$A$ millivoltmeter of $25 \, mV$ range is to be converted into an ammeter of $25 \, A$ range. The value (in $\Omega$) of the necessary shunt will be:

Assertion $(A)$: Rapidly changing temperatures can be measured by thermocouples. Reason $(R)$: The thermal capacity of the junction of a thermocouple is very small.

The function $f(x) = x e^{-x}, \forall x \in R$ attains a maximum value at $x$ equal to

If $a = \cos \left(\frac{8 \pi}{11}\right) + i \sin \left(\frac{8 \pi}{11}\right)$,then $\operatorname{Re}\left(a + a^2 + a^3 + a^4 + a^5\right) = $

The value of $c$ in the Lagrange's mean value theorem for $f(x)=\sqrt{x-2}$ in the interval $[2,6]$ is

$A$ series $LCR$ circuit is connected across a source of alternating $emf$ of changing frequency and resonates at frequency $f_0$. Keeping capacitance constant,if the inductance $(L)$ is increased by $\sqrt{3}$ times and resistance $(R)$ is increased by $1.4$ times,the resonant frequency now is