Given below are two statements: Statement \(I\): An \(AC\) circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement \(II\): An \(AC\) circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor. In the light of above statements, choose the correct answer from the options given below

A particle is travelling \(4\) times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is \(2: 1,\) the mass of the particle is

With reference to the observations in photo-electric effect, identify the correct statements from below: \(A.\) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light. \(B.\) The value of saturation current increases on moving the source of light away from the metal surface. \(C.\) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light. \(D.\) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves. \(E.\) Existence of threshold wavelength can not be explained by wave nature of light/electromagnetic waves. Choose the correct answer from the options given below:

Two simple harmonic waves having equal amplitudes of \(8\,cm\) and equal frequency of \(10\,Hz\) are moving along the same direction. The resultant amplitude is also \(8\,cm\). The phase difference between the individual waves is \(..................\) degree.

Temperature difference of \(120\,^oC\) is maintained between two ends of a uniform rod \(AB\) of length \(2L\). Another bent rod \(PQ\), of same cross-section as \(AB\) and length \(\frac{{3L}}{2}\),  is connected across \(AB\) (See figure). In steady state, temperature difference between \(P\) and \(Q\) will be close to .......... \(^oC\)

A pendulum is executing simple harmonic motion and its maximum kinetic energy is \(K_1\). If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is \(K_2\) then

In a screw gauge, \(5\) complete rotations of the screw cause it to move a linear distance of \(0.25\, cm\). There are \(100\) circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of \(4\) main scale divisions and \(30\) circular scale divisions . Assuming negligible zero error, the thickness of the wire is

A ball of mass \(10\, kg\) moving with a velocity \(10 \sqrt{3} m / s\) along the \(x-\)axis, hits another ball of mass \(20\, kg\) which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along \(y-\)axis with a speed of \(10\) \(m / s\). The second piece starts moving at an angle of \(30^{\circ}\) with respect to the \(x-\)axis. The velocity of the ball moving at \(30^{\circ}\) with \(x-\) axis is \(x\, m / s\). The configuration of pieces after collision is shown in the figure below. The value of \(x\) to the nearest integer is

Match list-\(I\) with list-\(II\):

List-\(I\)	List-\(II\)
\((A)\)Kinetic energy of plant	\((I)\) \(-\frac{\mathrm{GMm}}{\mathrm{a}}\)
\((B)\) Gravaitatioin potentiyal energy of sun -plant system	\((II)\) \(\frac{\mathrm{GMm}}{2 \mathrm{a}}\)
\((C)\)Total mecaniacal energy of palnt	\((III)\) \(\frac{\mathrm{Gm}}{\mathrm{r}}\)
\((D)\)Escap energyat the surface of plant for unit mass object	\((IV)\) \(-\frac{\mathrm{GMm}}{2 \mathrm{a}}\)

(Where \(\mathrm{a}=\) radius of planet orbit, \(\mathrm{r}=\) radius of planet, \(M=\) mass of Sun, \(m=\) mass of planet)
Choose the correct answer from the options given below:

Three masses \(M =100\,kg , m _{1}=10\,kg\) and \(m_{2}=20\,kg\) are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. \(A\) force \(F\) is applied on the system so that the mass \(m_{2}\) moves upward with an acceleration of \(2\,ms ^{-2}\). The value of \(F\) is \(......N\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)

In the given circuit, the breakdown voltage of the Zener diode is \(3.0 \mathrm{~V}\). What is the value of \(\mathrm{I}_z\) ?

One plano-convex and one plano-concave lens of same radius of curvature \(‘R’\) but of different materials are joined side by side as shown in the figure. If the refractive index of the material of \(1\) is \(\mu_1\) and that of \(2\) is \(\mu _2\), then the focal length of the combination is

The value of current \(i_{1}\) flowing from \(A\) to \(C\) in the circuit diagram is\(.......A\)