What is the half-life (in years) period of a radioactive material if its activity drops to \(1 / 16^{\text {th }}\) of its initial value of \(30\) years?

A particle having electric charge \(3 \times 10^{-19} C\) and mass \(6 \times 10^{-27} kg\) is accelerated by applying an electric potential of 1.21 V . Wavelength of the matter wave associated with the particle is \(\alpha \times 10^{-12} m\). The value of \(\alpha\) is _________ .
(Take Planck's constant \(\left.=6.6 \times 10^{-34} J . s \right)\)

An object of mass \(5\, kg\) is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of \(10\, N\) throughout the motion. The ratio of time of ascent to the time of descent will be equal to \(\left[\right.\)Use \(g =10 \,ms ^{-2}]\)

In the given circuit, the current flowing through the resistance \(20\ \Omega\) is \(0.3 \mathrm{~A}\), while the ammeter reads \(0.9 \mathrm{~A}\). The value of \(\mathrm{R}_1\) is _______ \(\Omega\).

A metal plate of area \(1\times10^{-4}\, m^2\) is illuminated by a radiation of intensity \(16\, m\,W/m^2\). The work function of the metal is \(5\,eV\). The energy of the incident photons is \(10\, eV\) and only \(10\%\) of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be : \([1\, eV = 1.6\times10^{-19}\, J]\)

When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of :

The relative permittivity of distilled water is \(81 .\) The velocity of light in it will be \(....\,\times 10^{7}\,{m} / {s}\) \(\left(\right.\) Given \(\left.\mu_{r}=1\right)\)

A copper wire of length \(1.0\, m\) and a steel wire of length \(0.5\, m\) having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by \(1\, mm\). If the Young's modulii of copper and steel are respectively \(1.0\times10^{11}\, Nm^{-2}\) and \(2.0\times10^{11}\, Nm^{- 2}\), the total extension of the composite wire is ........ \(mm\)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R / \sqrt{R^2+\omega^2 L^2}\right)\), where \(\omega\) is frequency of the supply across resistor \(R\) and inductor L . If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below :

An electric field is given by \((6 \hat{i}+5 \hat{j}+3 \hat{k}) \ N / C\). The electric flux through a surface area \(30 \hat{\mathrm{i}}\; m^2\) lying in \(YZ-\)plane (in SI unit) is _______.

The position-time graphs for two students \(A\) and \(B\) returning from the school to their homes are shown in figure \((A)\) \(A\) lives closer to the school \((B)\) \(B\) lives closer to the school \((C)\) \(A\) takes lesser time to reach home \((D)\) \(A\) travels faster than \(B\) \((E)\) \(B\) travels faster than \(A\) Choose the correct answer from the options given below :

An aluminium wire is stretched to make its length, \(0.4 \,\%\) larger. Then percentage change in resistance is \(.....\,\%\)

The torque due to the force \((2 \hat{i}+\hat{j}+2 \hat{k})\) about the origin, acting on a particle whose position vector is \((\hat{i}+\hat{j}+\hat{k})\), would be