In series LCR circuit, the capacitance is changed from C to 4C. To keep the resonance frequency unchanged, the new inductance should be :

A circular loop of radius $20\text{ cm}$ and resistance $2\ \Omega$ is placed in a time varying magnetic field $\vec{B} = (2t^2 + 2t + 3)\text{ T}$. At $t = 0$, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at $t = 3\text{ s}$ is $\dfrac{\alpha}{50}\text{ A}$. The value of $\alpha$ is _______. (Take $\pi = 22/7$)

A particle having charge $10^{-9}$ C moving in $x$-$y$ plane in fields of $0.4\hat{j}$ N/C and $4 \times 10^{-3} \hat{k}$ T experiences a force of $(4\hat{i} + 2\hat{j}) \times 10^{-10}$ N. The velocity of the particle at that instant is _______ m/s.

A current carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest. The particle moves along the axis of solenoid. If $g$ is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy :

Refer to the figure given below. The values of $I_1$, $I_2$ and $I_3$ are __________. 

Identify the correct statements : A. Electrostatic field lines form closed loops. B. The electric field lines point radially outward when charge is greater than zero. C. The Gauss - Law is valid only for inverse - square force. D. The workdone in moving a charged particle in a static electric field around a closed path is zero. E. The motion of a particle under Coulomb's force must take place in a plane. Choose the correct answer from the options given below :