An inductor coil stores $U$ energy when $i$ current is passed through it and dissipates energy at the rate of $P$. The time constant of the circuit,when this coil is connected across a battery of zero internal resistance is

$A$ simple harmonic progressive wave is given by $y = y_0 \sin 2 \pi (nt - \frac{x}{\lambda})$. If the wave velocity is $\left(\frac{1}{8}\right)^{\text{th}}$ of the maximum particle velocity,then the wavelength is:

Consider the following statements $A$ and $B$ and identify the correct answer given below.
$A$. Peltier coefficient is numerically equal to the potential difference across the junctions of the thermocouple through which current is flowing.
$B$. According to Thomson,energy is neither absorbed nor evolved at the junction of a thermocouple but is absorbed or evolved only along the lengths of both the conductors.

If $m$ and $M$ respectively denote the minimum and maximum of $f(x)=(x-1)^2+3$ for $x \in [-3, 1]$,then the ordered pair $(m, M)$ is equal to

The value of $\int_{0}^{1} \left( \prod_{r=1}^{n} (x+r) \right) \left( \sum_{k=1}^{n} \frac{1}{x+k} \right) dx$ equals

If $(1, a)$ and $(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$,then $4a+2b$ is equal to