The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines, is
Answer & explanation
Answer: (d) 36
Every choice of two lines from each family encloses exactly one parallelogram, so the count is 4C2 × 4C2 = 6 × 6 = 36.
- A parallelogram needs two lines from the first set and two from the second.
- Ways to choose 2 lines out of 4 = 4C2 = 6, for each set.
- Parallelograms = 6 × 6 = 36.
Remember · m parallel lines crossing n parallel lines form mC2 × nC2 parallelograms.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·