Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Torque	$(I)$ $kg\,m^{-1}\,s^{-2}$
$(B)$ Energy density	$(II)$ $kg\,m\,s^{-1}$
$(C)$ Pressure gradient	$(III)$ $kg\,m^{-2}\,s^{-2}$
$(D)$ Impulse	$(IV)$ $kg\,m^2\,s^{-2}$

Choose the correct answer from the options given below:

Which of the following is not represented in the correct unit?

Which of the following quantities has a unit but is dimensionless?

The unit of "impulse per unit area" is the same as that of

Which two of the following five physical parameters have the same dimensions $?$
$(1)$ energy density
$(2)$ refractive index
$(3)$ dielectric constant
$(4)$ Young's modulus
$(5)$ magnetic field

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)