Assertion (A) : The length of the longest rod that can be put in a room of dimensions 10 m × 10 m × 5 m is 15 m.

Reason (R) : Length of the diagonal of a cuboid = $\sqrt{l^2 + b^2 + h^2}$

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

Assertion (A) : The perimeter of one face of a cube is 20 cm. Its volume is 64 cm³.

Reason (R) : Volume of a cube of edge a is given by a³.

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

The volume of a cuboid of dimensions x, y and z is V and its surface area is S. The value of $\dfrac{1}{V}$ is :

1. $\dfrac{2}{S}\Big(\dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z}\Big)$

2. $\dfrac{S}{2} \Big(\dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z}\Big)$

3. $\dfrac{3}{S} \Big(\dfrac{1}{x} - \dfrac{1}{y} - \dfrac{1}{z}\Big)$

4. $\dfrac{S}{3} \Big(\dfrac{a + b + c}{abc}\Big)$

If a cube has surface area S and volume V, then the volume of the cube of surface area 2S is :

1. $\sqrt{2}V$

2. 2V

3. $2\sqrt{2}V$

4. $\dfrac{V}{\sqrt{2}}$