Assertion (A): Area of given rhombus = 10 cm x 10 cm = 100 cm²

Reason (R):

⇒ OA = $5\sqrt{3}$ cm
⇒ AC = 2 x $5\sqrt{3}$ cm = $10\sqrt{3}$ cm
⇒ OB = 5 cm
⇒ BD = 2 x 5 cm = 10 cm

Area of rhombus ABCD = AC x BD = 10 x 10 cm² = 100 cm²

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): CD = 3 x AB = 3 x 10 m = 30 m

Reason (R): In △ABC, tan30° = $\dfrac{10\text{m}}{\text{BC}}$
⇒ BC = 10 $\sqrt{3}$ m
tan 30° = $\dfrac{10\sqrt{3}\text{m}}{\text{CD}}$
⇒ CD = 30 m

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): 5 cos 40°.cosec 50° = 5.

Reason (R):
5 cos 40°.cosec 50° = 5 cos 40° x cosec (90° - 40°)

= 5 cos 40° x $\dfrac{1}{\text{cos }40°}$ = 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): (2x - 3y, 8) = (2, x + 2y)
⇒ x = 1 and y = -2

Reason (R): 2x - 3y = 2 and x + 2y = 8
Solving we get : x = 4 and y = 2

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.