In an astronomical telescope in normal adjustment,a straight black line of length $L$ is drawn on the objective lens. The eyepiece forms a real image of this line. The length of this image is $l$. The magnification of the telescope is

The product of the lengths of the perpendiculars from any point on the hyperbola $x^2-y^2=8$ to its asymptotes is

Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $k_1$ and $k_2$ respectively. $A$ steady temperature difference of $12^{\circ} C$ is maintained across the composite slab. If $k_1 = \frac{k_2}{2}$,the temperature difference across slab $A$ is (in $^{\circ} C$)

One mole of the complex compound $Co(NH_3)_5Cl_3$ gives $3$ moles of ions on dissolution in water. One mole of the same complex reacts with two moles of $AgNO_3$ solution to yield two moles of $AgCl_{(s)}$. The structure of the complex is :-

Two rain drops reach the earth with different terminal velocities having ratio $9:4$. Then the ratio of their volumes is

In which of the following reactions is an aromatic aldehyde treated with an acid anhydride in the presence of the corresponding salt of the acid to give an unsaturated aromatic acid?