Given below are two statements: Statement \((I)\) : In the Lanthanoids, the formation of \(\mathrm{Ce}^{+4}\) is favoured by its noble gas configuration. Statement \((II)\) : \(\mathrm{Ce}^{+4}\) is a strong oxidant reverting to the common \(+3\) state. In the light of the above statements, choose the most appropriate answer from the options given below:

In which of the following reactions, an increase in the volume of the container will favour the formation of products?

Arrange the following in increasing order of solubility product :
\(\mathrm{Ca}(\mathrm{OH})_2, \mathrm{AgBr}, \mathrm{PbS}, \mathrm{HgS}\)

The Born-Haber cycle for \(\mathrm{KCl}\) is evaluated with the following data : \(\Delta_{f} \mathrm{H}^{\ominus}\) for \(\mathrm{KCl}=-436.7 \,\mathrm{~kJ}\, \mathrm{~mol}^{-1}\) \(\Delta_{\text {sub }} \mathrm{H}^{\ominus}\) for \(\mathrm{K}=89.2 \,\mathrm{~kJ}\, \mathrm{~mol}^{-1}\) \(\Delta_{\text {ionization }} \,\mathrm{H}^{-}\) for \(\mathrm{K}=419.0\, \mathrm{~kJ}\, \mathrm{~mol}^{-1}\) \(\Delta_{\text {electron gain }} \mathrm{H}^{\ominus}\) for \(\mathrm{Cl}_{(\text {e) }}=-348.6 \,\mathrm{~kJ} \,\mathrm{~mol}^{-1}\) \(\Delta_{\mathrm{bond}} \mathrm{H}^{-}\) for \(\mathrm{Cl}_{2}=243.0 \,\mathrm{~kJ} \,\mathrm{~mol}^{-1}\) The magnitude of lattice enthalpy of \(\mathrm{KCl}\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is ..... . (Nearest integer)

How much amount of \(\mathrm{NaCl}\) should be added to \(600\; \mathrm{g}\) of water \((\rho=1.00\; \mathrm{g} / \mathrm{mL})\) to decrease the freezing point of water to \(-0.2^{\circ} \mathrm{C} ?\) ............. \(\mathrm{gm}\) (The freezing point depression constant for water \(=2\; \mathrm{K}\; \mathrm{kg} \;\mathrm{mol}^{-1}\) )

The species that can have a trans-isomer is: (en \(=\) ethane \(-1,2-\) diamine, \(ox =\) oxalate)

Number of stereo centers present in linear and cyclic structures of glucose are respectively

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

If the distance of the earth from Sun is \(1.5 \times 10^6\,km\). Then the distance of an imaginary planet from Sun, if its period of revolution is \(2.83\) years is \(.............\times 10^6\,km\)

Let the eccentricity \(e\) of a hyperbola satisfy the equation \(6e^2 - 11e + 3 = 0\). If the foci of the hyperbola are \((3, 5)\) and \((3, -4)\), then the length of its latus rectum is :

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) A pendulum clock when taken to Mount Everest becomes fast. Reason \(R:\) The value of \(g\) (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth. In the light of the above statements, choose the most appropriate answer from the options given below

Let \(y=y(x)\) be the solution of the differential equation \(\left(1+y^2\right) e^{\tan x} d x+\cos ^2 x\left(1+e^{2 \tan x}\right) d y=0\), \(y(0)=1\). Then \(y\left(\frac{\pi}{4}\right)\) is equal to :

Identify the characteristics of an adiabatic process in a monoatomic gas.
(A) Internal energy is constant.
(B) Work done in the process is equal to the charge in internal energy.
(C) The product of temperature and volume is a constant.
(D) The product of pressure and volume is a constant.
(E) The work done to change the temperature from \(\mathrm{T}_1\) to \(\mathrm{T}_2\) is proportional to \(\left(\mathrm{T}_2-\mathrm{T}_1\right)\)
Choose the correct answer from the options given below :