In the given branch $AB$ of a circuit, a current $I = (10t + 5) \, A$ is flowing, where $t$ is time in seconds. At $t = 0$, the potential difference between points $A$ and $B$ $(V_A - V_B)$ is......$V$.

If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$,where $[x]$ is the greatest integer function,then the range of $f$ is:

$A$ block of $200 \text{ g}$ mass moves with a uniform speed in a horizontal circular groove with vertical side walls of radius $20 \text{ cm}$. If the block takes $40 \text{ s}$ to complete one round,the normal force exerted by the side walls of the groove is:

The $V-I$ graph for a conductor at temperatures $T_1$ and $T_2$ is as shown in the figure. Then $(T_2 - T_1)$ is proportional to

An open vessel at $300 \ K$ is heated until $2/5$ of the air in it has been expelled. Assuming the volume of the vessel remains constant,find the temperature to which the vessel has been heated in $K$.

$\int \left( \frac{2 - \sin 2x}{1 - \cos 2x} \right) e^x \, dx$ is equal to