Calculate the standard enthalpy change of following reaction.

$$ \mathrm{C}_2 \mathrm{H}_{4(\mathrm{~g})}+3 \mathrm{O}_{2(\mathrm{~g})} \longrightarrow 2 \mathrm{CO}_{2(\mathrm{~g})}+2 \mathrm{H}_2 \mathrm{O}_{(l)} $$

If $\Delta_{\mathrm{f}} \mathrm{H}^{\circ}\left(\mathrm{C}_2 \mathrm{H}_4\right)=-52 \mathrm{~kJ} \mathrm{~mol}^{-1}$

$$ \begin{aligned} & \Delta_{\mathrm{f}} \mathrm{H}^{\circ}\left(\mathrm{CO}_2\right)=-390 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ & \Delta_{\mathrm{f}} \mathrm{H}^{\circ}\left(\mathrm{H}_2 \mathrm{O}\right)=-286 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned} $$

If $3 \sin 2 \theta=2 \sin 3 \theta$ and $0<\theta<\pi$, then the value of $\sin \theta$ is equal to

The number of integral values of $k$ for which $x^2+y^2+\mathrm{k} x+(1-\mathrm{k}) y+5=0$ represents a circle whose radius cannot exceeds 5 , are

In a triangle ABC with usual notations if $|\overline{\mathrm{BC}}|=8,|\overline{\mathrm{CA}}|=7,|\overline{\mathrm{AB}}|=10$ then the projection of $\overline{\mathrm{AB}}$ on $\overline{\mathrm{AC}}$ is