Assertion (A): When each side of a square is increased by 5 cm, its area increases by 75 sq. cm. The side of the square is 5 cm.

Reason (R):

⇒ (x+5)² = x² + 75 ⇒ x = 5cm

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): The ratio between radius and area of a circle is 7 : 44. If the radius of this circle is doubled, the ratio between the new radius and area of the resulting circle will be 7 : 176.

Reason (R): Given : $\dfrac{r}{πr^2} = \dfrac{7}{44}$

∴ $\dfrac{2r}{r(2r)^2} = \dfrac{r}{2πr^2} = \dfrac{1}{2} \times \dfrac{7}{44} = 7 : 88$

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): Two circles touch each other externally. The sum of their areas is 74π cm² and distance between their centres is 12 cm. Then difference between their radii is 2 cm.

Reason (R): When two circles touch each other internally, then two centres and point of contact lie on the same line and distance between their centres equals to the difference between two radii.

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): The ratio between the edges of three cubes is 2 : 3 : 4. The ratio between their volumes is 4 : 9 : 16.

Reason (R): The ratio between their volumes = 2³ : 3³ : 4³ = 8 : 27 : 64.

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.