IIT JEE DPP-Set Theory1 Welcome to your IIT JEE DPP-Set Theory1 Chapter Wise Test Topic - Set Theory Maximum Marks : 120 Marking Scheme: (+4) for Correct & (-1) for incorrect answer Time: 60Mins Please Don't Cheat! Name Email Phone 1. Let $A=\{(1,2),(3,4), 5\}$, then which of the following is incorrect? Deselect Answer $\{3,4\} \notin \mathrm{A}$ as $(3,4)$ is an element of $\mathrm{A}$ $\{5\},\{(3,4)\}$ are subsets of A but not elements of A $\{1,2\},\{5\}$ are subsets of $A$ $\{(1,2),(3,4), 5\}$ is subset of $A$ 2. A market research group conducted a survey of 1000 consumers and reported that 720 consumers liked product A and 450 consumers liked product $\mathrm{B}$. What is the least number that must have liked both products ? Deselect Answer 170 280 220 None of These 3.One of the partitions of the set $\{1,2,5, x, y, \sqrt{2}, \sqrt{3}\}$ is Deselect Answer $\{\{1,2, \mathrm{x}\},\{\mathrm{x}, 5, \mathrm{y}\},\{\sqrt{2}, \sqrt{3}\}\}$ $\{\{1,2, \sqrt{2}\},\{\mathrm{x}, \mathrm{y}, \sqrt{2}\},\{5, \sqrt{2}, \sqrt{3}\}\}$ $\{\{1,2\},\{5, \mathrm{x}\},\{\sqrt{2}, \sqrt{3}\}\}$ $\{\{1,2,5\},\{\mathrm{x}, \mathrm{y}\},\{\sqrt{2}, \sqrt{3}\}\}$ 4. Let $\mathrm{A}$ and $\mathrm{B}$ be two sets then $(\mathrm{A} \cup \mathrm{B})^{\prime} \cup\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)$ is equal to Deselect Answer $\mathrm{A}^{\prime}$ $\mathrm{A}$ None of these 5. Let $\mathrm{A}=\{(\mathrm{n}, 2 \mathrm{n}): \mathrm{n} \in \mathrm{N}\}$ and $\mathrm{B}=\{(2 \mathrm{n}, 3 \mathrm{n}): \mathrm{n} \in \mathrm{N}\}$. What is $\mathrm{A} \cap \mathrm{B}$ equal to ? Deselect Answer $\{(\mathrm{n}, 6 \mathrm{n}): \mathrm{n} \in \mathrm{N}\}$ $\{(2 n, 6 n): n \in N\}$ $\{(n, 3 n): n \in N\}$ $\phi$ 6. If $a \mathrm{~N}=\{\mathrm{ax}: \mathrm{x} \in \mathbf{N}\}$ and $\mathrm{bN} \cap \mathrm{cN}=\mathrm{dN}$, where $\mathrm{b}, \mathrm{c} \in \mathbf{N}$ are relatively prime, then Deselect Answer $d=b c$ $c=b d$ $b=c d$ None of these 7. In a class of 55 students, the number of students studying different subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is Deselect Answer 6 9 7 All of these 8. A set A has 3 elements and another set B has 6 elements.Then Deselect Answer $3 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 6$ $3 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 9$ $5 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 9$ $0 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 9$ 9. If $\mathrm{A}=\{1,2,5\}$ and $\mathrm{B}=\{3,4,5,9\}$, then $\mathrm{A} \Delta \mathrm{B}$ is equal to Deselect Answer $\{1,2,5,9\}$ $\{1,2,3,4,9\}$ $\{1,2,3,4,5,9\}$ None of these 10. At a certain conference of 100 people, there are 29 Indian women and 23 Indian men. Of these Indian people 4 are doctors and 24 are either men or doctors. There are no foreign doctors. How many foreigners and women doctors are attending the conference? Deselect Answer 48,1 34,3 46,4 42,2 11. Let $X$ and $Y$ be two non-empty sets such that $X \cap A=Y \cap A=\phi$ and $X \cup A=Y \cup A$ for some