Which of the following statements regarding the nature of physical laws is $NOT$ correct?

  • A
    All conserved quantities are necessarily scalars.
  • B
    The laws of nature do not change with time.
  • C
    The laws of nature are the same everywhere in the universe.
  • D
    The law of gravitation is the same both on the moon and the earth.

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The unit of length convenient on the atomic scale is known as an $\mathring{A}$ and is denoted by $\mathring{A}: 1 \mathring{A} = 10^{-10} \, m$. The size of a hydrogen atom is about $0.5 \mathring{A}$. What is the total atomic volume in $m^{3}$ of a mole of hydrogen atoms?

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

The ratio $\left(\frac{E}{W}\right)$ of relative strength of electromagnetic force $(E)$ to weak nuclear force $(W)$ is,

Match List $I$ with List $II$:
List $I$ List $II$
$A$. Torque $I$. $[M^1 L^1 T^{-2} A^{-2}]$
$B$. Magnetic field $II$. $[L^2 A^1]$
$C$. Magnetic moment $III$. $[M^1 T^{-2} A^{-1}]$
$D$. Permeability of free space $IV$. $[M^1 L^2 T^{-2}]$

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The equation of state of a gas is given by $\left( P + \frac{aT^2}{V} \right) V^c = (RT + b)$,where $a, b, c$ and $R$ are constants. The isotherms can be represented by $P = AV^m - BV^n$,where $A$ and $B$ depend only on temperature. Then:

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