$A$ cylindrical conductor of radius $R$ carries a current $i$. The value of the magnetic field at a point which is $R/4$ distance inside from the surface is $10 \ T$. Find the value of the magnetic field at a point which is $4R$ distance outside from the surface.

$A$ light wave is travelling along the $y-$ direction. If the corresponding $\vec E$ vector at any time is along the $x-$ axis,the direction of the $\vec B$ vector at that time is along:

Let $R$ be a relation on a set $A$ such that $R = R^{-1}$,then $R$ is

The apparent frequency of a sound wave as heard by an observer is $10\%$ more than the actual frequency. If the velocity of sound in air is $330 \, m/s$,then:
$(i)$ The source may be moving towards the observer with a velocity of $30 \, m/s$
$(ii)$ The source may be moving towards the observer with a velocity of $33 \, m/s$
$(iii)$ The observer may be moving towards the source with a velocity of $30 \, m/s$
$(iv)$ The observer may be moving towards the source with a velocity of $33 \, m/s$

Which of the following statements is correct regarding the ease of dehydration of alcohols?

The refractive index of the material of the prism for violet colour is $1.69$ and that for red is $1.65$. If the refractive index for mean colour is $1.66$,what is the dispersive power of the material of the prism?