$A$ convergent lens is placed $40 \,cm$ to the right of a diverging lens of focal length $15 \,cm$. $A$ parallel beam of light enters the diverging lens from the left, and the beam is again parallel when it emerges from the convergent lens. The focal length of the convergent lens is (in $\,cm$)

Two thin convex lenses are kept in contact coaxially. If the focal length of the combination of the lenses is $4 \ cm$ and the sum of the focal lengths of the two lenses is $18 \ cm$,then the focal length of the lens of lower power is (in $cm$)

Two similar thin equi-convex lenses,each of focal length $f$,are kept coaxially in contact with each other such that the focal length of the combination is $F_{1}$. When the space between the two lenses is filled with glycerin (which has the same refractive index $\mu = 1.5$ as that of glass),the equivalent focal length is $F_{2}$. The ratio $F_{1} : F_{2}$ will be

$A$ combination of two thin lenses with focal lengths $f_1$ and $f_2$ respectively forms an image of a distant object at a distance of $60 \ cm$ when the lenses are in contact. The position of this image shifts by $30 \ cm$ towards the combination when the two lenses are separated by $10 \ cm$. The corresponding values of $f_1$ and $f_2$ are:

Two lenses are placed in contact with each other and the focal length of the combination is $80 \ cm$. If the focal length of one lens is $20 \ cm$,then the power of the other lens will be: (in $D$)

Two lenses of power $6D$ and $-2D$ are combined to form a single lens. The focal length of this lens will be (in $m$)