Choose the correct statement regarding the formation of carbocations \(A\) and \(B\) given :- \({C{H_3} - C{H_2} - CH = C{H_2} + HBr\\,\to \,CH _{3}- CH _{2}- CH _{2}- C^{+}H _{2}+ Br ^{-}} _{"A"}\) \({C{H_3} - C{H_2} - CH = C{H_2} + HBr\\, \to \,CH _{3}- CH _{2}- C^{+}H - CH _{3}+ Br ^{-}}_{"B"}\)

Which one of the following reactions will not result in the formation of carbon-carbon bond?

Time required for completion of \(99.9 \%\) of a First order reaction is_________ times of half life \(\left(\mathrm{t}_{1 / 2}\right)\) of the reaction.

In an oligopeptide named Alanylglycylphenyl alanyl isoleucine, the number of \(sp ^2\) hybridised carbons is \(...........\).

The molar solubility(s) of zirconium phosphate with molecular formula \(\left(\mathrm{Zr}^{4+}\right)_3\left(\mathrm{PO}_4^{3-}\right)_4\) is given by relation :

From the magnetic behaviour of \(\left[\mathrm{NiCl}_4\right]^{2-}\) (paramagnetic) and \(\left[\mathrm{Ni}(\mathrm{CO})_4\right]\) (diamagnetic), choose the correct geometry and oxidation state.

For there action of \(H_2\) with \(I_2,\) the rate constant is \(2.5\times 10^{-4}\,dm^3\,mol^{-1}\,s^{-1}\) at \(327\,^oC\) and \(1.0\,dm^3\,mol^{-1}\,s^{-1}\) at \(527\,^oC\). The activation energy for the reaction, in \(kJ\,mol^{-1}\) is: \((R = 8.314\,J\,K^{-1}\,mol^{-1} )\)

The equation of wave is given by \(Y=10^{-2} \sin 2 \pi\left(160 t-0.5 x+\frac{\pi}{4}\right)\) Where \(x\) and \(Y\) are in \(m\) and \(t\) in \(s\). The speed of the wave is \(.....\,km h ^{-1}\)

The unit of the van der Waals gas equation parameter \('a'\) in \(\left(\mathrm{P}+\frac{\mathrm{an}^{2}}{\mathrm{~V}^{2}}\right)(\mathrm{V}-\mathrm{nb})=\mathrm{n} \mathrm{RT}\) is :

Three containers \(\mathrm{C}_{1}, \mathrm{C}_{2}\) and \(\mathrm{C}_{3}\) have water at different temperatures. The table below shows the final temperature \(T\) when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process) \(\begin{array}{|c|c|c|c|}\hline \mathrm{C_{1 }} & {\mathrm{C}_{2}} & {\mathrm{C}_{3}} & {\mathrm{T}} \\ \hline {1 l} & {2 l} & {-} & {60^{\circ} \mathrm{C}} \\ \hline {-} & {1 l} & {2 l} & {30^{\circ} \mathrm{C}} \\ \hline  {2 l} & {-} & {1 l} & {60^{\circ} \mathrm{C}} \\ \hline  {1 l} & {1 l} & {1 l} & {\theta} \\ \hline\end{array}\) The value of \(\theta\) (in \(^{\circ} \mathrm{C}\) to the nearest integer) is

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is ___________ -

Four identical particles of mass \(m\) are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \(\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{\mathrm{~L}^2}\), the length of the sides of the square is _______.

Let \(\theta=\frac{\pi}{5}\) and \(A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right] \cdot\) If \(B=A + A ^{4},\) then \(\operatorname{det}( B )\)