non-empty set $A$. Then Deselect Answer $X$ is a proper subset of $Y$ $Y$ is a proper subset of $X$ $X=Y$ $X$ and $Y$ are disjoint sets 12. Let $A$ and $B$ are two sets in a universal set $U$. Then which of these is/are correct? Deselect Answer $\mathrm{A}-\mathrm{B}=\mathrm{A}^{\prime}-\mathrm{B}^{\prime}$ $\mathrm{A}-(\mathrm{A}-\mathrm{B})=\mathrm{A} \cap \mathrm{B}$ $\mathrm{A}-\mathrm{B}=\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}$ $A \cup B=(A-B) \cup(B-A) \cup(A \cap B)$ 13. If $A$ and $B$ are non-empty sets such that $A \supset B$, then Deselect Answer $\mathrm{B}^{\prime}-\mathrm{A}^{\prime}=\mathrm{A}-\mathrm{B}$ $\mathrm{B}^{\prime}-\mathrm{A}^{\prime}=\mathrm{B}-\mathrm{A}$ $\mathrm{A}^{\prime}-\mathrm{B}^{\prime}=\mathrm{A}-\mathrm{B}$ $\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}=\mathrm{B}-\mathrm{A}$ 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 buy newspaper C. $5 \%$ families buy $\mathrm{A}$ and B, $3 \%$ buy $B$ and $C$ and $4 \%$ buy $A$ and $C$. If $2 \%$ families buy all the newspapers, then Deselect Answer 3,300 families buy A only 1,400 families buy B only. 4000 families buy none of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ All are correct 15. In a battle $70 \%$ of the combatants lost one eye, $80 \%$ an ear, $75 \%$ an arm, $85 \%$ a leg, $x \%$ lost all the four limbs. The minimum value of $x$ is Deselect Answer 10 12 15 None of these 16. Let $n(\mathrm{U})=700, n(\mathrm{~A})=200, n(\mathrm{~B})=300, n(\mathrm{~A} \cap \mathrm{B})=100$, then $n\left(\mathrm{~A}^{\prime} \cap \mathrm{B}^{\prime}\right)$ is equal to Deselect Answer 400 600 300 None of these 17. Statement-1 : If $\mathrm{B}=\mathrm{U}-\mathrm{A}$, then $n(\mathrm{~B})=n(\mathrm{U})-n(\mathrm{~A})$ where $\mathrm{U}$ is universal set. Statement-2 : For any three arbitrary set A, B, C we have if $\mathrm{C}=\mathrm{A}-\mathrm{B}$, then $n(\mathrm{C})=n(\mathrm{~A})-n(\mathrm{~B})$. Deselect Answer Statement - 1 is true, Statement- 2 is true; Statement $-2$ is a correct explanation for Statement-1. Statement $-1$ is true, Statement- 2 is true; Statement $-2$ is not a correct explanation for Statement-1. Statement -1 is false, Statement- 2 is true. Statement $-1$ is true, Statement- 2 is false. 18. Each student in a class of 40 , studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is Deselect Answer 7 5 10 4 19. In a class of 80 students numbered a to 80 , all odd numbered students opt of Cricket, students whose numbers are divisible by 5 opt for Football and those whose numbers are divisible by 7 opt for Hockey. The number of students who do not opt any of the three games, is Deselect Answer 13 24 28 52 20. In a class of 60 students, 23 play Hockey 15 Play Basket-ball and 20 play cricket. 