Consider the following cell reaction : \(\mathrm{Cd}_{(s)}+\mathrm{Hg}_{2} \mathrm{SO}_{4(s)}+\frac{9}{5} \mathrm{H}_{2} \mathrm{O}_{(l)} \rightleftharpoons \mathrm{CdSO}_{4} \cdot \frac{9}{5} \mathrm{H}_{2} \mathrm{O}_{(s)}+2 \mathrm{Hg}_{(l)}\) The value of \(\mathrm{E}_{\text {cell }}^{0}\) is \(4.315\, \mathrm{~V}\) at \(25^{\circ} \mathrm{C}\). If \(\Delta \mathrm{H}^{\circ}=-825.2\, \mathrm{~kJ} \,\mathrm{~mol}^{-1}\), the standard entropy change \(\Delta \mathrm{S}^{\circ}\) in \(\mathrm{J} \,\mathrm{K}^{-1}\) is ........ . (Nearest integer) [Given : Faraday constant \(=96487\, \mathrm{C}\, \mathrm{mol}^{-1}\) ]

Combustion of \(1\) mole of benzene is expressed at \(\mathrm{C}_6 \mathrm{H}_6(1)+\frac{15}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(1) \text {. }\) The standard enthalpy of combustion of \(2 \mathrm{~mol}\) of benzene is - ' \(x\) ' \(k J\). \(\mathrm{x}=\) _______ \((1)\) standard Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{C}_6 \mathrm{H}_6(1)\), for the reaction \(6 \mathrm{C}\) (graphite) \(+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{C}_6 \mathrm{H}_n(1)\) is \(48.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). \((2)\) Standard Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{CO}_2(\mathrm{~g})\), for the reaction \(\mathrm{C}\) (graphite) \(+\mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{CO}_2(\mathrm{~g})\) is \(-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). \((3)\) Standard and Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{H}_2 \mathrm{O}(1)\), for the reaction \(\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(1)\) is \(-286 \mathrm{~kJ} \mathrm{~mol}^{-1}\).

Given below are two statements: Statement \((I)\): A solution of \(\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}\) is green in colour. Statement \((II)\): A solution of \(\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}\) is colourless. In the light of the above statements, choose the most appropriate answer from the options given below:

Number of grams of bromine that will completely react with \(5.0\, g\) of pent\(-1-\)ene is \(......10^{-2} \,g\). (Atomic mass of \(Br =80\, g / mol\) ) [Nearest Integer)

Identify the reaction which does not liberate hydrogen

The vapour pressures of two volatile liquids \(A\) and \(B\) at \(25^{\circ} C\) are \(50\, Torr\) and \(100\, Torr,\) respectively. If the liquid mixture contains \(0.3\) mole fraction of \(A\), then the mole fraction of liquid \(B\) in the vapour phase is \(\frac{x}{17}\). The value of \(x\) is \(...\)

Given below are two statements:
Statement I : Hyperconjugation is not a permanent effect.
Statement II : In general, greater the number of alkyl groups attached to a positively charged C -atom, greater is the hyperconjugation interaction and stabilization of the cation.
In the light of the above statements, choose the correct answer from the options given below

If \(I _{ n }=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \cot ^{ n } x dx ,\) then :

A satellite of mass \(\mathrm{m}\) is launched vertically upwards with an initial speed \(u\) from the surface of the earth. After it reaches height \(\mathrm{R}\) (\(R =\) radius of the earth), it ejects a rocket of mass \(\frac{\mathrm{m}}{10}\) so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (\(G\) is the gravitational constant: \(\mathrm{M}\) is the mass of the earth)

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is \(\frac{m}{n}\), where \(\operatorname{gcd}(m, n)=1\), then \(m+n\) is equal to :

Let \(A=\left[a_{i j}\right]_{2 \times 2}\) where \(a_{i j} \neq 0\) for all \(i, j\) and \(A^2=I\). Let a be the sum of all diagonal elements of \(A\) and \(b =| A |\), then \(3 a ^2+4 b ^2\) is equal to

Which of the following complex is octahedral, diamagnetic and the most stable?

If the solution curve of the differential equation \(\left(y-2 \log _e x\right) d x+\left(x \log _e x^2\right) d y=0, x > 1\) passes through the points \(\left(e, \frac{4}{3}\right)\) and \(\left(e^4, \alpha\right)\), then \(\alpha\) is equal to \(................\).