Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is 

A large glass slab \(\left(\mu=\frac{5}{3}\right)\) of thickness 8 \(\mathrm{cm}\) is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius \(R \mathrm{~cm}\). What is the value of \(R\) ?

A photoelectric material having work-function ${\varphi }_0$ is illuminated with a light of wavelength $\lambda \left(\lambda <\frac{hc}{{\varphi }_0}\right)$. The fastest photoelectron has a de Broglie wavelength ${\lambda }_d$. A change in wavelength of the incident light by $\mathrm{\Delta }\lambda$ results in a change $\mathrm{\Delta }{\lambda }_d$ in ${\lambda }_d$. The ratio $\frac{\mathrm{\Delta }{\lambda }_d}{\mathrm{\Delta }\lambda }$ is proportional to

Paragraph :
One twirls a circular ring (of mass \(M\) and radius \(R\) ) near the tip of one's finger as shown in Figure 1 . In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is \(r\). The finger rotates with an angular velocity \(\omega_{0}\). The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact (Figure 2). The coefficient of friction between the ring and the finger is \(\mu\) and the acceleration due to gravity is \(g\).


Question :
The total kinetic energy of the ring is

An extended object is placed at point $O$, $10 \mathrm{cm}$ in front of a convex lens $L_1$ and a concave lens $L_2$ is placed $10 \mathrm{cm}$ behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are $20 \mathrm{cm}$. The refractive index of both the lenses is $1.5$. The total magnification of this lens system is:

A vernier calipers has \(1 \mathrm{~mm}\) marks on the main scale. It has 20 equal divisions on the vernier scale which match with 16 main scale divisions. For this vernier calipers, the least count is

A thin and uniform rod of mass $\mathrm{M}$ and length $\mathrm{L}$ is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement(s) is/are correct, when the rod makes an angle ${60}^{\mathrm{o}}$ with vertical?
[ $\mathrm{g}$ is the acceleration due to gravity]

Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in K ) at which the reduction of cassiterite by coke would take place.

\(298 K: \Delta_{ f } H ^0\left( SnO _2(s)\right)=-581.0 kJ mol ^{-1}\), \(\Delta_{ f } H ^0\left( CO _2(g)\right)=-394.0 kJ mol ^{-1}\)

\(S ^0\left( SnO _2(s)\right)=56.0 JK ^{-1} mol^{-1}, S^0( Sn ( s ))\) \(=52.0 JK ^{-1} mol^{-1}\)

\(S ^0( C ( s ))=6.0 JK ^{-1} mol^{-1}, S^0\left( CO _2(g)\right)\) \(=210.0 JK ^{-1} mol^{-1}\)

Assume that the enthalpies and the entropies are temperature independent.

Statement I If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic \(X\)-rays do not change.
Statement II When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.

Choose the correct statement(s) among the following.

When the following aldohexose exists in its D-configuration, the total number of stereoisomers in its pyranose form is :
\(\mathrm{CHO}-\mathrm{CH}_{2}-\mathrm{CHOH}-\mathrm{CHOH}-\mathrm{CHOH}\) \(-~\mathrm{CH}_{2} \mathrm{OH}\)

For the resistance network shown in the figure, choose the correct option(s)

The reaction of white phosphorus with aqueous \(\mathrm{NaOH}\) gives phosphine along with another phosphorus containing compound. The reaction type; the oxidation states of phosphorus in phosphine and the other product are respectively