The de Broglie wavelength of an electron with kinetic energy of 2.5 eV is (in m )
\(\left(1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}, m_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg}\right)\)

Arrange the following in decreasing order of their basicity

(i) \(\mathrm{H}_3 \mathrm{PO}_4(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{H}_2 \mathrm{PO}_4^{-}(a q)\)
(ii) \(\mathrm{H}_2 \mathrm{PO}_4^{-}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HPO}_4^{2-}(a q)\)
(iii) \(\mathrm{HPO}_4^{2-}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{PO}_4^{3-}(a q)\)
The equilibrium constants for the above reactions at a certain temperature are \(K_1, K_2\) and \(K_3\) respectively. The equilibrium constant for the reaction \(\mathrm{H}_3 \mathrm{PO}_4(a q) \rightleftharpoons 3 \mathrm{H}^{+}(a q)+\mathrm{PO}_4^{3-}(a q)\) in terms of \(K_1, K_2\) and \(K_3\) is

In the face centered unit cell, the lattice points are present at

When sodium is dissolved in liquid ammonia, a deep blue coloured solution obtained. This colour of the solution is due to

The rate of a reaction doubles, when the temperature is changed from \(300 \mathrm{~K}\) to \(310 \mathrm{~K}\). Activation energy of the change is....... \(\left(R=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}, \log 2=0.301\right)\)

If two particles $A$ and $B$ are moving with the same velocity, but wavelength of $A$ is found to be double than that of $B.$ Which of the following statements are correct?

If \(m=1\) is the slope of a line \(L\), then the product of the slopes of non-parallel lines which are inclined at an angle of \(60^{\circ}\) with \(L\) is

If \(s=60 t-5 t^2\) denotes the distance covered by a particle in time \(t\), then the distance it covers before coming to rest is.... units.

In a Carnot's engine if the temperatures of the source and the sink are decreased by \(100 \mathrm{~K}\) each then the efficiency of the engine

In the reaction sequence,
\(\mathrm{C}_2 \mathrm{H}_5 \mathrm{Cl}+\mathrm{KCN} \stackrel{\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}}{\longrightarrow} X \underset{\Delta}{\stackrel{\mathrm{H}_3 \mathrm{O}^{\oplus}}{\longrightarrow}}$$Y\)
What is the molecular formula of \(Y\) ?

If \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) are three vectors such that \(|\mathbf{a}|=1,|\mathbf{b}|=2\), \(|\mathbf{c}|=3\) and \(\mathbf{a} \cdot \mathbf{b}=\mathbf{b} \cdot \mathbf{c}=\mathbf{c} \cdot \mathbf{a}=0\), then \(\|[\mathbf{a} \mathbf{b} \mathbf{c}] \mid\) is equal to

Which of the following reactions produce ethyl cyanide as a major product?
1. \(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}=\mathrm{NOH} \xrightarrow{\left(\mathrm{CH}_3 \mathrm{O}\right)_2 \mathrm{O}}\)
2. \(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Cl} \xrightarrow{\text { Ethanolic } \mathrm{KCN}}\)
3. \(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Cl} \xrightarrow{\text { Ethanolic } \mathrm{KCN}}\)
4. \(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CON}\left(\mathrm{CH}_3\right)_2 \xrightarrow[\text { Pyridine, } 70^{\circ} \mathrm{C}]{\stackrel{\mathrm{C}_6 \mathrm{H}_5 \mathrm{SO}_2 \mathrm{Cl}}{\longrightarrow}}\)