$\text{PQ} =\dfrac{1}{2}\text{BD}=\dfrac{1}{2}\times 20 \text{cm}= 10 \text{cm}$

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): 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.