1.84 g of a mixture of \(\mathrm{CaCO}_3\) and \(\mathrm{MgCO}_3\) is strongly heated to get a residue of 0.96 g. The percentage of \(\mathrm{CaCO}_3\) in the mixture is

Assertion: Transition metals and their complexes show catalytic activity. Reason: The activation energy of a reaction is lowered by the catalyst.

The following graph is obtained for a gas at different temperatures \(\left(\mathrm{T}_1, \mathrm{~T}_2, \mathrm{~T}_3\right)\). What is the correct order of temperature \(（x\)-axis \(=\) velocity; \(y\)-axis \(=\) number of molecules)

The formation of oxide ion \(\mathrm{O}^{2-}\) from oxygen atom requires an exothermic reaction, followed by an endothermic step as shown below. The process of formation of \(\mathrm{O}^{2-}\) in gas phase is unfavorable \(\left(\Delta H^{\ominus}=+\right.\) ve \()\), even though it has stable configuration of the nearest noble gas neon. This is because
\(\begin{aligned} & \mathrm{O}(g)+e^{-} \longrightarrow \mathrm{O}^{-}(g) ; \Delta H^{\ominus}=-141 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ & \mathrm{O}^{-}(g)+e^{-} \longrightarrow \mathrm{O}^{2-}(g) ; \Delta H^{\ominus}=+760 \mathrm{~kJ} \mathrm{~mol}^{-1}\end{aligned}\)

What are X and Y respectively in the following reaction sequence?

What are \(X\) and \(Y\) in the following reactions?

Which one of the following ions exhibit paramagnetic property?

\(\begin{aligned} & \text { Given, } \frac{\sin 1^{\circ}}{\sin x^{\circ} \sin (x+1)^{\circ}}=\cot x^{\circ}-\cot (x+1)^{\circ}, \\ & \text { then the value of } \frac{1}{\sin 45^{\circ} \sin 46^{\circ}} \\ & +\frac{1}{\sin 46^{\circ} \sin 47^{\circ}}+\ldots+\frac{1}{\sin 89^{\circ} \sin 90^{\circ}} \text { is }\end{aligned}\)

The ratios of lengths, areas of cross-section and Young's modulii of steel to that of brass wires shown in the figure are \(a, b\) and \(c\) respectively. The ratio of increase in the lengths of brass to that of steel wires is [Assume that the masses of steel and brass wires are negligible]

The reaction \(X \rightarrow\) products is a first order reaction. In 40 minutes, the concentration of \(X\) changes from \(1.0 \mathrm{M}\) to \(0.25 \mathrm{M}\). What is the initial rate of reaction when \([X]=0.1 \mathrm{M}\) ? \((\log 4=0.60)\)

A solution which is \(10^{-3} \mathrm{M}\) each in \(\mathrm{Mn}^{2+}, \mathrm{Fe}^{2+}, \mathrm{Zn}^{2+}\) and \(\mathrm{Hg}^{2+}\) is treated with \(10^{-16} \mathrm{M}\) sulphide ion. If the \(\mathrm{K}_{\mathrm{sp}}\) of MnS, FeS, \(\mathrm{ZnS}\) and \(\mathrm{HgS}\) are \(10^{-15}, 10^{-23}, 10^{-20}\) and \(10^{-54}\) respectively, which one will precipitate first?

If \(\mathrm{A}(1,2,3), \mathrm{B}(2,3,-1), \mathrm{C}(3,-1,-2)\) are the vertices of a triangle ABC, then the direction ratios of the bisector of \(\triangle \mathrm{ABC}\) are

In \(\triangle A B C\), if \(a=3, b=4, c=6\), then \(\frac{\cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}}{\cot A+\cot B+\cot C}=\)