In the given circuit- the value of current \(I _{ L }\) will be \(mA\). (When \(R _{ L }=1 \,k\, \Omega\) )

Two long current carrying thin wires, both with current \(I\), are held by insulating threads oflength \(L\) and are in equilibrium as shown in the figure, with threads making an angle '\(\theta\)' with the vertical. If wires have mass \(\lambda\) per unit length then the value of \(l\) is 
(\(g =\) gravitational acceleration)

Match List - \(I\) with List - \(II\).

List - \(I\) \((Number)\)	List - \(II\) \((Significant figure)\)
\((A)\) \(1001\)	\((I)\) \(3\)
\((B)\) \(010.1\)	\((II)\) \(4\)
\((C)\) \(100.100\)	\((III)\) \(5\)
\((D)\) \(0.0010010\)	\((IV)\) \(6\)

Choose the correct answer from the options given below :

Match List-I with List-II.

List-I	List-II
(A) Mass density	(I) [ML2T-3]
(B) Impulse	(II) [MLT-1]
(C) Power	(III) [ML2T0]
(D) Moment of inertia	(IV) [ML-3T0]

Choose the correct answer from the options given below :

In the given figure, two wheels \(P\) and \(Q\) are connected by a belt \(B\). The radius of \(P\) is three times as that of \(Q\). In case of same rotational kinetic energy, the ratio of rotational inertias \(\left(\frac{{I}_{1}}{{I}_{2}}\right)\) will be \({x}: 1\). The value of \({x}\) will be \(.....\, .\)

The point \(A\) moves with a uniform speed along the circumference of a circle of radius \(0.36\, m\) and covers \(30^{\circ}\) in \(0.1\, s\). The perpendicular projection \('P'\) from \('A'\) on the diameter \(MN\) represents the simple harmonic motion of \('P'.\) The restoration force per unit mass when \(P\) touches \(M\) will be ...... \(N\)

The correct relation between \(\gamma=\frac{ C _p}{ c _v}\) and temperature \(T\) is :

A monochromatic light of wavelength \(6000\)A is incident on the single slit of width \(0.01 \mathrm{~mm}\). If the diffraction pattern is formed at the focus of the convex lens of focal length \(20 \mathrm{~cm}\), the linear width of the central maximum is _______.

A proton, a deuteron and an \(\alpha\) particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is.......... and their speed is.................. in the ratio.

A solid disc of radius \('a'\) and mass \('m'\) rolls down without slipping on an inclined plane making an angle \(\theta\) with the horizontal. The acceleration of the disc will be \(\frac{2}{ b } g \sin \theta\) where \(b\) is \(........\). (Round off to the Nearest Integer) \(( g =\) acceleration due to gravity) \((\theta=\) angle as shown in figure \()\)

A piece of wood of mass \(0.03\, kg\) is dropped from the top of a \(100\, m\) height building. At the same time, a bullet of mass \(0.02\, kg\) is fired vertically upward, with a velocity \(100\, ms^{- 1}\), from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is ........ \(m\). \((g = 10\, ms^{-2})\)

Within a spherical charge distribution of charge density \(\rho \left( r \right)\), \(N\) equipotential surfaces of potential \({V_0},{V_0} + \Delta V,{V_0} + 2\Delta V,\)\(.....{V_0} + N\Delta V\left( {\Delta V > 0} \right),\) are drawn and have increasing radii \(r_0, r_1, r_2,......r_N\), respectively. If the difference in the radii of the surfaces is constant for all values of \(V_0\) and \(\Delta V\) then

The figure shows a Young’s double slit experimental setup. It is observed that when a thin transparent sheet of thickness \(t\) and refractive index \(\mu \) is put in front of one of the slits, the central maximum gets shifted by a distance equal to \(n\) fringe widths. If the wavelength of light used is \(\lambda ,\,t\) will be