Which one of the following molecules is paramagnetic?

A solution containing \(10 \mathrm{~g}\) of an electrolyte \(\mathrm{AB}_2\) in \(100 \mathrm{~g}\) of water boils at \(100.52^{\circ} \mathrm{C}\). The degree of ionization of the electrolyte \((\alpha)\) is _______ \(\times 10^{-1}\). (nearest integer) [Given : Molar mass of \(\mathrm{AB}_2=200 \mathrm{~g} \mathrm{~mol}^{-1} \cdot \mathrm{K}_{\mathrm{b}}\) (molal boiling point elevation const. of water) \(=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\), boiling point of water \(=100^{\circ} \mathrm{C}\); \(\mathrm{AB}_2\) ionises as \(\left.\mathrm{AB}_2 \rightarrow \mathrm{A}^{2+}+2 \mathrm{~B}^{-}\right]\)

Given below are two statements: Statement - \(I\): High concentration of strong nucleophilic reagent with secondary alkyl halides which do not have bulky substituents will follow \(\mathrm{S}_{\mathrm{N}} 2\) mechanism. Statement - \(II\): A secondary alkyl halide when treated with a large excess of ethanol follows \(\mathrm{S}_{\mathrm{N}} 1\) mechanism. In the the light of the above statements, choose the most appropriate from the questions given below:

Consider the following half cell reaction
\(\mathrm{Cr}_2 \mathrm{O}_7^{2-}(\mathrm{aq})+6 \mathrm{e}^{-}+14 \mathrm{H}^{+}(\mathrm{aq})\) \(\rightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+7 \mathrm{H}_2 \mathrm{O}(\mathrm{l})\)
The reaction was conducted with the ratio of \(\frac{\left[\mathrm{Cr}^{3+}\right]^2}{\left[\mathrm{Cr}_2 \mathrm{O}_7^{2-}\right]}=10^{-6}\). The pH value at which the EMF of the half cell will become zero is ________. (nearest integer value)
[Given : standard half cell reduction potential
\(\left.\mathrm{E}_{\mathrm{Cr}_2 \mathrm{O}_7^{2-}, \mathrm{H}^{+} / \mathrm{Cr}^{3+}}^{\mathrm{o}}=1.33 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{~F}}=0.059 \mathrm{~V}\right]\)

Consider \(|x|\) is the difference in oxidation states of Mn in highest manganese fluoride and highest manganese oxide. The ions with \(|x|\) number of unpaired electrons from the following are:
A. \(Sc^{3+}\)
B. \(Zn^{2+}\)
C. \(V^{2+}\)
D. \(Fe^{2+}\)
E. \(Co^{2+}\)
Choose the correct answer from the options given below:

The major product obtained from \(E _{2}\) \(-\)elimination of \(3\) \(-\)bromo\(-\) \(2-\)fluoropentane is

The increasing basicity order of the following compounds is \((1)\)   \(C{H_3}C{H_2}N{H_2}\)                    \((2)\)   \(\begin{array}{*{20}{c}}
{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C{H_2}C{H_3}}\\
{\,\,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,}\\
{\,C{H_3}C{H_2}NH\,\,\,\,\,\,\,}
\end{array}\) \((3)\)   \(\begin{array}{*{20}{c}}
{\,\,\,\,\,\,\,C{H_3}}\\
{\,|}\\
{{H_3}C - N - C{H_3}}
\end{array}\)                                \((4)\)     \(\begin{array}{*{20}{c}}
{\,\,\,\,\,\,\,C{H_3}}\\
{\,|}\\
{Ph - N - H}
\end{array}\)

The sum of possible values of \(x\) for \(\tan ^{-1}( x +1)+\cot ^{-1}\left(\frac{1}{ x -1}\right)=\tan ^{-1}\left(\frac{8}{31}\right)\) is

If the equations \(x^2 + bx - 1 = 0\) and  \(x^2 + x + b= 0\) have a common root different from \(-1,\)  then \(\left| b \right|\)  is equal to

Which of the following statements are correct about \(\mathrm{Zn}, \mathrm{Cd}\) and \(\mathrm{Hg}\) ? \(A\). They exhibit high enthalpy of atomization as the d-subshell is full. \(B\). \(\mathrm{Zn}\) and \(\mathrm{Cd}\) do not show variable oxidation state while \(\mathrm{Hg}\) shows \(+\mathrm{I}\) and + \(II.\) \(C\). Compounds of \(\mathrm{Zn}, \mathrm{Cd}\) and \(\mathrm{Hg}\) are paramagnetic in nature. \(D\). \(\mathrm{Zn}, \mathrm{Cd}\) and \(\mathrm{Hg}\) are called soft metals. Choose the most appropriate from the options given below:

The sum of bridging carbonyls in \(W ( CO )_6\) and \(Mn _2\) \(( CO )_{10}\) 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

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of \(10\) to each of the students. Which of the following statistical measures will not change even after the grace marks were given \(?\)