The time period of a simple pendulum is given by \(T =2 \pi \sqrt{\frac{\ell}{ g }}\). The measured value of the length of pendulum is \(10\, cm\) known to a \(1\, mm\) accuracy. The time for \(200\) oscillations of the pendulum is found to be \(100\) second using a clock of \(1s\) resolution. The percentage accuracy in the determination of \('g'\) using this pendulum is \('x'\). The value of \('x'\) to the nearest integer is ...........\(\%\)

Match the List \(-I\) (Phenomenon associated with electromagnetic radiation) with List \(-II\) (Part of electromagnetic spectrum) and select the correct code from the choices given below this lists

List \(I\)	List \(II\)
\(I\) Doublet of sodium	\((A)\) Visible radiation
\(II\) Wavelength corresponding to temperature associated with the isotropic radiation filling all space	\((B)\) Microwave
\(III\) Wavelength emitted by atomic hydrogen in interstellar space	\((C)\) Short radio wave
\(IV\) Wavelength of radiation arising from two close energy levels in hydrogen	\((D)\) \(X-\) rays

Given below are two statements. One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion A :Two identical balls \(A\) and \(B\) thrown with same velocity '\(u\) ' at two different angles with horizontal attained the same range \(R\). If \(A\) and \(B\) reached the maximum height \(h_{1}\) and \(h_{2}\) respectively, then \(R =4 \sqrt{ h _{1} h _{2}}\) Reason R: Product of said heights. \(h _{1} h _{2}=\left(\frac{u^{2} \sin ^{2} \theta}{2 g }\right) \cdot\left(\frac{u^{2} \cos ^{2} \theta}{2 g }\right)\) Choose the \(CORRECT\) answer 

An object is kept at rest at a distance of 3 R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :
(Assume \(\mathrm{M}=\) mass of earth, \(\mathrm{G}=\) Universal gravitational constant)

If the initial velocity in horizontal direction of a projectile is unit vector \(\hat{i}\) and the equation of trajectory is \(y =5 x (1- x )\). The \(y\) component vector of the initial velocity is. (Take \(g=10\,m / s ^{2}\) )

The electrostatic force \(\left(\vec{F}_1\right)\) and magnetic force \(\left(\vec{F}_2\right)\) acting on a charge \(q\) moving with velocity \(v\) can be written _______.

The magnetic field at the centre of a current carrying circular loop of radius \(R\) is 16 \(\mu\)T. The magnetic field at a distance \(x = \sqrt{3}R\) on its axis from the centre is ________ \(\mu\)T.

For a given gas at \(1\,atm\) pressure, \(rms\) speed of the molecules is \(200\,m/s\) at \(127\,^oC.\) At \(2\,atm\) pressure and at \(227\,^oC,\) the \(rms\) speed of the molecules will be

Suppose two planets (spherical in shape) of radii \({R}\) and \(2 {R}\), but mass \({M}\) and \(9\, {M}\) respectively have a centre to centre separation \(8\, {R}\) as shown in the figure. A satellite of mass \('{m}'\) is projected from the surface of the planet of mass \('M'\) directly towards the centre of the second planet. The minimum speed \('v'\) required for the satellite to reach the surface of the second planets is \(\sqrt{\frac{a}{7} \frac{G M}{R}}\) then the value of \('a'\) is \(....\) [Given: The two planets are fixed in their position]

With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is \((A)\) directly proportional to the length of the potentiometer wire \((B)\) directly proportional to the potential gradient of the wire \((C)\) inversely proportional to the potential gradient of the wire \((D)\) inversely proportional to the length of the potentiometer wire Choose the correct option for the above statements:

Three blocks \(A\), \(B\) and \(C\) are pulled on a horizontal smooth surface by a force of \(80 \mathrm{~N}\) as shown in figure. The tensions \(T_1\) and \(T_2\) in the string are respectively _______ and _______.

In a double slit experiment shown in figure, when light of wavelength \(400 \mathrm{~nm}\) is used, dark fringe is observed at \(P\). If \(D=0.2 \mathrm{~m}\). the minimum distance between the slits \(S_1\) and \(S_2\) is ____________ \(mm\).