Five lumen/watt is the luminous efficiency of a lamp and its luminous intensity is $35$ candela. The power of the lamp is.......$W$

For a candle of $40$ power,the exposure time required for a photographic print at a distance of $0.6 \, m$ is $20 \, s$. What will be the exposure time required for the same print at a distance of $1.2 \, m$ using a candle of $20$ power?

$A$ convex lens of focal length $30\,cm$,a concave lens of focal length $120\,cm$,and a plane mirror are arranged as shown. For an object kept at a distance of $60\,cm$ from the convex lens,the final image,formed by the combination,is a real image at a distance of:

For a concave mirror, if a virtual image is formed, the graph between $m$ and $u$ is of the form:

$A$ particle is oscillating on the $X-$ axis with an amplitude $2\, cm$ about the point $x_0 = 10\, cm$ with a frequency $\omega $. $A$ concave mirror of focal length $5\, cm$ is placed at the origin (see figure). Identify the correct statements.
$(A)$ The image executes periodic motion
$(B)$ The image executes non-periodic motion
$(C)$ The turning points of the image are asymmetric w.r.t the image of the point at $x = 10\, cm$
$(D)$ The distance between the turning points of the oscillation of the image is $\frac{100}{21}\, cm$

$A$ container is filled with water $(\mu = 1.33)$ up to a height of $33.25\ cm$. $A$ concave mirror is placed $15\ cm$ above the water level and the image of an object placed at the bottom is formed $25\ cm$ below the water level. The focal length of the mirror is (in $cm$)