There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then, the number of students failing in all the three subjects

• A

  is 12
• B

  is 4
• Correct answer
  C

  is 2
• D

  cannot be determined from the given information

Solution

According to question,
$\begin{array}{c}<br />a+b+c+d+e+f+g+h=100 \\<br />h=1 \\<br />a+b+d+e=50<br />\end{array}$

Venn diagram shows failed students $b+c+d+f=45$
$\begin{array}{l}<br />d+e+f+g=40 \\<br />b+e+f=32<br />\end{array}$
On solving, the above equations, we get $d=2$

Hence, the correct answer is option: 'C'.