The current in the windings of a toroid is $2.0\,A$. There are $400$ turns and the mean circumferential length is $40\,cm$. If the magnetic field inside the toroid is $1.0\,T$,the relative permeability is near to:

If a set $A$ has $n$ elements,then the total number of subsets of $A$ is:

Which one of the following is correctly matched?

Sodium is heated in air at $300^{\circ} C$ to form $X$. $X$ absorbs $CO_2$ and forms $Na_2CO_3$ and $Y$. Which of the following is $Y$?

Three rods $A, B,$ and $C$ of thermal conductivities $K, 2K,$ and $4K$ and equal cross-sectional areas and lengths $2l, l,$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100\ ^oC, 50\ ^oC,$ and $0\ ^oC$ respectively,then the temperature $\theta$ of the junction is

For $x \in \mathbb{R}$,the range of $3 \cos (4x - 5) + 4$ lies in the interval