Q.1. In a survey of 400 students in a school, 100 were listed as taking apple juice. 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.
Q.2. There are 200 individuals with a skin disorder, 120 had been exposed to chemical C1, 50 to chemical C2, and 30 to both chemicals C1 and C2. Find the number of individuals exposed to Chemical C1, but not chemical C2, (ii) Chemical C2 but not chemical C1, (iii) Chemical C1 or chemical C2.
Q.3. A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports?
Q.4. In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H & I, 11 read both H and T. 8 read both T & I, 3 read all three newspapers. Find: (i) The number of people who read at least one of the newspapers. (ii) The number of people who read exactly one newspaper.
Q.5. From 50 students taking examinations in Mathematics, Physics and Chemistry, each of the student 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. What is the largest possible number that could have passed all three examinations?
Q.6. In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A & B, 12 people liked products C & A, 14 people liked products B & C and 8 liked all the three products. Find how many liked product C only.
Q.7. In a survey of 25 students, it was found that 15 had taken mathematics, 12 had taken physics and 11 had taken chemistry, 5 had taken mathematics and chemistry, 9 had taken mathematics and physics, 4 had taken physics and chemistry and 3 had taken all the 3 subjects. Find the number of students that had (i) only chemistry,(ii) physics and chemistry, but not mathematics, (iii) only one of the subjects, (iv) at least one of the three subjects, (v) none of the subjects.
Q.8. For all set A, B and C is (A ∩ B) ∪ C = A ∩ (B ∪ C)? Justify your answer.
Q.9. Is it true that for any sets A and B, P (A) ∪ P (B) = P ( A ∪ B ) ? Justify your answer.
Q.10. Two sets A and B are such that n( A ∪ B ) = 21 , n( A ) = 10 & n( B ) = 15 find the value of n( A ∩ B ) and n( A-B).
Lesson = 3 [ Trigonometric Functions ] Important Questions
Q.11. Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7} Verify the following identity A ∪ (B ∩ C) = (A ∩ B) ∪ (A ∩ C).
Q.12. Show that A ∪ B = A ∩ B implies A = B.
Q.13. Assume that P(A) = P(B) , Show that A = B.
Q.14. In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families by newspaper C. 5% families buy A and B, 3%, buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, find the no of families which buy(1) A only (2) B only (3) none of A, B and C (4) exactly two newspapers (5) exactly one newspaper (6) A and C but not B (7) at least one of A, B, C. What is the importance of reading newspaper?
Q.15. Let A and B be two events such that P(A)=0.3 and P(A ∪ B)= 0.8. Find P(B), if P(A ∩ B) = P(A) P(B).
Q.16. A survey shows that 63% of the people watch a News channelwhereas 76% watch another channel. If %% of the people watch both channel, then findthe interval in which % lies.
Q.17. Let A, B and C be sets. Then show that
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
Q.18. Let A, B and C be sets. Then show that
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
Q.19. For all sets A and B, (A – B)∪ (A∩ B) = A
Q.20. In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows: French = 17, English = 13, Sanskrit = 15, French and English = 09, English and Sanskrit = 4,French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study
(i) French only(ii) English only
(iii) Sanskrit only
(iv) English and Sanskrit
(v) French and Sanskrit but not English
(vi) French and English but not Sanskrit
(vii) at least one of the three languages
(viii) none of the three languages but not French
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