7 play Hockey and Basket-ball, 5 play cricket and Basket-ball, 4 play Hockey and Cricket and 15 students do not play any of these games. Then Deselect Answer 4 play Hockey, Basket-ball and Cricket 20 play Hockey but not Cricket 1 plays Hockey and Cricket but not Basket-ball All above are correct 21. The set $(A \backslash B) \cup(B \backslash A)$ is equal to Deselect Answer $[A \backslash(A \cap B)] \cap[B \backslash(A \cap B)]$ $(A \cup B) \backslash(A \cap B)$ $A \backslash(A \cap B)$ $\overline{A \cap B} \backslash A \cup B$ 22. If $\mathrm{A}$ is the set of the divisors of the number $15, \mathrm{~B}$ is the set of prime numbers smaller than 10 and $\mathrm{C}$ is the set of even numbers smaller than 9 , then $(\mathrm{A} \cup \mathrm{C}) \cap \mathrm{B}$ is the set Deselect Answer $\{1,3,5\}$ $\{2,3,5\}$ $\{1,2,3\}$ $\{2,5\}$ 23. Two finite sets have $m$ and $n$ elements. The number of subsets of the first set is 112 more than that of the second set. The values of $m$ and $n$ are, respectively, Deselect Answer 4,7 7,4 4,4 7,7 24. The number of students who take both the subjects mathematics and chemistry is 30 . This represents $10 \%$ of the enrolment in mathematics and $12 \%$ of the enrolment in chemistry. How many students take at least one of these two subjects? Deselect Answer 520 560 490 480 25. If $n(\mathrm{~A})=1000, n(\mathrm{~B})=500$ and if $n(\mathrm{~A} \cap \mathrm{B}) \geq 1$ and $n(\mathrm{~A} \cup \mathrm{B})=p$, then Deselect Answer $500 \leq p \leq 1000$ $1001 \leq p \leq 1498$ $1000 \leq p \leq 1498$ $1000 \leq p \leq 1499$ 26. The number of elements in the set $\left\{(a, b): 2 a^{2}+3 b^{2}=35, a, b \in \mathrm{Z}\right\}$, where $\mathrm{Z}$ is the set of all integers, is Deselect Answer 2 4 8 12 27. Let A, B, C be finite sets. Suppose that $n(A)=10, n(B)=15, n$ $(C)=20, n(A \cap B)=8$ and $n(B \cap C)=9$. Then the possible value of $n(A \cup B \cup C)$ is Deselect Answer 26 27 28 Any of the Three Values 26, 27, 28 Possible 28. The value of $(\mathrm{A} \cup \mathrm{B} \cup \mathrm{C}) \cap\left(\mathrm{A} \cap \mathrm{B}^{c} \cap \mathrm{C}^{c}\right)^{c} \cap \mathrm{C}^{c}$, is Deselect Answer $\mathrm{B} \cap \mathrm{C}^{c}$ $\mathrm{B}^{c} \cap \mathrm{C}^{c}$ $\mathrm{B} \cap \mathrm{C}$ $\mathrm{A} \cap \mathrm{B} \cap \mathrm{C}$ 29. In a town of 10,000 families it was found that $40 \%$ family buy newspaper A, $20 \%$ buy newspaper B and $10 \%$ families buy newspaper C, $5 \%$ families buy $\mathrm{A}$ and $\mathrm{B}, 3 \%$ buy $\mathrm{B}$ and $\mathrm{C}$ and $4 \%$ buy $\mathrm{A}$ and $\mathrm{C}$. If $2 \%$ families buy all the three newspapers, then number of families which buy A only is Deselect Answer 3100 2900 3300 2400 30. Statement-1 : If $\mathrm{A} \cup \mathrm{B}=\mathrm{A} \cup \mathrm{C}$ and $\mathrm{A} \cap \mathrm{B}=\mathrm{A} \cap \mathrm{C}$, then $\mathrm{B}=\mathrm{C}$. Statement-2 $: \mathrm{A} \cup(\mathrm{B} \cap \mathrm{C})=(\mathrm{A} \cup \mathrm{B}) \cap(\mathrm{A} \cup \mathrm{C})$. Deselect Answer Statement $-1$ is true, Statement- 2 is true; Statement $-2$ is a correct explanation for Statement-1. Statement - 1 is true, Statement- 2 is true; Statement-2 is not a correct explanation for Statement-1. Statement -1 is false, Statement- 2 is true. Statement $-1$ is true, Statement- 2 is false.