In free space, an electromagnetic wave of \(3 \; GHz\) of \(3 \; GHz\) frequency strikes over the edge of an object of size \(\frac{\lambda}{100}\), where \(\lambda\) is the wavelength of the wave in free space. The phenomenon, which happens there will be .....

Two cells are connected in opposition as shown. Cell \(\mathrm{E}_1\) is of \(8 \mathrm{~V}\) emf and \(2 \ \Omega\) internal resistance; the cell \(E_2\) is of \(2 \mathrm{~V}\) emf and \(4\ \Omega\) internal resistance. The terminal potential difference of cell \(\mathrm{E}_2\) is _______.

Two simple harmonic motions are represented by the equations \({x}_{1}=5 \sin \left(2 \pi {t}+\frac{\pi}{4}\right)\) and \({x}_{2}=5 \sqrt{2}(\sin 2 \pi {t}+\cos 2 \pi {t})\) The amplitude of second motion is ....... times the amplitude in first motion.

The distance between two plates of a capacitor is \(d\) and its capacitance is \(C _1\), when air is the medium between the plates. If a metal sheet of thickness \(\frac{2 d }{3}\) and of same area as plate is introduced between the plates, the capacitance of the capacitor becomes \(C _2\). The ratio \(\frac{ C _2}{ C _1}\) is:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion \(A:\) Alloys such as constantan and manganin are used in making standard resistance coils. Reason \(R:\) Constantan and manganin have very small value of temperature coefficient of resistance.In the light of the above statements, choose the correct answer from the options given below.

Considering Bohr's atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of \(\mathrm{He}^{+}\)ion in its first excited state.
(B) the energy of H atom in ground state is same as that for \(\mathrm{Li}^{++}\)ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of \(\mathrm{He}^{+}\)ion for its ground state.
(D) the energy of \(\mathrm{He}^{+}\)ion in its first excited state is same as that for \(\mathrm{Li}^{++}\)ion in its ground state
Choose the correct answer from the options given below :

The electric field due to a short electric dipole at a large distance (r) from center of dipole on the equatorial plane varies with distance as

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

List\(-I\)	List\(-II\)
\((a)\) Phase difference between current and voltage in a purely resistive \(AC\) circuit	\((i)\) \(\frac{\pi}{2} ;\) current leads voltage
\((b)\) Phase difference between current and voltage in a pure inductive \(AC\) circuit	\((ii)\) zero
\((c)\) Phase difference between current and voltage in a pure capacitive \(AC\) circuit	\((iii)\) \(\frac{\pi}{2} ;\) current lags voltage
\((d)\) Phase difference between current and voltage in an \(LCR\) series circuit	\((iv)\) \(\tan ^{-1}\left(\frac{X_{C}-X_{L}}{R}\right)\)

Choose the most appropriate answer from the options given below:

A bulb and a capacitor are connected in series across an AC supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:

A cord is wound round the circumference of wheel of radius \(r\). The axis of the wheel is horizontal and the moment of inertia about it is \(I. \,A\) weight \(mg\) is attached to the cord at the end. The weight falls from rest. After falling through a distance \( 'h '\), the square of angular velocity of wheel will be ..... .

Two sources of sound \(S_1\) and \(S_2\) produce sound waves of same frequency \(660\, Hz\). A listener is moving from source \(S_1\) towards \(S_2\) with a constant speed \(u\, m/s\) and he hears \(10\, beats/s\). The velocity of sound is \(330\, m/s\). Then, \(u\) equals ... \(m/s\)

A person of mass \(M\) is, sitting on a swing of length \(L\) and swinging with an angular amplitude \(\theta_0\). If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance \(l\, ( l < < L)\), is close to

A galvanometer is used in laboratory for the null point in electrical experiments. If, on passing a current of \(6 \,m A\) it produces a deflection of \(2^{\circ},\) its figure of merit is close to :