Match the following (Take the relative strength of the strongest fundamental forces in nature as $1$):

$I$ (Fundamental forces in nature)	$II$ (Relative strength)
$(A)$ Strong nuclear force	$(e)$ $10^{-2}$
$(B)$ Weak nuclear force	$(f)$ $1$
$(C)$ Electromagnetic force	$(g)$ $10^{10}$
$(D)$ Gravitational force	$(h)$ $10^{-13}$
	$(i)$ $10^{-39}$

The correct match is:

Find the rate of change of the volume of a sphere with respect to its surface area when the radius is $2 \ cm$.

Which of the following pairs of physical quantities does not have the same dimensional formula?

Express:
$(a)$ The energy required to break one bond in $DNA$ in $eV$.
$(b)$ The kinetic energy of an air molecule $(10^{-21} \; J)$ in $eV$.
$(c)$ The daily intake of a human adult in kilocalories.

The diameter of a wire measured by a screw gauge of least count $0.001 \text{ cm}$ is $0.08 \text{ cm}$. The length measured by a scale of least count $0.1 \text{ cm}$ is $150 \text{ cm}$. When a weight of $100 \text{ N}$ is applied to the wire, the extension in length is $0.5 \text{ cm}$, measured by a micrometer of least count $0.001 \text{ cm}$. The error in the measured Young's modulus is $\alpha \times 10^9 \text{ N/m}^2$. The value of $\alpha$ is . . . . . . . (Ignore the contribution of the load to Young's modulus error calculation)

State whether the following statements are true or false:
$(a)$ $A$ physical quantity can have units but still be dimensionless.
$(b)$ Impulse and the gradient of energy have the same units.
$(c)$ The absolute error in every measurement is equal to the least count of the measuring instrument.