The major product formed in the following reaction is : \(CH _{3} CH = CHCH \left( CH _{3}\right)_{2} \stackrel{ HBr }{\longrightarrow}\)

The group having isoelectronic species is :

Which of the following reactions will not produce a racemic product ?

The number of species from the following which are paramagnetic and with bond order equal to one is _______. \(\mathrm{H}_2, \mathrm{He}_2^{+}, \mathrm{O}_2^{+}, \mathrm{N}_2^{2-}, \mathrm{O}_2^{2-}, \mathrm{F}_2, \mathrm{Ne}_2^{+}, \mathrm{B}_2\)

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

List \(I\) Complex	List \(II\) \(CFSE(\Delta_0)\)
\(A\) \(\left[ Cu \left( NH _3\right)_6\right]^{2+}\)	\(I\) \(-0.6\)
\(B\) \(\left[\operatorname{Ti}\left( N _2 O \right)_6\right]^{3+}\)	\(II\) \(-2.0\)
\(C\) \(\left[ Fe ( CN )_6\right]^{3-}\)	\(III\) \(-1.2\)
\(D\) \(\left[ NiF _6\right]^{4-}\)	\(IV\) \(-0.4\)

Choose the correct answer from the options given below:

When \(10\, \mathrm{~mL}\) of an aqueous solution of \(\mathrm{KMnO}_{4}\) was titrated in acidic medium, equal volume of \(0.1\) \(\mathrm{M}\) of an aqueous solution of ferrous sulphate was required for complete discharge of colour. The strength of \(\mathrm{KMnO}_{4}\) in grams per litre is \(......\,\times 10^{-2} .\) (Nearest integer) Atomic mass of \(\mathrm{K}=39, \mathrm{Mn}=55, \mathrm{O}=16]\)

Total number of tripeptides possible by mixing of valine and proline is \(............\).

Let \(z_1, z_2\) and \(z_3\) be three complex numbers on the circle \(|z|=1\) with \(\arg \left(z_1\right)=\frac{-\pi}{4}, \arg \left(z_2\right)=0\) and \(\arg \left(z_3\right)=\frac{\pi}{4}\). If \(\left|z_1 \bar{z}_2+z_2 \bar{z}_3+z_3 \bar{z}_1\right|^2=\alpha+\beta \sqrt{2}, \alpha, \beta \in \mathbf{Z}\), then the value of \(\alpha^2+\beta^2\) is :

The material filled between the plates of a parallel plate capacitor has resistivity \(200 \Omega \, {m}\). The value of capacitance of the capacitor is \(2\, {pF}\). If a potential difference of \(40 \,{V}\) is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is (given the value of relative permitivity of material is \(50\) )

In a double slit experiment shown in figure, when light of wavelength \(400 \mathrm{~nm}\) is used, dark fringe is observed at \(P\). If \(D=0.2 \mathrm{~m}\). the minimum distance between the slits \(S_1\) and \(S_2\) is ____________ \(mm\).

For the reaction, \( N_{2}O_{4}\rightleftharpoons 2NO_{2}, \) graph is plotted as shown below. Identify correct statements.
A. Standard free energy change for the reaction is -5.40 kJ mol⁻¹.
B. As \( \Delta G^{\ominus} \) in graph is positive, \( N_{2}O_{4} \) will not dissociate into \( NO_{2} \) at all.
C. Reverse reaction will go to completion.
D. When 1 mole of \( N_{2}O_{4} \) changes into equilibrium mixture, value of \( \Delta G^{\ominus}=-0.84 \, kJ \, mol^{-1} \).
E. When 2 mole of \( NO_{2} \) changes into equilibrium mixture, \( \Delta G^{\ominus} \) for equilibrium mixture is -6.24 kJ mol⁻¹.

Choose the correct answer from the options given below:

The number of ways in which an examiner can assign \(30\) marks to \(8\) questions, giving not less than \(2\) marks to any question, is

Let \(O\) be the origin and the position vector of \(A\) and \(B\) be \(2 \hat{i}+2 \hat{j}+\hat{k}\) and \(2 \hat{i}+4 \hat{j}+4 \hat{k}\) respectively. If the internal bisector of \(\angle A O B\) meets the line \(A B\) at \(\mathrm{C}\), then the length of \(\mathrm{OC}\) is