The figure shows a closed dotted surface which intersects a conducting uncharged sphere. If a positive charge is placed at the point $P$, the flux of the electric field through the closed surface

The correct option is C will become negative.
When a positive charge is placed at $P$, in front of a conducting sphere, the surface facing charge $q$ will become negatively charged due to induction.


However, due to conservation of total charge, the opposite surface becomes positively charged.
So, the charge enclosed ($q_{in}$) by the dotted Gaussian surface is negative.
Thus, by Gauss's law
Electric flux, $\varphi =\frac{q_{in}}{{ϵ}_o}$
Hence, flux through the closed surface is negative.