The speed of light in vacuum is taken as unity. If light takes $6 \text{ min } 40 \text{ s}$ to reach the Earth from the Sun,the distance between the Sun and the Earth in new units is:

  • A
    $3 \times 10^8$
  • B
    $500$
  • C
    $3 \times 10^{10}$
  • D
    $400$

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If $F_1, F_2$,and $F_3$ are the relative strengths of the gravitational,the weak nuclear,and the electromagnetic forces respectively,then

Match the physical quantities in Column-$I$ with those in Column-$II$ having the same dimensions. The correct matching is:
$A$. Entropy$I$. Angular velocity
$B$. Young's modulus of elasticity$II$. Boltzmann constant
$C$. Angular momentum$III$. Energy density
$D$. Decay constant$IV$. Planck's constant

Which relation is wrong?

Match the physical quantities given in List-$I$ with their dimensions in List-$II$.
List-$I$List-$II$
$A$. Gravitational potential$I$. $M^0 L^2 T^{-2} K^{-1}$
$B$. Stefan's constant$II$. $M^0 L^2 T^{-2}$
$C$. Permittivity$III$. $M L^0 T^{-3} K^{-4}$
$D$. Specific heat capacity$IV$. $M^{-1} L^{-3} T^4 I^2$

$(The dimensions of mass, length, time, temperature and current are $M$, $L$, $T$, $K$ and $I$ respectively.)$

Which of the following pairs does not have similar dimensions?

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