Nickel \((Z\, = 28)\) combines with a uninegative monodentate ligand to form a diamagnetic complex \([NiL_4]^{2-}\). The hybridisation involved and the number of unpaired electrons present in the complex are respectively

The reaction occurs in which of the following galvanic cell?

Given below are two statement: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A:\) \(5 f\) electrons can participate in bonding to a far greater extent than \(4 f\) electrons Reason \(R:\) \(5 f\) orbitals are not as buried as \(4 f\) orbitals In the light of the above statements, choose the correct answer from the options given below

Consider the following sequence of reactions.

Total number of \(\mathrm{sp}^3\) hybridised carbon atoms in the major product C formed is ________.

According to Bohr's atomic theory :- \((A)\) Kinetic energy of electron is \(\propto \frac{ Z ^{2}}{ n ^{2}}\). \((B)\) The product of velocity (v) of electron and principal quantum number (n), 'vn' \(\propto Z ^{2}\). \((C)\) Frequency of revolution of electron in an orbit is \(\propto \frac{ Z ^{3}}{ n ^{3}}\). \((D)\) Coulombic force of attraction on the electron is \(\propto \frac{ Z ^{3}}{ n ^{4}}\). Choose the most appropriate answer from the options given below :

Reaction \(\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})\) is a first order reaction. It was started with pure A

t / min	Pressure of system at time t / mm Hg
10	160
∞	240

Which of the following option is incorrect?

The electronic spectrum of \(\left[ Ti \left( H _{2} O \right)_{6}\right]^{3+}\) shows a single broad peak with a maximum at \(20,300\, cm ^{-1} .\) The crystal field stabilization energy \((CFSE)\) of the complex ion, in \(kJ\, mol ^{-1}\), is :

The major product of the following reaction is \(C{H_3}CH = CHC{O_2}C{H_3}\,\xrightarrow{{LiAl{H_4}}}\) 

Let \(f(x)\) be a function satisfying \(f(x)+f(\pi-x)=\) \(\pi^2, \forall x \in R\). Then \(\int \limits_0^\pi f(x) \sin x d x\) is equal to \(...........\).

A sample of gas with \(\gamma=1.5\) is taken through an adiabatic process in which the volume is compressed from \(1200\, {cm}^{3}\) to \(300\, {cm}^{3}\). If the initial pressure is \(200\, {kPa}\). The absolute value of the workdone by the gas in the process \(= \,..... J.\)

Statement \(-1\) : The system of linear equations \(x + \left( {\sin \,\alpha } \right)y + \left( {\cos \,\alpha } \right)z = 0\) \(x + \left( {\cos \,\alpha } \right)y + \left( {\sin \alpha } \right)z = 0\) \(x - \left( {\sin \,\alpha } \right)y - \left( {\cos \alpha } \right)z = 0\) has a non-trivial solution for only one value of \(\alpha \) lying in the interval \(\left( {0\,,\,\frac{\pi }{2}} \right)\)  Statement \(-2\) : The equation in \(\alpha \) \(\left| {\begin{array}{*{20}{c}}
  {\cos {\mkern 1mu} \alpha }&{\sin {\mkern 1mu} \alpha }&{\cos {\mkern 1mu} \alpha } \\ 
  {\sin {\mkern 1mu} \alpha }&{\cos {\mkern 1mu} \alpha }&{\sin {\mkern 1mu} \alpha } \\ 
  {\cos {\mkern 1mu} \alpha }&{ - \sin {\mkern 1mu} \alpha }&{ - \cos {\mkern 1mu} \alpha } 
\end{array}} \right| = 0\) has only one solution lying in the interval \(\left( {0\,,\,\frac{\pi }{2}} \right)\)

Which of the following statement is correct for paper chromatography ?

If \(\int\left(\frac{1}{x}+\frac{1}{x^3}\right) \left(\sqrt[23]{3 x^{-24}+x^{-26}}\right) d x \) \( =-\frac{\alpha}{3(\alpha+1)}\left(3 x^\beta+x^\gamma\right)^{\frac{\alpha+1}{\alpha}}+C, x \gt 0,\) \((\alpha, \beta, \gamma \in Z)\), where \(C\) is the constant of integration, then \(\alpha+\beta+\gamma\) is equal to ________ .