The increasing order of \(pK _{ b }\) values of the following compounds is 

\(0.3\,g\) of ethane undergoes combustion at \(27^{\circ}\,C\) in a bomb calorimeter. The temperature of calorimeter system (including the water) is found to rise by \(0.5^{\circ}\,C\). The heat evolved during combustion of ethane at constant pressure is \(.......kJ\,mol { }^{-1}\). (Nearest integer) [Given : The heat capacity of the calorimeter system is \(20\, kJ\, K ^{-1}, R =8.3\, JK ^{-1}\, mol ^{-1}\). Assume ideal gas behaviour. Atomic mass of \(C\) and \(H\) are \(12\) and \(1\, g\, mol ^{-1}\) respectively]

Identify the structure of the final product (D) in the following sequence of the reactions.

Total number of \(\mathrm{sp}^2\) hybridised carbon atoms in product D is _______.

Number of stereoisomers possible for the complexes, \(\left[\mathrm{CrCl}_3(\mathrm{py})_3\right]\) and \(\left[\mathrm{CrCl}_2(\mathrm{ox})_2\right]^{3-}\) are respectively
( \(\mathrm{py}=\) pyridine, \(\mathrm{ox}=\) oxalate)

For the following reactions \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br}+\mathrm{Z}^{-}\)\(\xrightarrow[{{\text{Sublimation}}}]{{{k_s}}} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Z}+\mathrm{Br}^{-}\) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br}+\mathrm{Z}^{-}\)\(\xrightarrow[{{\text{elimination}}}]{{{k_e}}}\mathrm{CH}_{3} \mathrm{CH}= \mathrm{CH}_{2} +\mathrm{HZ}+\mathrm{Br}^{-}\) where  \(\mathrm{Z}^{-}=\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{O}^{-}(\mathrm{A})\) or \(\begin{array}{*{20}{c}}
  {\,C{H_3}} \\ 
  {|\,\,\,\,\,} \\ 
  {C{H_3} - C - {O^ - }(B)} \\ 
  {|\,\,\,\,} \\ 
  {\,\,C{H_3}} 
\end{array}\) \(\mathrm{k}_{\mathrm{s}}\) and \(\mathrm{k}_{\mathrm{e}},\) are \(,\) respectively, the rate constants for the substitution and elimination, and \(\mu=\frac{\mathrm{k}_{\mathrm{s}}}{\mathrm{k}_{\mathrm{e}}},\) the correct options is

The highest possible oxidation states of uranium and plutonium, respectively, are

Formaldehyde can be distinguished from acetaldehyde by the use of

If \(f\left( x \right) = \left| \begin{array}{*{20}{c}}
{\cos x}&x&1\\
{2\sin x}&{{x^2}}&{2x}\\
{\tan x}&x&1
\end{array}\right|\) , then \(\mathop {\lim }\limits_{x \to 0} \frac{{f'\left( x \right)}}{x}\)

Let \(A=\{0,1,2,3,4,5,6,7\} .\) Then the number of bijective functions \(f: A \rightarrow A\)such that \(f(1)+f(2)=3-f(3)\) is equal to \(.....\)

Let \(A=\left[a_{i j}\right]\) be a square matrix of order 2 with entries either 0 or 1 . Let \(E\) be the event that \(A\) is an invertible matrix. Then the probability \(\mathrm{P}(\mathrm{E})\) is :

A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is \(\sqrt{n}\) cm. The value of n is

The order of reactivity of the given haloalkanes towards nucleophile is

If the area of the region \(\left\{(\mathrm{x}, \mathrm{y}): 1+\mathrm{x}^2 \leq \mathrm{y} \leq \min \{\mathrm{x}+7,11-3 \mathrm{x}\}\right\}\) is A , then 3 A is equal to