Which of the following two molecular species are Diamagnetic in nature?
\([\mathrm{A}]=\mathrm{O}_2^{-} \quad[\mathrm{B}] .=\mathrm{N}_2^{+} \quad[\mathrm{C}]=\mathrm{C}_2 \quad[\mathrm{D}]=\mathrm{O}_2{ }^{2-}\)

Two statements, Assertion and Reason are given. With reference to them, choose the correct option.
Assertion: Hydrolysis of 2-Bromo-2-methylpropane follows \(S_N1\) mechanism which involves 2 steps and the first step is:

Reason: The energy required to cleave C – Br is taken from the energy released due to Inductive effect and hyper-conjugative effect.

What would be the EMF of the cell in which the following reaction occurs:
\(\begin{aligned}
& \mathrm{Cd}(\mathrm{S})+2 \mathrm{H}^{+} \rightarrow \mathrm{Cd}^{2+}+\mathrm{H}_{2(\mathrm{~g})} \\
& {\left[\mathrm{H}^{+}\right]=0.02 \mathrm{M} \quad \mathrm{E}^0\left(\mathrm{Cd}^{2+} / \mathrm{Cd}\right)=-0.4 \mathrm{~V},\left[\mathrm{Cd}^{2+}\right]=0.01 \mathrm{M} \text { and partial pressure of } \mathrm{H}_2 \text { gas }=0.8 \mathrm{~atm} .}
\end{aligned}\)

The ionisation energy of hydrogen atom is 13.6 eV . The ionisation energy of \(\mathrm{Li}^{2+}\) ion will be

Which of the following is highly basic?

When \(\mathrm{KBr}\) is dissolved in water, \(\mathrm{K}^{+}\)ions are

Liquor ammonia bottles are opened only after cooling. This is because

The value of \(\int \frac{d x}{\sqrt{x}+\sqrt[3]{x}}\) is

If the tangent to the curve \(x y+a x+b y=0\) at \((1,1)\) is inclined at an angle \(\tan ^{-1} 2\) with \(X\)-axis, then

Match the metals in Column II with their characteristic properties given in Column I.
\(\begin{array}{|c|l|c|c|} \hline & \text { Properties } & & \text { Metals } \\ \hline \text { A } & \text { Lanthanoid with low value of } 3^{\text {rd }} \text { ionisation enthalpy. } & P & V \\ \hline \text { B } & \text { f-Block element with electronic configuration }[\mathrm{Rn}] 6 \mathrm{~d}^2 7 \mathrm{~s}^2 & Q & G d \\ \hline \text { C } & 3 \mathrm{~d} \text {-series metal whose } \mathrm{M}^{3+}{ }_{(\mathrm{aq})} \text { is colourless. } & R & T h \\ \hline \text { D } & 3 \mathrm{~d} \text {-series metal with highest } \Delta \mathrm{H}_{(\text {atomisation })} & S & S c \\ \hline \end{array}\)

If for any \(2 \times 2\) square matrix \(A\), \(A(\operatorname{adj} A)=\left[\begin{array}{ll}8 & 0 \\ 0 & 8\end{array}\right]\), then the value of \(\operatorname{det}(A) .\)

In 3rd series as we move from scandium to zinc the paramagnetism

The width of the fringes obtained with a light of wave length \(6.2 \times 10^{-8}\) m is 1.82 mm. If the whole apparatus is immersed in a liquid of refractive index 1.3, what will be the width of the resulting fringe?