Question

There are 3 straight lines, 4 circles and 5 parabolas in xy plane. Maximum number of their intersection point, is

• A. 129
• B. 149
• C. 169
• D. 189

Answer 1

Answer: (D)

Line v/s line: ${}^3{C}_2\cdot 1=3$
Circle v/s circle: ${}^4{C}_2\cdot 2=12$
Parabola v/s Parabola: ${}^5{C}_2\cdot 4=40$
Line v/s Circle: ${}^3{C}_1\cdot {}^4{C}_1\cdot 2=24$
Line v/s Parabola: ${}^3{C}_1\cdot {}^5{C}_1\cdot 2=30$
Circle v/s Parabola: ${}^4{C}_1\cdot {}^5{C}_1\cdot 4=80$
Total $=189$