The standard free energy change \(\left(\Delta G ^{\circ}\right)\) for \(50 \%\) dissociation of \(N _{2} O _{4}\) into \(NO _{2}\) at \(27^{\circ} C\) and \(1\, atm\) pressure is \(- x\, J \,mol ^{-1}\). The value of \(x\) is \(......\) (Nearest Integer) [Given \(: R =8.31 \,J \,K ^{-1} \,mol ^{-1}, \log 1.33=0.1239\) \(\ln 10=2.3]\)

The number of paramagnetic species from the following is \(............\). \({\left[ Ni ( CN )_4\right]^{2-},\left[ Ni ( CO )_4\right],\left[ NiCl _4\right]^{2-}}\) \({\left[ Fe ( CN )_6\right]^{4-},\left[ Cu \left( NH _3\right)_4\right]^{2+}}\) \({\left[ Fe ( CN )_6\right]^{3-} \text { and }\left[ Fe \left( H_2O\right)_6\right]^{2+}}\)

Number of colourless lanthanoid ions among the following is _______. \(\mathrm{Eu}^{3+}, \mathrm{Lu}^{3+}, \mathrm{Nd}^{3+}, \mathrm{La}^{3+}, \mathrm{Sm}^{3+}\)

The standard reduction potentials at \(298 \mathrm{~K}\) for the following half cells are given below : \(\mathrm{Cr}_2 \mathrm{O}_7{ }^{2-}+14 \mathrm{H}^{+}+6 \mathrm{e}^{-} \rightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_2 \mathrm{O}, \mathrm{E}^{\circ}=1.33 \mathrm{~V}\) \(\mathrm{Fe}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow \mathrm{Fe}  \mathrm{E}^{\circ}=-0.04 \mathrm{~V}\) \(\mathrm{Ni}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{Ni}  \mathrm{E}^{\circ}=-0.25 \mathrm{~V}\) \(\mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow \mathrm{Ag} \mathrm{E}^{\circ}=0.80 \mathrm{~V}\) \(\mathrm{Au}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow \mathrm{Au} \mathrm{E}^{\circ}=1.40 \mathrm{~V}\) Consider the given electrochemical reactions, The number of metal\((s)\) which will be oxidized be \(\mathrm{Cr}_2 \mathrm{O}_7{ }^{2-}\), in aqueous solution is _______.

The number of species from the following that are involved in \(\mathrm{sp}^3 \mathrm{~d}^2\) hybridization is :\(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}, \mathrm{SF}_6,\left[\mathrm{CrF}_6\right]^{3-},\left[\mathrm{CoF}_6\right]^{3-},\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}\) and \(\left[\mathrm{MnCl}_6\right]^3\).

Give below are two statements: Statement-\(I\) : Noble gases have very high boiling points. Statement-\(II\): Noble gases are monoatomic gases. They are held together by strong dispersion forces. Because of this they are liquefied at very low temperature. Hence, they have very high boiling points. In the light of the above statements. choose the correct answer from the options given below:

Consider the reaction \(\mathrm{X}_2 \mathrm{Y}(\mathrm{~g})=\mathrm{X}_2(\mathrm{~g})+\frac{1}{2} \mathrm{Y}_2(\mathrm{~g})\)
The equation representing correct relationship between the degree of dissociation (x) of \(\mathrm{X}_2 \mathrm{Y}(\mathrm{g})\) with its equilibrium constant Kp is ______ .
Assume \(x\) to be very very small.

\(\operatorname{cosec} 18^{\circ}\) is a root of the equation :

The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be ____ A.

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of \(\frac{C_p}{C_V}\) for the gas is _______.

If \(f\left( {\frac{{x - 4}}{{x + 2}}} \right) = 2x + 1,(x \in R = \left\{ {1, - 2} \right\}),\) then \(\int {f(x)} \,dx\) is equal to (where \(C\) is a constant of integration)

Identify the incorrect statement about tertiary structure of proteins.

Given below are two statements: Statement \((I)\) : \(A\) Buffer solution is the mixture of a salt and an acid or a base mixed in any particular quantities. Statement \((II)\) : Blood is naturally occurring buffer solution whose \(\mathrm{pH}\) is maintained by \(\mathrm{H}_2 \mathrm{CO}_3 / \mathrm{HCO}_3\) concentrations. In the light of the above statements, choose the correct answer from the options given below.