$A$ candle flame of $3\, cm$ is placed at $3\, m$ from a wall. $A$ concave mirror is kept at a distance $x$ from the wall in such a way that the image of the flame on the wall is $9\, cm$. Then $x$ is......$cm$.

For a concave mirror,the $\frac{1}{u}$ versus $\frac{1}{v}$ graph obtained by the parallax method is as shown in the figure. The graph is a straight line with a slope of $-1$. The estimated value of the focal length of the mirror is: (in $cm$)

$A$ square wire frame of side length $3.0 \, cm$ is placed $25 \, cm$ away from a concave mirror of focal length $10 \, cm$. The center of the wire frame is on the axis of the mirror,with two of its sides perpendicular to the axis. The area of the image will be $..... \, cm^2$.

$A$ short linear object of length $l$ lies along the axis of a concave mirror of focal length $f$ at a distance $u$ from the pole of the mirror. The size of the image is approximately equal to

Incident parallel rays make an angle of $5^{\circ}$ with the axis of a concave mirror of focal length $20 \ cm$. The perpendicular distance of the image from the axis is nearly $-$ (in $cm$)

The sun (diameter $d$) subtends an angle $\theta$ radian at the pole of a concave mirror of focal length $f$. What is the diameter of the image of the sun formed by the mirror?