2. Solved Papers
  3. BCECE Engineering

BCECE Engineering BCECE Engineering Solved Paper-2015

  • question_answer
    From 50 students taking examinations in 1 Mathematics, Physics and Chemistry, 37 passed in Mathematics, 24 in Physics and 43 in Chemistry. Atmost 19 passed in Mathematics and Physics, atmost 29 passed in Mathematics and Chemistry and atmost 20 passed in Physics and Chemistry. The largest possible-number that could have passed all three examinations, is

    A)  11                         

    B)  12    

    C)  13                         

    D) 14

    Correct Answer: D

    Solution :

    Let M,P and C be the sets of students taking examinations in Mathematics, Physics and Chemistry, respectively. We have, \[n(M\cup P\cup C)=50,n(M)=37,n(P)=24,\] \[n(C)=43\]                 \[n(M\cap P)<19,n(M\cap C)\le 29,n(P\cap C)\le 20\]                 Now, \[n(M\cup P\cup C)=n(M)+n(P)+n(C)\] \[-n(M\cap P)\]\[-n(M\cap C)-n(P\cap C)+n\] \[(M\cap P\cap C)\] \[\Rightarrow \]\[50=37+24+43-\{n(M\cap P)+n(M\cap C)\] \[+n(P\cap C)\}\]\[+n(M\cap P\cap C)\] \[\Rightarrow \]\[n(M\cap P\cap C)=n(M\cap P)+n(M\cap C)\] \[+n(P\cap C)-54\] \[\Rightarrow \]\[n(M\cap P)+n(M\cap C)+n(P\cap C)\] \[=n(M\cap P\cap C)+54\]                                           ? (i) Now, \[n(M\cap P)\le 19,n(M\cap C)\le 29,\]                                 \[n(P\cap C)\le 20\] \[\Rightarrow \]               \[n(M\cap P)+n(M\cap C)+n(P\cap C)\] \[\le 19+29+20\] [using Eq. (i)]                 \[\Rightarrow \]               \[n(M\cap P\cap C)+54\le 68\]                 \[\Rightarrow \]               \[n(M\cap P\cap C)\le 14\]


You need to login to perform this action.
You will be redirected in 3 sec spinner