In the circuit diagram shown in figure given below, the current flowing through resistance \(3\, \Omega\) is \(\frac{ x }{3}\,A\). The value of \(x\) is \(...........\)

Given below are two statements: Statement \(I:\) Area under velocity- time graph gives the distance travelled by the body in a given time. Statement \(II:\) Area under acceleration- time graph is equal to the change in velocity- in the given time. In the light of given statements, choose the correct answer from the options given below.

A plane electromagnetic wave travels in free space along the \(x -\) direction. The electric field component of the wave at a particular point of space and time is \(E =6\; Vm^{-1}\) along \(y -\) direction. Its corresponding magnetic filed component, \(B\) would be

During the propagation of electromagnetic waves in a medium

A small spherical droplet of density \(d\) is floating exactly half immersed in a liquid of density \(\rho\) and surface tension \(\mathrm{T}\). The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) 

An inductor of inductance \(10\) mH having resistance of \(100\,\Omega\) is connected to battery of E.M.F. \(1.0\) V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is \(2\) mA and \(4\) mA is _______.

A passenger sitting in a train A moving at \(90\,km / h\) observes another train \(B\) moving in the opposite direction for \(8\,s\). If the velocity of the train \(B\) is \(54\,km / h\), then length of train \(B\) is \(..........\,m\)

A solid body of constant heat capacity \(1\ J/^o C\) is being heated by keeping it in contact with reservoirs in two ways : \((i)\) Sequentially keeping in contact with \(2\) reservoirs such that each reservoir supplies same amount of heat. \((ii)\) Sequentially keeping in contact with \(8\) reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature \(100^o C\) to final temperature \(200^o C\). Entropy change of the body in the two cases respectively is :

A particle moves in \(\mathrm{x}-\mathrm{y}\) plane under the influence of a force \(\vec{F}\) such that its linear momentum is \(\vec{P}(t)=\hat{i} \cos (k t)-\hat{j} \sin (k t)\). If \(k\) is constant, the angle between \(\overrightarrow{\mathrm{F}}\) and \(\overrightarrow{\mathrm{P}}\) will be _______.

Water is flowing at a speed of \(1.5\, ms^{-1}\) through a horizontal tube of cross-sectional area  \(10^{-2}\, m^2\) and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm. the minimum force that you must exert should be ......... \(N\) (density of water \(= 10^3\, kgm^{-3}\))

On interchanging the resistances, the balance point of a meter bridge shifts to the left by \(10\ cm\). The resistance of their series combination is \(1\ k\Omega\). How much was the resistance on the left slot before interchanging the resistances?  ..................  \(\Omega\)