Solute \(A\) associates in water. When \(0.7\, g\) of solute \(A\) is dissolved in \(42.0\, g\) of water, it depresses the freezing point by \(0.2^{\circ} C\). The percentage association of solute \(A\) in water, is \(.....\,\%\) [Given : Molar mass of \(A =93\, g\, mol ^{-1}\). Molal depression constant of water is \(1.86\, K \,kg\, mol ^{-1}\) ]

Potassium dichromate when heated with concentrated sulphuric acid and a soluble chloride, gives brown-red vapours of:

Which of the following statements are correct, if the threshold frequency of caesium is \(5.16 \times 10^{14} \mathrm{~Hz}\) ?
A. When Cs is placed inside a vacuum chamber with an ammeter connected to it and yellow light is focused on Cs the ammeter shows the presence of current.
B. When the brightness of the yellow light is dimmed, the value of the current in the ammeter is reduced.
C. When a red light is used instead to the yellow light, the current produced is higher with respect to the yellow light.
D. When a blue light is used, the ammeter shows the formation of current.
E. When a white light is used, the ammeter shows formation of current.
Choose the correct answer from the options given below :

The spin-only magnetic moment value for the complex \(\left[\mathrm{Co}\left(\mathrm{CN}_{6}\right)\right]^{4-}\) is \(......\,BM\) [At. no. of \(\mathrm{Co}=27\) ]

The ratio of number of water molecules in Mohr's salt and potash alum is \(....\,\times 10^{-1}\)

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

List - \(I\)	List - \(II\)
(A). \(ICI\)	(I). \(\mathrm{T}\)-Shape
(B). \(\mathrm{ICI}_3\)	(II). Square pyramidal
(C). \(\mathrm{CIF}_5\)	(III). Pentagonal bipyramidal
(D). \(\mathrm{IF}_7\)	(IV). Linear

Choose the correct answer from the options given below:

\(20\,mL\) of \(0.02\,M\,K _{2} Cr _{2} O _{7}\) solution is used for the titration of \(10 \,mL\) of \(Fe ^{2+}\) solution in the acidic medium.The molarity of \(Fe ^{2+}\) solution is ........... \(\times 10^{-2}\,M\) (Nearest Integer)

For a natural number \(n\), let \(a _{ n }=19^{ n }-12^{ n }\). Then, the value of \(\frac{31 \alpha_{9}-\alpha_{10}}{57 \alpha_{8}}\) is

The shortest distance between lines \(\mathrm{L}_1\) and \(\mathrm{L}_2\), where \(L_1: \frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2}\) and \(L_2\) is the line passing through the points \(\mathrm{A}(-4,4,3) \cdot \mathrm{B}(-1,6,3)\) and perpendicular to the line \(\frac{x-3}{-2}=\frac{y}{3}=\frac{z-1}{1}\), is

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is __________ \( kg.m^{2} \).

Monochromatic light is incident on a glass prism of angle \(A\). If the refractive index of the material of the prism is \(μ\), a ray, incident at an angle \(\theta\), on the face \(AB\) would get transmitted through the face \(AC\) of the prism provided

A solution containing \(10 \mathrm{~g}\) of an electrolyte \(\mathrm{AB}_2\) in \(100 \mathrm{~g}\) of water boils at \(100.52^{\circ} \mathrm{C}\). The degree of ionization of the electrolyte \((\alpha)\) is _______ \(\times 10^{-1}\). (nearest integer) [Given : Molar mass of \(\mathrm{AB}_2=200 \mathrm{~g} \mathrm{~mol}^{-1} \cdot \mathrm{K}_{\mathrm{b}}\) (molal boiling point elevation const. of water) \(=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\), boiling point of water \(=100^{\circ} \mathrm{C}\); \(\mathrm{AB}_2\) ionises as \(\left.\mathrm{AB}_2 \rightarrow \mathrm{A}^{2+}+2 \mathrm{~B}^{-}\right]\)

A capacitor has capacitance \(5 \mu F\) when it's parallel plates are separated by air medium of thickness \(d\). A slab of material of dielectric constant \(1.5\) having area equal to that of plates but thickness \(\frac{ d }{2}\) is inserted between the plates. Capacitance of the capacitor in the presence of slab will be \(..........\mu F\)