Explanation

(d) The image formation by a convex lens is as follows
Image formed is diminished, when objects lies between $2F$ and infinity.
Magnification
$(M) = \frac{image\ size}{object\ size}$
$= \frac{1}{2} = \frac{v}{u}\ \ \ \ \ldots.(i)$
From lens formula
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\ \ \ldots.(ii)$
Where, $f$ is focal length, $v$ the image distance and $u$ the object distance.
From eqs. (i) and (ii), we get
$\frac{1}{f} = \frac{1}{u} + \frac{2}{u}$
As $\ u = 90\ cm$
$\frac{1}{30} = \frac{3}{u}$
$\Longrightarrow u = 90\ cm$