Among the following metal carbonyls, the \(\mathrm{C}-\mathrm{O}\) bond order is lowest in

We have taken a saturated solution of \(\mathrm{AgBr}, K_{\mathrm{sp}}\) is \(12 \times 10^{-14}\). If \(10^{-7}\) mole of \(\mathrm{AgNO}_3\) are added to 1 litre of this solution, find conductivity (specific conductance) of this solution in terms of \(10^{-7} \mathrm{Sm}^{-1}\) units.
\( \text {Given, } \lambda_{\left(\mathrm{Ag}^{+}\right)}^{\circ} =6 \times 10^{-3} \mathrm{Sm}^2 \mathrm{~mol}^{-1},\) \(\lambda_{\left(\mathrm{Br}^{-}\right)}^{\circ}=8 \times 10^{-3} \mathrm{Sm}^2 \mathrm{~mol}^{-1}, \)
\( \lambda_{\left(\mathrm{NO}_3^{-}\right)} =7 \times 10^{-3} \mathrm{Sm}^2 \mathrm{~mol}^{-1},\)

The correct statement(s) regarding defects in solids is (are)

During sodium nitroprusside test of sulphide ion in an aqueous solution, one of the ligands coordinated to the metal ion is converted to

A closed vessel with rigid walls contains 1 mol of ${}_{92}{}^{238}\mathrm{U}$ and 1 mol of air at 298 K. Considering complete decay of ${}_{92}{}^{238}\mathrm{U}$ to ${}_{82}{}^{206}\mathrm{P}\mathrm{b}$ , the ratio of the final pressure to the initial pressure of the system at 298 K is

Among PbS, CuS, HgS, MnS, $\mathrm{A}{\mathrm{g}}_2\mathrm{S}$ , NiS, CoS, $\mathrm{B}{\mathrm{i}}_2{\mathrm{S}}_3$ and $\mathrm{S}\mathrm{n}{\mathrm{S}}_2$ , the total number of black coloured sulphides is

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Thermal decomposition of gaseous \(\mathrm{X}_{2}\) to gaseous \(\mathrm{X}\) at \(298 \mathrm{~K}\) takes place according to the following equation:

\(\mathrm{X}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{X}(\mathrm{g})\)

The standard reaction Gibbs energy, \(\Delta_{r} G^{\circ}\), of this reaction is positive. At the start of the reaction, there is one mole of \(\mathrm{X}_{2}\) and no \(\mathrm{X}\). As the reaction proceeds, the number of moles of \(\mathrm{X}\) formed is given by \(\beta\). Thus, \(\beta_{\text {equilibrium }}\) is the number of moles of \(\mathrm{X}\) formed at equilibrium. The reaction is carried out at a constant total pressure of \(2\) bar. Consider the gases to behave ideally. (Given : \(R=0.083 \mathrm{~L}\) bar \(\mathrm{K}^{-1} \mathrm{~mol}^{-1}\) )

Question:
The INCORRECT statement among the following, for this reaction, is

Let $f\text{ : }\left[\frac{1}{2},1\right]⟶R$ (the set of all real numbers) be a positive, non-constant and differentiable function such that $f^{\text{'}}\left(x\right)<2f\left(x\right)$ and $f\left(\frac{1}{2}\right)=1$. Then the value of $\underset{1/2}{\overset{1}{\int }}f\left(x\right)\mathit{\text{dx}}$ lies in the interval:

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Let \(V_r\) denotes the sum of the first \(r\) terms of an arithmetic progression \((A P)\) whose first term is \(r\) and the common difference is \((2 r-1)\). Let \(T_r=V_{r+1}-V_r-2\) and \(Q_r=T_{r+1}-T_r\) for \(r=1,2, \ldots\)
Question:
The sum \(V_1+V_2+\ldots+V_n\) is

\(5.6 \mathrm{~L}\) of helium gas at STP is adiabatically compressed to \(0.7 \mathrm{~L}\). Taking the initial temperature to be \(T_1\), the work done in the process is

Which one of the following statement is WRONG in the context of X-rays generated from X-ray tube?

The concentration of \(R\) in the reaction \(R \longrightarrow P\) was measured as a function of time and the following data is obtained :
\(\begin{array}{lllll}{[R] \text { (molar) }} & 1.0 & 0.75 & 0.40 & 0.10 \\ t \text { (min) } & 0.0 & 0.05 & 0.12 & 0.18\end{array}\)
The order of the reaction is

KI in acetone, undergoes S_N2 reaction with each of P, Q, R and S. The rates of the reaction vary as