The standard electrode potential of \(M ^{+} / M\) in aqueous solution does not depend on

On heating, lead\((II)\) nitrate gives a brown gas \((A).\) The gas \((A)\) on cooling changes to a colourless solid/liquid \((B).\) \((B)\) on heating with \(NO\) changes to a blue solid \((C).\) The oxidation number of nitrogen in solid \((C)\) is :

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

List - \(I\) (Pair of Compounds)	List - \(II\) (Isomerism)
(\(A\)) n-propanol and Isopropanol	\((I)\) Metamerism
(\(B\)) Methoxypropane and ethoxyethane	\((II)\) Chain Isomerism
(\(C\)) Propanone and propanal	\((III)\) Position Isomerism
(\(D\)) Neopentane and Isopentane	\((IV)\) Functional Isomerism

Choose the correct answer from the options given below:

In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic?

X and Y are the number of electrons involved, respectively during the oxidation of \( I^{-} \) to \( I_{2} \) and \( S^{2-} \) to S by acidified \( K_{2}Cr_{2}O_{7} \). The value of X + Y is ______.

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\). Assertion \((A)\) : \(\mathrm{PH}_3\) has lower boiling point than \(\mathrm{NH}_3\). Reason \((R)\) : In liquid state \(\mathrm{NH}_3\) molecules are associated through vander waal's forces, but \(\mathrm{PH}_3\) molecules are associated through hydrogen bonding. In the light of the above statements, choose the most appropriate answer from the options given below:

The technique used for purification of steam volatile water immiscible substance is:

For \(0<\theta<\pi / 2\), if the eccentricity of the hyperbola \(\mathrm{x}^2-\mathrm{y}^2 \operatorname{cosec}^2 \theta=5\) is \(\sqrt{7}\) times eccentricity of the ellipse \(x^2 \operatorname{cosec}^2 \theta+y^2=5\), then the value of \(\theta\) is :

\(20\, mL\) of \(0.1\, M\, H_2SO_4\) is added to \(30\, mL\) of \(0.2\, M\, NH_4OH\) solution. The \(pH\) of the resultant mixture is [\(pk_b\) of \(NH_4OH = 4.7\)]

A particle is subjected two simple harmonic motions as :
\(\mathrm{x}_1=\sqrt{7} \sin 5 \mathrm{tcm}\)
and \(x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}\)
where x is displacement and \(t\) is time in seconds. The maximum acceleration of the particle is \(\mathrm{x} \times 10^{-2} \mathrm{~ms}^{-2}\). The value of x is :

The coefficient of \(x^{1012}\) in the expansion of \({\left( {1 + {x^n} + {x^{253}}} \right)^{10}}\) , (where \(n \leq 22\) is any positive integer), is

Among the statements \((a)-(d)\), the incorrect ones are \((a)\) Octahedral \(Co(III)\) complexes with strong field ligands have very high magnetic moments \((b)\) When \(\Delta_{0}< P\), the \(d-\)electron configuration of \(Co(III)\) in an octahedral complex is \(t_{\text {eg }}^{4} e_{g}^{2}\) \((c)\) Wavelength of light absorbed by \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) is lower than that of \(\left[\mathrm{CoF}_{6}\right]^{3-}\) \((d)\) If the \(\Delta_{0}\) for an octahedral complex of \(\mathrm{Co}(\mathrm{III})\) is \(18,000 \;\mathrm{cm}^{-1},\) the \(\Delta_{\mathrm{t}}\) for its tetrahedral complex with the same ligand will be \(16,000\;\mathrm{cm}^{-1}\)

The integral \(\int_0^\pi \frac{(x+3) \sin x}{1+3 \cos ^2 x} d x\) is equal to :