Given below are two statements: Statement-\(I\): The orbitals having same energy are called as degenerate orbitals. Statement-\(II\): In hydrogen atom, \(3 \mathrm{p}\) and \(3 \mathrm{~d}\) orbitals are not degenerate orbitals. In the light of the above statements, choose the most appropriate answer from the options given

Consider the coordination compound, \([Co(NH_3)_6]Cl_3\). In the fonnation of this complex, the species which acts as the Lewis acid is

Which one of the following is an example of disproportionation reaction?

Consider the following reactions: \(PCl _{3}+ H _{2} O \longrightarrow A + HCl\) \(A + H _{2} O \longrightarrow B + HCl\) number of ionisable protons present in the product \(B\,.....\)

The major product of the following reaction is :

Among the following organic acids, the acid present in rancid butter is

Consider the following two half-cell reactions along with the standard reduction potential given:
\(CO_2 + 6H^+ + 6e^- \rightarrow CH_3 OH + H_2 O \quad E°_{red} = 0.02\) V
\(\dfrac{1}{2} O_2 + 2H^+ + 2e^- \rightarrow H_2 O \quad E°_{red} = 1.23\) V
A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of \(1\) bar pressure and \(298\) K temperature. The fuel cell works with \(80\%\) efficiency. If the work derived from the cell using \(1\) mol of \(CH_3 OH\) is used to compress an ideal gas isothermally against a constant pressure of \(1\) kPa, then the change in the volume of the gas, \(\Delta V = \) _____ m\(^3\). (nearest integer)
Given: \(F = 96500\) C mol\(^{-1}\)

Let the coefficients of the middle terms in the expansion of \(\left(\frac{1}{\sqrt{6}}+\beta x\right)^{4},(1-3 \beta x)^{2}\) and \(\left(1-\frac{\beta}{2} x\right)^{6}, \beta>0\), respectively form the first three terms of an \(A.P.\) If \(d\) is the common difference of this \(A.P.\), then \(50-\frac{2 d}{\beta^{2}}\) is equal to.

A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is \(q\). If \(p : q = m\) \(: n\), where \(m\) and \(n\) are coprime, then \(m + n\) is equal to \(..........\).

If \(\int \operatorname{cosec}^5 x d x=\alpha \cot x \operatorname{cosec} x\left(\operatorname{cosec}^2 x+\frac{3}{2}\right)+\beta \log _e\left|\tan \frac{x}{2}\right|+C\) where \(\alpha, \beta \in \mathbb{R}\) and \(\mathrm{C}\) is constant of integration , then the value of \(8(\alpha+\beta)\) equals ...........

A simple pendulum is being used to determine the value of gravitational acceleration \(\mathrm{g}\) at a certain place. The length of the pendulum is \(25.0\; \mathrm{cm}\) and a stop watch with \(1\; \mathrm{s}\) resolution measures the time taken for \(40\) oscillations to be \(50\; s\). The accuracy in \(g\) is  ....... \(\%\)

The peptide that gives positive ceric ammonium nitrate and carbylamine tests is

A liquid drop having \(6\) excess electrons is kept stationary under a uniform electric field of \(25.5\, k\,Vm^{-1}\) . The density of liquid is \(1.26\times10^3\, kg\, m^{-3}\) . The radius of the drop is (neglect buoyancy)