A meter bridge with two resistances \( R_{1} \) and \( R_{2} \) as shown in figure was balanced (null point) at 40 cm from the point P. The null point changed to 50 cm from the point P, when 16 \( \Omega \) resistance is connected in parallel to \( R_{2} \). The values of resistances \( R_{1} \) and \( R_{2} \) are __________ .

The atomic mass of \({ }_6 \mathrm{C}^{12}\) is \(12.000000\ \mathrm{u}\) and that of \({ }_6 \mathrm{C}^{13}\) is \(13.003354 \ \mathrm{u}\). The required energy to remove a neutron from \({ }_6 \mathrm{C}^{13}\), if mass of neutron is \(1.008665 \ \mathrm{u}\), will be :

A body of mass 4 kg is placed on a plane at a point P having coordinate \((3,4) \mathrm{m}\). Under the action of force \(\overrightarrow{\mathrm{F}}=(2 \hat{i}+3 \hat{j}) \mathrm{N}\), it moves to a new point Q having coordinates \((6,10) \mathrm{m}\) in 4 sec . The average power and instanteous power at the end of 4 sec are in the ratio of :

An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity \(10^6 \mathrm{~m} / \mathrm{s}\). If the magnitude of the electric field between the plates is \(9.1 \mathrm{~V} / \mathrm{cm}\), then the vertical component of velocity of electron is (mass of electron \(=9.1 \times 10^{-31} \mathrm{~kg}\) and charge of electron \(=1.6 \times 10^{-19} \mathrm{C}\) )

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire Q is ___________.

\(\left(\mu_0=4 \pi \times 10^{-7} T . m / A \right)\)

An upright object is placed at a distance of \(40\, cm\) in front of a convergent lens of focal length \(20\, cm\). A convergent mirror of focal length \(10\, cm\) is placed at a distance of \(60\, cm\) on the other side of the lens. The position and size of the final image will be

Two point charges \(-4 \mu c\) and \(4 \mu c\), constituting an electric dipole, are placed at \((-9,0,0) \mathrm{cm}\) and \((9,0,0) \mathrm{cm}\) in a uniform electric field of strength \(10^4 \mathrm{NC}^{-1}\). The work done on the dipole in rotating it from the equilibrium through \(180^{\circ}\) is :

A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is \(\frac{4}{3}\),  and the diver's eyes are \(15\, cm\) below the surface of water. Then the radius of the circle is

Given below are two statements Statement\(-I :\) Two photons having equal linear momenta have equal wavelengths. Statement\(-II :\) If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease. In the light of the above statements, choose the correct answer from the options given below.

A point particle of mass, moves along the uniformly rough track \(PQR\) as shown in the figure. The coefficient of friction, between the particle and the rough track equals \(\mu\). The particle is released, from rest, from the point \(P\) and it comes to rest at a point \(R\). The energies, lost by the ball, over the parts, \(PQ\) and \(PR\), of the track, are equal to each other, and no energy is lost when particle changes direction from \(PQ\) to \(QR\). The values of the coefficient of friction \(\mu\) and the distance \(x(=QR)\) are, respecitvely close to

Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is _______.

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

List\(-I\) (Layer of atmosphere)	List\(-II\) (Approximate height over earth's surface)
\((A)\) \(F_1\) - Layer	\((I)\) \(10\,km\)
\((B)\) \(D-\) Layer	\((II)\) \(170-190\,km\)
\((C)\) Troposphere	\((III)\) \(100\,km\)
\((D)\) \(E-\)layer	\((IV)\) \(65-75\,km\)

Choose the correct answer from the options given below: