Consider the reaction \({H_2}S{O_3}\left( {aq} \right) + S{n^{4 + }}\left( {aq} \right) + {H_2}O\left( l \right) \to S{n^{2 + }}\left( {aq} \right) + HSO_4^ - \left( {aq} \right) + 3{H^ + }\left( {aq} \right)\) Which of the following statements is correct?

The total number of unpaired electrons present in the complex \(K _{3}\left[ Cr \right.\) (oxalate) \(\left._{3}\right]\) is ..........

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 _______.

Given that \((i)\, {\Delta _f}{H^o}\) of \(N_2O\) is \(82\, kJ\, mol^{-1}\) \((ii)\) Bond energies of \(N \equiv N,N = N,O = O\) and \(N = O\) are \(946, 418, 498\) and \(607\, kJ\, mol^{- 1}\) respectively The resonance energy of \(N_2O\) is......\(kJ\)

In an atom how many orbital \((s)\) will have the quantum numbers; \(n = 3, l = 2\) and \(m_l = + 2\) ?

A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2 A . The amount of the aluminium deposited at the cathode is _______.
[Given : molar mass of aluminium and chlorine are \(27 \mathrm{~g} \mathrm{~mol}^{-1}\) and \(35.5 \mathrm{~g} \mathrm{~mol}^{-1}\) respectively. Faraday constant \(\left.=96500 \mathrm{C} \mathrm{mol}^{-1}\right]\)

Given below are two statements :
Statement (I) : On nitration of m-xylene with \(\mathrm{HNO}_3, \mathrm{H}_2 \mathrm{SO}_4\) followed by oxidation, 4-nitrobenzene-1,3-dicarboxylic acid is obtained as the major product.
Statement (II) : \(-\mathrm{CH}_3\) group is o/p-directing while \(-\mathrm{NO}_2\) group is m-directing group.
In the light of the above statements, choose the correct answer from the options given below :

Let the lines \(y+2 x=\sqrt{11}+7 \sqrt{7}\) and \(2 y + x =2 \sqrt{11}+6 \sqrt{7}\) be normal to a circle \(C:(x-h)^{2}+(y-k)^{2}=r^{2}\). If the line \(\sqrt{11} y -3 x =\frac{5 \sqrt{77}}{3}+11\) is tangent to the circle \(C\), then the value of \((5 h-8 k)^{2}+5 r^{2}\) is equal to.......

Let \(A = \{1, 2, 3, 4, 5, 6\}\). The number of one-one functions \(f: A \rightarrow A\) such that \(f(1) \geq 3\), \(f(3) \leq 4\) and \(f(2) + f(3) = 5\), is __________.

Tho damnin of tho finction \(\cos ^{-1}\left(\frac{2 \sin ^{-1}\left(\frac{1}{4 x^{2}-1}\right)}{\pi}\right)\) is

The letters of the word '\(MANKIND\)' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word '\(MANKIND\)' is \(.....\)

If the vectors, \(\overrightarrow{\mathrm{p}}=(a+1) \hat{\mathrm{i}}+a \hat{\mathrm{j}}+a \hat{\mathrm{k}}\)  ; \(\overrightarrow{\mathrm{q}}=\mathrm{a} \hat{\mathrm{i}}+(\mathrm{a}+1) \hat{\mathrm{j}}+\mathrm{a} \hat{\mathrm{k}}\) and  \(\overrightarrow{\mathrm{r}}=\mathrm{a} \hat{\mathrm{i}}+\mathrm{a} \hat{\mathrm{j}}+(\mathrm{a}+1) \hat{\mathrm{k}}(\mathrm{a} \in \mathrm{R})\) are coplanar and \(3(\overrightarrow{\mathrm{p}} \cdot \overrightarrow{\mathrm{q}})^{2}-\lambda|\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{q}}|^{2}=0,\) then the value of \(\lambda\) is

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation: \(K(x) = K_0 + \lambda x\) ( \(\lambda  =\) constant) The capacitance \(C,\) of the capacitor, would be related to its vacuum capacitance \(C_0\) for the relation