There are 10 parallel lines intersected by a family of 5 parallel lines. The number of parallelograms thus formed in the net work is

A set of 10 parallel lines intersect a family of 5 parallel lines.

No of parallelograms formed=Number of ways of selecting two lines from each set of parallel lines

No of parallelograms formed$=10{\mathrm{C}}_2\times 5{\mathrm{C}}_2$

$$\begin{gathered} =\frac{10\times 9}{1\times 2}\times \frac{5\times 4}{1\times 2} \\ =450 \end{gathered}$$