100 mL of \(\frac{M}{10} \mathrm{Ca}\left(\mathrm{NO}_3\right)_2\) and 200 mL of \(\frac{M}{10} \mathrm{KNO}_3\) solutions are mixed. What is the normality of resulted solution with respect to \(\mathrm{NO}_3^{-}\)?

Arrange \(L \dot{I}, \mathrm{Be}, \mathrm{B}\) and \(\mathrm{C}\) in decreasing order of their first ionisation enthalpies.

\(\mathrm{K}_{\mathrm{c}}\) for the following reaction is 99.0
\(\mathrm{A}_2(\mathrm{~g}) \stackrel{\mathrm{T}(\mathrm{~K})}{\rightleftharpoons} \mathrm{B}_2(\mathrm{~g})\)
In a one litre flask, 2 moles of \(\mathrm{A}_2\) was heated to \(\mathrm{T}(\mathrm{K})\) and the above equilibrium is reached. The concentrations at equilibrium of \(\mathrm{A}_2\) and \(\mathrm{B}_2\) are \(\mathrm{C}_1\left(\mathrm{~A}_2\right)\) and \(\mathrm{C}_2\left(\mathrm{~B}_2\right)\) respectively. Now, one mole of \(\mathrm{A}_2\) was added to flask and heated to \(\mathrm{T}(\mathrm{K})\) to establish the equilibrium again. The concentrations of \(\mathrm{A}_2\) and \(\mathrm{B}_2\) are \(\mathrm{C}_3\left(\mathrm{~A}_2\right)\) and \(\mathrm{C}_4\left(\mathrm{~B}_2\right)\) respectively. What is the value of \(\mathrm{C}_3\left(\mathrm{~A}_2\right)\) in \(\mathrm{mol}^{-1}\) ?

The correct order of density of \(\mathrm{Be}, \mathrm{Mg}, \mathrm{Ca}, \mathrm{Sr}\) is

What are \(\mathrm{X}\) and \(\mathrm{Y}\) in the following reaction?
\(\mathrm{R}-\mathrm{OH}+\mathrm{PCl}_5 \rightarrow \mathrm{X}+\mathrm{Y}+\mathrm{HCl}\)

In which of the following reactions of \(\mathrm{H}_2 \mathrm{O}_2\) acts as an oxidising agent (either in acidic, alkaline or neutral medium)?
(i) \(2 \mathrm{Fe}^{2+}+\mathrm{H}_2 \mathrm{O}_2 \rightarrow\)
(ii) \(2 \mathrm{MnO}_4^{-}+6 \mathrm{H}^{+}+5 \mathrm{H}_2 \mathrm{O}_2 \rightarrow\)
(iii) \(\mathrm{I}_2+\mathrm{H}_2 \mathrm{O}_2+2 \mathrm{OH}^{-} \rightarrow\)
(iv) \(\mathrm{Mn}^{2+}+\mathrm{H}_2 \mathrm{O}_2 \rightarrow\)

When $20 \mathrm{g}$ of ${\mathrm{CaCO}}_3$  is treated with $20 \mathrm{g}$ $\mathrm{HCl}$, the mass of ${\mathrm{CO}}_2$ formed would be

From a group of 50 students, two sections comprising of 20 and 30 students are formed. If Ram and Rahim are two particular students among the 50 students, then the probability that they both belong to the same section is

A block of mass ' \(\mathrm{m}\) ' and charge ' \(\mathrm{q}\) ' is connected to a point ' \(O\) ' with an inextensible string. This system is on a horizontal table. An electric field (E) is applied perpendicular to the string and in the plane of the horizontal table. The tension in the string when it becomes parallel to the electric field is

The probability that A speaks truth is \(75 \%\) and the probability that B speaks truth is \(80 \%\). The probability that they contradict each other when asked to speak on a fact is

The \(\mathrm{C}_{\mathrm{p}}\) of \(\mathrm{H}_2 \mathrm{O}(l)\) is \(75.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\). What is the energy (in J ) required to raise 180 g of liquid water from \(10^{\circ} \mathrm{C}\) to \(15^{\circ} \mathrm{C}\) ? \(\left(\mathrm{H}_2 \mathrm{O}=18 \mathrm{u}\right)\)

\(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}\) are any 4 points and
\(|\overline{A B} \times \overline{C D}+\overline{B C} \times \overline{A D}+\overline{C A} \times \overline{B D}|=\lambda\)
(Area of \(\triangle A B C\) ) then \(\lambda=\)

If \(-\frac{\pi}{4} < x < \frac{\pi}{4}\), then the general solution of the differential equation \(\cos ^2 x \cdot \frac{d y}{d x}-(\tan 2 x) y=\cos ^4 x\) is