Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure

In an ammeter, \(5 \%\) of the main current passes through the galvanometer. If resistance of the galvanometer is G, the resistance of ammeter will be _______.

Two sitar strings, \(A\)  and \(B,\)  playing the note \('Dha'\)  are slightly out of tune and produce beats and frequency  \(5\,Hz.\)  The tension of the string \(B\) is slightly increased and the beat frequency is found to decrease by  \(3\,Hz\) . If the frequency of \(A\) is \(425\,Hz,\)  the original frequency of \(B\) is  ... \(Hz\)

The refractive index of a converging lens is \(1.4.\) What will be the focal length of this lens if it is placed in a medium of same refractive index ? (Assume the radii of curvature of the faces of lens are \(R _{1}\) and \(R _{2}\) respectively)

A thin half ring of radius \(35\) cm is uniformly charged with a total charge of \(Q\) coulomb. If the magnitude of the electric field at centre of the half ring is \(100\) V/m, then the value of \(Q\) is _______ nC. (\(\epsilon_o = 8.85 \times 10^{-12}\) C\(^2\)/Nm\(^2\) and \(\pi = 3.14\))

Given below are two statements: Statement \(I\) : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit \(\left( E _{1}\right)\) to higher energy orbit \(\left( E _{2}\right)\), is given as \(hf = E _{1}- E _{2}\). Statement \(II\) : The jumping of electron from higher energy orbit \(\left(E_{2}\right)\) to lower energy orbit \(\left(E_{1}\right)\) is associated with frequency of radiation given as \(f\) \(=\left( E _{2}- E _{1}\right) / h\) This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below

Distance between object and its image \(\left( \text{magnified by } -\frac{1}{3}\right)\) is 30 cm. The focal length of the mirror used is \(\left(\frac{x}{4}\right) \mathrm{cm}\),
where magnitude of value of \(x\) is _________.

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

	List \(-I\)		List \(-II\)
\(A\).	Coefficient of Viscosity	\(I\).	\([M L^2T^{–2}]\)
\(B\).	Surface Tension	\(II\).	\([M L^2T^{–1}]\)
\(C\).	Angular momentum	\(III\).	\([M L^{-1}T^{–1}]\)
\(D\).	Rotational Kimeatic energy	\(IV\).	\([M L^0T^{–2}]\)

The figure shows a region of length \('l'\) with a uniform magnetic field of \(0.3\, T\) in it and a proton entering the region with velocity \(4 \times 10^{5}\, ms ^{-1}\) making an angle \(60^{\circ}\) with the field. If the proton completes \(10\) revolution by the time it cross the region shown, \(l\) is close to....... \(m\) (mass of proton \(=1.67 \times 10^{-27} \,kg ,\) charge of the proton \(\left.=1.6 \times 10^{-19}\, C \right)\)

A beam of protons with speed \(4 \times 10^{5}\, ms ^{-1}\) enters a uniform magnetic field of \(0.3\, T\) at an angle of \(60^{\circ}\) to the magnetic field. The pitch of the resulting helical path of protons is close to....\(cm\) (Mass of the proton \(=1.67 \times 10^{-27}\, kg\), charge of the proton \(=1.69 \times 10^{-19}\,C\))

Two wavelengths \(\lambda_1\) and \(\lambda_2\) are used in Young's double slit experiment \(\lambda_1=450 \mathrm{~nm}\) and \(\lambda_2=650 \mathrm{~nm}\). The minimum order of fringe produced by \(\lambda_2\) which overlaps with the fringe produced by \(\lambda_1\) is \(n\). The value of \(n\) is _________.

Two capacitors \(C_1\) and \(C_2\) are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are \(U_1\) and \(U_2\), respectively. Which of the given statements is true?

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: