JEE PYQ: Permutation And Combination Question 42
Question 42 - 2019 (10 Jan Shift 1)
In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is:
(1) 102
(2) 42
(3) 1
(4) 38
Show Answer
Answer: (4)
Solution
Using inclusion-exclusion: Math (even): 70, Physics (div 3): 46, Chemistry (div 5): 28. Div 6: 23, div 10: 14, div 15: 9, div 30: 4. Union $= 70 + 46 + 28 - 23 - 14 - 9 + 4 = 102$. Not opted $= 140 - 102 = 38$.
BETA
