Match List-$I$ with List-$II$:
List-$I$List-$II$
$(A)$ Torque$(I)$ $ML^{-2}T^{-2}$
$(B)$ Stress$(II)$ $ML^2T^{-2}$
$(C)$ Pressure gradient$(III)$ $ML^{-1}T^{-1}$
$(D)$ Coefficient of viscosity$(IV)$ $ML^{-1}T^{-2}$

Choose the correct answer from the options given below:

  • A
    $(A)-(III), (B)-(IV), (C)-(I), (D)-(II)$
  • B
    $(A)-(IV), (B)-(II), (C)-(III), (D)-(I)$
  • C
    $(A)-(II), (B)-(IV), (C)-(I), (D)-(III)$
  • D
    $(A)-(II), (B)-(I), (C)-(IV), (D)-(III)$

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In an electromagnetic system,a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimensions of $[M^P L^Q T^R A^S]$. The values of $P$ and $Q$ are:

Some physical constants are given in List-$I$ and their dimensional formulae are given in List-$II$. Match the following:
List-$I$List-$II$
$(1)$ Planck's constant$(i)$ $[ML^{-1} T^{-2}]$
$(2)$ Gravitational constant(ii) $[ML^{-1} T^{-1}]$
$(3)$ Bulk modulus(iii) $[ML^2 T^{-1}]$
$(4)$ Coefficient of viscosity(iv) $[M^{-1} L^3 T^{-2}]$

The correct answer is:

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$(a)$ $A$ dimensionally incorrect equation can be correct.
$(b)$ $1 \ AU = 9.46 \times 10^{15} \ m$
$(c)$ The dimensional formula of force and stress are the same.
$(d)$ The dimensions of a physical quantity are different in different systems of units.

The graph between two quantities $P$ and $Q$ is a straight line passing through the origin when:

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