For a reversible reaction, if the concentration of reactants is increased, the equilibrium constant of the reaction

During the electrolysis of copper sulphate aqueous solution using copper electrode, the reaction takine place at the cathode is

An ideal gas mixture of \(\mathrm{C}_2 \mathrm{H}_6\) and \(\mathrm{C}_2 \mathrm{H}_4\) occupies a volume of 28 L at 1 atm and 273 K. This mixture reacts completely with 128g of \(\mathrm{O}_2\) to produce \(\mathrm{CO}_2\) and \(\mathrm{H}_2 \mathrm{O}(l)\). What is the mole fraction of \(\mathrm{C}_2 \mathrm{H}_4\) in the mixture ?

If one litre of an ideal gas at a pressure of \(20 \mathrm{~atm}\) expands isothermally and reversibly to a final volume of ' \(\mathrm{X}\) ' \(\mathrm{L}\) by absorbing 92.12 L. atm heat, ' \(\mathrm{X}\) ' (in L) is

The trend in acidic behaviour of the following hydrocarbons is

Match the following?

	Molecule		Geometry
(a)	${\mathrm{SnCl}}_2$	(i)	Angular (or) Bent
(b)	${\mathrm{XeF}}_4$	(ii)	See-saw
(c)	${\mathrm{ClF}}_3$	(iii)	Square pyramidal
(d)	${\mathrm{IF}}_5$	(iv)	T-shape
			Square planar

What are \(X, Y\) and \(Z\) in the following reactions?
\[
\begin{aligned}
& \mathrm{CaCO}_3 \stackrel{\Delta}{\rightleftharpoons} \mathrm{CO}_2+X \\
& X+\mathrm{H}_2 \mathrm{O} \longrightarrow Y \\
& Y+\mathrm{Cl}_2 \longrightarrow Z \\
& X \quad Y \quad Z
\end{aligned}
\]

If \(P(\sin \alpha, \cos \alpha)\) lies inside the triangle formed by the vertices \((0,0),\left(\sqrt{\frac{3}{2}}, 0\right)\) and \(\left(0, \sqrt{\frac{3}{2}}\right)\), then \(\alpha\) lies in the interval

The range of the real valued function \(\mathrm{f}(\mathrm{x})=\frac{x^2+x+1}{x}\) is

Three vectors of magnitudes \(a, 2 a, 3 a\) are along the directions of the diagonals of 3 adjacent faces of a cube that meet in a point. Then, the magnitude of the sum of those diagonals is

Aluminium (III) chloride forms a dimer because aluminium

Match the items of List - I with those of the entires of List - II
\(List - I\)
\(\begin{aligned} & \text { (I) } \sin ^2 5^{\circ}+\sin ^2 10^{\circ}+ \\ & \sin ^2 15^{\circ}+\ldots+\sin ^2 90^{\circ}=\end{aligned}\)
\(\begin{aligned} & \text { (II) } \tan ^2 5^{\circ} \cdot \tan ^2 10^{\circ} \text {. } \\ & \tan ^2 15^{\circ} \ldots \tan ^2 85^{\circ}= \\ & \end{aligned}\)
\(\begin{aligned} & \text { (III) } \cos ^2 5^{\circ}+\cos ^2 10^{\circ} \\ & +\cos ^2 15^{\circ}+\ldots+\cos ^2 180^{\circ}=\end{aligned}\)
\(\begin{gathered}\text { (IV) } \cot 5^{\circ}+\cot 10^{\circ}+\cot 15^{\circ} \\ +\ldots .+\cot 175^{\circ}=\end{gathered}\)
\(List - II\)
(A) \(0\)
(B) \(\frac{19}{2}\)
(C) \(18\)
(D) \(1\)
(E) \(-1\)

In SI units, $\mathrm{kg} {\mathrm{m}}^2 {\mathrm{s}}^{-2}$ is equivalent to which of the following?