The utility of a microorganism like $Trichoderma$ $harzianum$ has been proven in which of the following?

Which of the following statements is $NOT$ correct for potash alum?

$A$ thin prism $P_1$ with angle $4^o$ and made from a glass of refractive index $1.54$ is combined with another thin prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of the prism $P_2$ is.....$^o$

Which one of the following statements is not correct?

When $MnO_2$ is fused with $KOH$ in the presence of air,a coloured compound is formed. Identify the product and its colour.

If $x=a\left[\cos \theta+\log \left\{\tan \left(\frac{\theta}{2}\right)\right\}\right]$ and $y=a \sin \theta$,then $\frac{dy}{dx}$ is equal to