To find the focal length of a convex mirror, a student records the following data

Object Pin	Convex Lens	Convex Mirror	Image Pin
\(22.2\,cm\)	\(32.2\,cm\)	\(45.8\,cm\)	\(71.2\,cm\)

The focal length of the convex lens is \(f_1\)  and that of mirror is \(f_2\). Then taking index correction to be negligibly small, \(f_1\)  and  \(f_2\) are close to

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The outer body of an air craft is made of metal which protects persons sitting inside from lightning-strikes.
Reason (R) : The electric field inside the cavity enclosed by a conductor is zero.
In the light of the above statements, chose the most appropriate answer from the options given below :

A soap bubble of radius \(3\, {cm}\) is formed inside the another soap bubble of radius \(6\, {cm}\). The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is .......... \({cm}\) 

The magnetic field in a plane electromagnetic wave is \(\mathrm{B}_y=\left(3.5 \times 10^{-7}\right) \sin \left(1.5 \times 10^3 \mathrm{x}+0.5\right.\) \(\left.\times 10^{11} \mathrm{t}\right) \mathrm{T}\). The corresponding electric field will be _______.

The electrostatic potential due to an electric dipole at a distance '\(r\)' varies as _______.

An object with mass 500 g moves along x -axis with speed \(v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}\). The force acting on the object is :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion A : Efficiency of a reversible heat engine will be highest at \(-273^{\circ} C\) temperature of cold reservoir. Reason \(R\) : The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as \(\eta=\left(1-\frac{ T _2}{ T _1}\right)\). In the light of the above statements, choose the correct answer from the options given below

From the statements given below :
\((A)\) The angular momentum of an electron in \(n^{\text {th }}\) orbit is an integral multiple of \(h\).
\((B)\) Nuclear forces do not obey inverse square law.
\((C)\) Nuclear forces are spin dependent.
\((D)\) Nuclear forces are central and charge independent.
\((E)\) Stability of nucleus is inversely proportional to the value of packing fraction. Choose the correct answer from the options given below :

Two identical parallel plate capacitors, of capacitance \(C\) each, have plates of area \(A\), separated by a distance \(d\). The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants \(K_1\) , \(K_2\) and \(K_3\) . The first capacitor is filled as shown in fig. \(I\), and the second one is filled as shown in fig. \(II\). If these two modified capacitors are charged by the same potential \(V\), the ratio of the energy stored in the two, would be ( \(E_1\) refers to capacitor \((I)\) and \(E_2\) to capacitor \((II)\)) 

An inductance coil has a reactance of \(100\, \Omega\). When an \(AC\) signal of frequency \(1000\, Hz\) is applied to the coil, the applied voltage leads the current by \(45^{\circ}\). The self- inductance of the coil is

A small cube of side \(1\) mm is placed at the centre of a circular loop of radius \(10\) cm carrying a current of \(2\) A. The magnetic energy stored inside the cube is \(\alpha \times 10^{-14}\) J. The value of \(\alpha\) is _______. (\(\mu_o = 4\pi \times 10^{-7}\) Tm/A, \(\pi = 3.14\))

A Laser light of wavelength \(660\,nm\) is used to weld Retina detachment. If a Laser pulse of width \(60\, ms\) and power \(0.5\, kW\) is used the approximate number of photons in the pulse are : [Take Planck's constant \(h\, = 6.62\times10^{- 34}\, Js\)]

Two cars \(A\) and \(B\) are moving away from each other in opposite directions. Both the cars are moving with a speed of \(20\, ms^{-1}\) with respect to the ground. If an observer in car \(A\) detects a frequency \(2000\, Hz\) of the sound coming from car \(B\), what is the natural frequency of the sound source of car \(B\) ....  \(Hz\) ? (speed of sound in air \(= 340\, ms^{-1}\))