Disha Expert Team Solutions for Chapter: Set Theory, Exercise 1: Exercise

In an examination out of $100$ students, $75$ passed in English $60$ passed in Mathematics and $45$ passed in both English and Mathematics. What is the number of students passed in exactly one of the two subjects?

In a car agency one day, $120$ cars were decorated with three different accessories' viz., power window, AC and music system. $80$ cars were decorated with power windows, $84$ cars were decorated with AC and $80$ cars were decorated with music systems. What are the minimum and the maximum number of cars which were decorated with all three accessories?

In an examination, $70\%$ of the candidates passed in English, $65\%$ in Mathematics, $27\%$ failed in both the subjects. If $248$ candidates passed in both the subjects, then find the total number of candidates?

Out of $800$ boys in a school, $224$ played cricket, $240$ played hockey and $336$ played basketball. Of the total, $64$ played both basketball and hockey, $80$ played cricket and basketball, $40$ played cricket and hockey and $24$ played all three games. The number of boys who did not play any game is:

From $50$ students taking the examination in Mathematics, Physics and Chemistry, each of the students has passed in at least one of the subject, $37$ passed Mathematics, $24$ Physics and $43$ Chemistry. At most $19$ passed Mathematics and Physics, at most $29$ Mathematics and Chemistry and at most $20$ Physics and Chemistry. Then, the largest numbers that could have passed all three examinations are:

A market research group conducted a survey of $2000$ consumers and reported that $1720$ consumers like product $P_1$ and $1450$ consumers like product $P_2$. What is the least number that must have liked both the products?

ln a town of $10000$ families, it was found that 40% families buy newspaper A, $20\%$ families buy newspaper B and $10\%$ families buy newspaper C. $5\%$ buy A and B, $3\%$ buy B and C and $4\%$ buy A and C. If $2\%$ families buy all of three newspapers, then the number of families which buy A only, is _____.

A survey of $500$ television viewers produced the following information. $285$ watch football, $195$ watch hockey, $115$ watch basketball, $45$ watch football and basketball, $70$ watch football and hockey, $50$ watch hockey and basketball, $50$ do not watch any of the three games. The number of viewers, who watch exactly one of the three games are: