In the given circuit, rms value of current \(\left( I _{ rms }\right)\) through the resistor \(R\) is :\(..........\,A\)

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is \(30^{\circ}\) in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is _______ \(\mu \mathrm{m}\).

An alternating current is given by the equation \(i=i_{1} \sin \omega t+i_{2} \cos \omega t\). The rms current will be

In a parallel plate capacitor set up, the plate area of capacitor is \(2 \,m ^{2}\) and the plates are separated by \(1\, m\). If the space between the plates are filled with a dielectric material of thickness \(0.5\, m\) and area \(2\, m ^{2}\) (see \(fig.\)) the capacitance of the set-up will be \(.........\, \varepsilon_{0}\) (Dielectric constant of the material \(=3.2\) ) and (Round off to the Nearest Integer)

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area \('a'\) is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is \((a\,<\,<\,A)\)

A uniform metal chain of mass \(m\) and length ' \(L\) ' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' \(l\) ' is hanging on one side and rest of its length ' \(L -l\) ' is hanging on the other side of the pulley. At a certain point of time, when \(l=\frac{L}{x}\), the acceleration of the chain is \(\frac{g}{2}\). The value of \(x\) is ........

Statement \(I:\) If three forces \(\vec{F}_{1}, \vec{F}_{2}\) and \(\vec{F}_{3}\) are represented by three sides of a triangle and \(\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}\), then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement \(II:\) A triangle made up of three forces \(\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}\) and \(\overrightarrow{{F}}_{3}\) as its sides taken in the same order, satisfy the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below:

The current \((i)\) at time \(t =0\) and \(t =\infty\) respectively for the given circuit is

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modules of the material of the wire will :

In \(5\, minutes,\) a body cools from \(75^{\circ} {C}\) to \(65^{\circ} {C}\) at room temperature of \(25^{\circ} {C}\). The temperature of body at the end of next \(5\, minutes\) is \(......\,{ }^{\circ} {C} .\)