Consider that $\sigma_s, k_B, b$ represents Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of $\sigma_s k_B^{-1} b$ is

One main scale division of a Vernier calliper is equal to 1 mm and the number of divisions on the Vernier scale is 10 . When both the jaws touch each other, the Vernier scale shifts to the left of zero of the main scale in such a way that $4^{\text {th }}$ Vernier division coincides with a division of the main scale. If this Vernier calliper measures the length of the wire to be 1 cm , the actual length of the wire is :

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

Each side of a metallic cube of mass 5.580 kg is measured to the 9.0 cm . Keeping the significant figures in view, the density of the material of the cube can be best expressed as $X \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ where the value of $X$ is: