The length of AC is :

1. $(60 - 20\sqrt{3})$ m

2. $60\sqrt{3}$ m

3. $(60 + 20\sqrt{3})$ m

4. $20\sqrt{3}$ m

BCDE is a square with side 90 cm and ∠F = 45°. The length of AF is :

1. $60\sqrt{2}$ cm

2. $90\sqrt{2}$ cm

3. $120\sqrt{2}$ cm

4. $180\sqrt{2}$ cm

The ratio of the length of a vertical pole and length of its shadow on the horizontal surface is 3 : $\sqrt{3}$

Assertion(A): The angle of elevation of the sun is 60°.

Reason(R): If angle of elevation of the sun is θ, tan θ = $\dfrac{3}{\sqrt{3}} = \sqrt{3}$ = tan 60°.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

The length of the ladder placed against a vertical wall is twice the distance between the foot of the ladder and the wall.

Assertion(A): The angle that the ladder makes with the wall is 60°.

Reason(R): If ladder makes angle θ with the wall then sin θ = $\dfrac{\text{base}}{\text{hypotenuse}} = \dfrac{x}{2x} = \dfrac{1}{2}$.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.