Question

State $T$ for true and $F$ for false. In a class of $140$ students, $60$ play football, $74$ play hockey and $75$ play cricket, $30$ play hockey and cricket, $18$ play football and cricket, $42$ play football and hockey and $8$ play all the three games. Then (i) The number of students who do not play any of these three games is $42$. (ii) The number of students who play only cricket is $35$. (iii) The number of students who play football and hockey, but not cricket is $34$.

• A. a
• B. b
• C. c
• D. d

Answer 1

The Correct Option is B

$n(U) = 140$, $n(F) = 60$, $n(H) = 74$, $n(C) = 75$ $n(F \cap B) = 42$, $H(F \cap C) = 18$, $n(H \cap C) = 30$ $n(F \cap H \cap C ) = 8$ $\therefore n(F \cup H \cup C) = n(F) + n(H) + n(C) + n(F \cap H \cap C)$ $- n(F \cap C ) - n(H \cap C ) - n(F \cap H)$ $= 60 + 74 +75 +8 - 42 - 18 - 30 = 127$ (i) Number of students who do not play any of three games $= n (U) -n(F \cup H \cup C)= 140- 127= 13$ (ii) Number of students who play only cricket $= 75 - (10 + 8 + 22) = 75 - 40 = 35$ (iii) Number of students who play football and hockey, but not cricket $= n (F \cap H) - n(F \cap H \cap C) = 42 - 8 = 34$