A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is \(I_0\). If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be :

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A\): Steel is used in the construction of buildings and bridges. Reason \(R:\) Steel is more elastic and its elastic limit is high. In the light of above statements, choose the most appropriate answer from the options given below

A rod of mass \(M\) and length \(L\) is lying on a horizontal frictionless surface. A particle of mass ' \(m\) ' travelling along the surface hits at one end of the rod with velocity \('u'\) in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses \(\left(\frac{m}{M}\right)\) is \(\frac{1}{x}\). The value of ' \(x\) ' will be ..... .

Critical angle of incidence for a pair of optical media is \(45^{\circ}\). The refractive indices of first and second media are in the ratio _______.

A uniform electric field of \(10\,N / C\) is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy \(0.5\,eV\). The length of each plate is \(10\,cm\). The angle \((\theta)\) of deviation of the path of electron as it comes out of the field is  \(.........\)(in degree).

The least count of the main scale of a vernier callipers is \(1\, mm\). Its vernier scale is divided into \(10\) divisions and coincide with \(9\) divisions of the main scale. When jaws are touching each other, the \(7\) th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between \(3.1\, cm\) and \(3.2\, cm\) and \(4^{th}\) \(VSD\) coincides with a main scale division.The length of the cylinder is \(.....cm\) (\(VSD\) is vernier scale division)

A \(16\, \Omega\) wire is bend to form a square loop. A \(9 \,{V}\) supply having internal resistance of \(1 \,\Omega\) is connected across one of its sides. The potential drop across the diagonals of the square loop is \(.......\,\times 10^{-1} \,{V}\)

Four particles, each of mass \(M\) and equidistant from each other, move along a circle of radius \(R\) under the action of their mutual gravitational attraction. The speed of each particle is

A capacitor \(C _{1}\) of capacitance \(5\,\mu F\) is charged to a potential of \(30\,V\) using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor \(C _{2}\) of capacitance \(10\,\mu F\) as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor \(C _{2}\) is________ \(\mu C\)

Nitrogen gas is at \(300^{\circ} C\) temperature. The temperature (in \(K\)) at which the \(rms\) speed of a \(H _{2}\), molecule would be equal to the \(rms\) speed of a nitrogen molecule, is........ (Molar mass of \(N _{2}\) gas \(28\, g\) )

Sodium light of wavelengths \(650\, nm\) and \(655\, nm\) is used to study diffraction at a single slit of aperture \(0.5\, mm\). The distance between the slit and the screen is \(2.0 \,m\). The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is \(\times 10^{-5} \,m\)

Two capacitors, each having capacitance \(40\,\mu F\) are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant \(K\) such that the equivalence capacitance of the system became \(24\,\mu F\). The value of \(K\) will be.