One mole of the octahedral complex compound \(\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}_3\) gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with excess of \(\mathrm{AgNO}_3\) solution to yield two moles of \(\mathrm{AgCl}_{(\mathrm{s})}\). The structure of the complex is which?

If \(K_{sp}\) of \(Ag_2CO_3\) is \(8 \times10^{-12},\) the molar solubility of \(Ag_2CO_3\) in \(0.1\,M\,AgNO_3\) is

Which of the following cannot be explained by crystal field theory?

The bond dissociation enthalpy of \(\mathrm{X}_2 \Delta \mathrm{H}_{\text {bond }}\) calculated from the given data is _______ \(\mathrm{kJ} \mathrm{mol}^{-1}\). (Nearest integer)
\(\begin{aligned}
& \mathrm{M}^{+} \mathrm{X}^{-}(\mathrm{s}) \rightarrow \mathrm{M}^{+}(\mathrm{g})+\mathrm{X}^{-}(\mathrm{g}) \Delta \mathrm{H}_{\text {lattice }}^*=800 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{M}(\mathrm{~s}) \rightarrow \mathrm{M}(\mathrm{~g}) \Delta \mathrm{H}_{\text {sub }}^{\circ}=100 \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{aligned}\)
\(\mathrm{M}(\mathrm{~g}) \rightarrow \mathrm{M}^{+}(\mathrm{g})+\mathrm{e}^{-}(\mathrm{g}) \Delta \mathrm{H}_{\mathrm{i}}=500 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
\(\mathrm{X}(\mathrm{~g})+\mathrm{e}^{-}(\mathrm{g}) \rightarrow \mathrm{X}^{-}(\mathrm{g}) \Delta \mathrm{H}_{\mathrm{eg}}^*=-300 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
\(\mathrm{M}(\mathrm{~s})+\frac{1}{2} \mathrm{X}_2(\mathrm{~g}) \rightarrow \mathrm{M}^{+} \mathrm{X}^{-}(\mathrm{s}) \Delta \mathrm{H}_f^{\circ}=-400 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
[Given : \(\mathrm{M}^{+} \mathrm{X}^{-}\)is a pure ionic compound and X forms a diatomic molecule \(\mathrm{X}_2\) in gaseous state]

\(XeO_4\) molecule is tetrahedral having

Which of the following gives a positive test with ninhydrin?

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a \('k'\) value of \(3.3 \times 10^{-4} s ^{-1}\) at \(153^{\circ} C\). The time in minutes it takes for the isomerization to proceed \(40 \%\) to completion at this temperature is .......... (Rounded off to the nearest integer)

The area of the region above the \(x-\) axis bounded by the curve \(y\, = tan\, x\), \(0 \leq x \leq \frac{\pi }{2}\) and the tangent to the curve at \(x\, = \frac{\pi}{4}\) is

If the co-efficient of \(x^9\) in \(\left(\alpha x^3+\frac{1}{\beta x}\right)^{11}\) and the co-efficient of \(x^{-9}\) in \(\left(\alpha x-\frac{1}{\beta x^3}\right)^{11}\) are equal, then \((\alpha \beta)^2\) is equal to \(.............\).

\(19.5\) g of fluoro acetic acid (molar mass \(= 78\) g mol\(^{-1}\)) is dissolved in \(500\) g of water at \(298\) K. The depression in the freezing point of water was \(1°\)C. What is \(K_a\) of fluoro acetic acid? (For water, \(K_f = 1.86\) K kg mol\(^{-1}\)). Assume molarity and molality to have same values.

A horizontal park is in the shape of a triangle \(OAB\) with \(AB =16\). \(A\) vertical lamp post \(OP\) is erected at the point \(O\) such that \(\angle PAO =\angle PBO =15^{\circ}\) and \(\angle PCO =45^{\circ}\), where \(C\) is the midpoint of \(AB\). Then \(( OP )^{2}\) is equal to.

A person throws two fair dice. He wins \(Rs.\, 15\) for throwing a doublet (same numbers on the two dice), wins \(Rs.\,12\) when the throw results in the sum of \(9\), and loses \(Rs.\, 6\) for any other outcome on the throw. Then the expected gain/loss (in \(Rs.\)) of the person is

Consider the following statements \((a)\) The \(pH\) of a mixture containing \(400\, mL\) of \(0.1\, M\, H_2SO_4\) and \(400\, mL\) of \(0.1\, M\, NaOH\) will be approximately \(1.3\). \((b)\) Ionic product of water is temperature dependent. \((c)\) A monobasic acid with \(K_a = 10^{-5}\) has a \(pH = 5\). the degree of dissociation of this acid is \(50\%\). \((d)\) The Le Chatelier’s principle is not applicable to common-ion effect. The correct statements are: