If the radii of curvature of both convex surfaces of a lens are $20 \, cm$,find the focal length of the lens in the given arrangement. (in $, cm$)

Look at the ray diagram shown. What will be the focal length of the $1^{st}$ and the $2^{nd}$ lens,if the incident light ray passes without any net deviation?

The word $KVPY$ is written on a board and viewed through different lenses such that the board is at a distance beyond the focal length of the lens.
Ignoring magnification effects,consider the following statements.
$(I)$ First image has been viewed from the planar side of a plano-concave lens and second image from the planar side of a plano-convex lens.
$(II)$ First image has been viewed from the concave side of a plano-concave lens and second image from the convex side of a plano-convex lens.
$(III)$ First image has been viewed from the concave side of a plano-concave lens and second image from the planar side of a plano-convex lens.
$(IV)$ First image has been viewed from the planar side of a plano-concave lens and second image from the convex side of a plano-convex lens.
Which of the above statements are correct?

The graph between $\frac{1}{u}$ and $\frac{1}{v}$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of the lens is $1.5$ and both its surfaces have the same radius of curvature $R$. The value of $R$ will be in $cm$.
(Where $u =$ object distance,$v =$ image distance)

$A$ candle placed $25 \ cm$ from a lens forms an image on a screen placed $75 \ cm$ on the other side of the lens. The focal length and type of the lens should be

Two convex lenses of focal lengths $f_1$ and $f_2$ form images with magnification $m_1$ and $m_2$,when used individually for an object kept at the same distance from the lenses. Then,$f_1 / f_2$ is