Three forces acting on a body are shown in the figure. To have the resultant force only along the $y-$ direction,the magnitude of the minimum additional force needed is.........$N$.

Which of the following halides has the maximum melting point?

$CH_3COOH \xrightarrow{LiAlH_4} A$
$A + CH_3COOH \xrightarrow{H_3O^{+}} B + H_2O$
In the above reactions '$A$' and '$B$' respectively are

Evaluate the following determinants: $(i)$ $\left|\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right|$ (ii) $\left|\begin{array}{cc}x^{2}-x+1 & x-1 \\ x+1 & x+1\end{array}\right|$

$A$ glass capillary tube of inner diameter $0.28 \ mm$ is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that the water level in the tube is the same as that in the vessel (in $N/m^2$) is:
(Surface tension of water $= 0.07 \ N/m$,Atmospheric pressure $= 10^5 \ N/m^2$)

Three waves of equal frequency having amplitudes $10\, \mu m, 4\, \mu m$ and $7\, \mu m$ arrive at a given point with successive phase difference of $\pi/2$. The amplitude of the resulting wave in $\mu m$ is given by