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Remesh’s, Mathematics, , [XI MATHEMATICS QUESTION BANK], , CHAPTER 1 - SETS, , is 63, then the number of elements of the, set is ……….., (1), b) If A =  x : x is a letter in the word, , DECEMBER 2020, 1. i), , If U={1,2,3,4,5,6,7,8,9} and, B={3,4,5,6,7}, find, (A) 𝐴 ∪ 𝐵, (B) (𝐴 ∪ 𝐵)′, (2), ii) If P and Q are two sets such that n(P) =12,, n(Q−P) = 7, then which among the, following is the value of 𝑛(𝑃 ∪ 𝑄)?, (1), (A) 12, (B) 7, (C) 19, (D) 5, 2. i) If P = {1,2}, write all subsets of P., (1), ii) If 𝑀 ⊂ 𝑁, then draw the Venn diagram, of 𝑁 − 𝑀., (1), iii) If 𝐴 = {𝑥: 𝑥 ∈ 𝑅, −2 ≤ 𝑥 ≤ 5} and, 𝐵 = {𝑥: 𝑥 ∈ 𝑅, 2 < 𝑥 ≤ 6}, then which, among the following is 𝐴 ∩ 𝐵?, (1), (A) [2,5], (B) (2,5], (C) [2,5), (C) [−2,6], , If A={x:x is a natural number, x<5 and, x>7}, then n(A) is, , a) 1, b) 0, c) 2, d) 3, ii) The set builder form of (6,12) is, a)  x : x  R,6  x  12, , (1), (1), , b)  x : x  R,6  x  12, c)  x : x  R,6  x  12, d)  x : x  R,6  x  12, iii) If A and B are two sets such that, A  B , then A  B is, a) A, b) Null set, c) B, , d) , , (1), , 4. In a survey of 600 students in a school, 150, students were found to be taking tea and 225, students were taking coffee. 100 were taking both, tea and coffee. Find how many students were, taking neither tea nor coffee., (3), IMPROVEMENT 2019, 5. a) If the number of proper subsets of a set, Teaching Mathematics since 1990, , B =  y : y is a letter in the word, , “STATISTICS” , then, find, i) A − B, (ii) A  B, (2), 6. a) In a survey of 600 students in a school, 150 students were found to be taking tea, and 225 taking coffee, 100 were taking, both tea and coffee. Find how many, students were taking neither tea nor, coffee., (2), b) Draw Venn diagrams which represents:, i) ( A  B ), , ii) A  B, , (2), , MARCH 2019, 7. Let A =  x : x is a prime number, , less than 11 and, , MARCH 2020, 3. i), , “ MATHEMATICS ” and, , 𝐵 = {𝑥: 𝑥𝑖𝑠𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 2 ≤ 𝑥 ≤ 8}, a) Write C = A  B, (1), b) Find the number of subsets of C which, has 3 elements., (1), c) What is the probability of getting a subset, of 3 elements from the power set of C?, (1), 8. In a school, a survey among400 students, 100, were listed as taking apple juice, 150 as, taking orange juice, and 75 were listed as, taking both apple juice as well as orange, juice., a) How many students take apple juice or, orange juice?, (2), b) How many take apple juice alone but, not orange juice?, (1), c) How many students were taking neither, apple juice nor orange juice?, (1), IMPROVEMENT 2018, 9. a) If A = 2,3, 4,5 and B = 4,5, 6, 7 ,, then write:, i) A  B, , ii) A  B, , (2), , | [email protected]

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Remesh’s, Mathematics, , [XI MATHEMATICS QUESTION BANK], , b) Which one of the following is equal to,  x : x  R, 2  x  4 ?, i) {2,3,4}, iii) [2,4], , ii) {3,4}, iv) (2,4], , IMPROVEMENT 2017, 14. Let A =  x : x  N , 1  x  5 ; B = 2,3, 6,9, (1), , 10. Consider the set A =  x : x is an integer,, , a) Find the number of elements of A., , a) Write A in Roster form., (1), b) If B = {5,6}, then write A  B ., (1), c) Write the number of possible relations, from A to B., (1), 11. a) If U = {1,2,3,4,5,6,7,8,9}; A = {2,4,6,8}, B = {2,3,5,7},, b) If A and B are two disjoint sets with, n(A) = 4 and n(B) = 2, then n(A −B) =, …………, , (3), , (1), , MARCH 2018, , c) If X and Y are two sets such that, , n ( X ) = 17, n (Y ) = 23 and, , n ( X  Y ) = 38, , then find n ( X  Y ) ., , (2), , MARCH 2017, 15. a) If U is the universal set and A is any set, then U  A = .......... ....., i) U, ii) A, iii) , iv) A, , (1), , b) Consider the set U = a, b, c, d , e, f , g ,, , A = b, c, d , e and B = a , c, g . Find A and, , 12. a) If A = a, b, c , then write the power, set of P(A)., (1), b) If the number of subsets with two, elements of a set P is 10, then find the, total number of elements in the set P., (2), c) Find the number of elements of the, power set of P., (1), 13. Consider a Venn diagram of the Universal set, U = {1,2,3,4,5,6,7,8,9,10,11,12,13}, a) Write sets A, B in Roster form., (1), b) Verify ( A  B ) ' = A  B', (2), c) Find n ( A  B ), , (1), , b) Verify A  ( B  C ) = ( A  B )  ( A  C ) (2), , 0  x  4, , Verify ( A  B ) ' = A  B', , and C = 1, 4,5,8,9,10, , (1), , B  and then verify that ( A  B )' = A  B., , (2), c) In a group of 400 people, 250 can speak, Hindi and 200 can speak Malayalam. How, many people can speak both Hindi and, Malayalam?, , (2), , IMPROVEMENT 2016, 16. If U = 1, 2,3, 4,5, 6, 7,8 , A = 2, 4, 6,8, , and, , B = 2, 4,8 ,then:, a) Write A' and B ', , (1), , b) For the above sets A and B,, , prove that ( A  B ) ' = A  B', , c) Check whether ( A  B ) ' = A '  B ' ., , Teaching Mathematics since 1990, , (2), (2), , | [email protected]

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Remesh’s, Mathematics, , [XI MATHEMATICS QUESTION BANK], , MARCH 2016, , among the following is true?, , 17. a) If A is a subset of the set B, then, , A  B = ..............., , (1), , ii) A  B = B, , iii) A  B = B, , iv) A  B = , , x 2 + x − 2 = 0 in roster form., , (2), , (1), , c) In a group of students, 100 students know, , c) In a school there are 20 teachers who teach, Mathematics or Physics. Of these, 12, , Hindi, 50 know English and 33 know both., , teach Mathematics, 12 teach Physics., , Each of the students know either Hindi or, , How many teach both the subjects?, , (1), , b) Find the solution set of the equation, , b) Represent the above set A  B by Venn, diagram., , i) A  B = A, , English. How many students are there in, , (2), , the group?, IMPROVEMENT 2015, 18. a), , MARCH 2014, , A = {x / x , is a prime number , x  6} ., i), , Represent A in roster form., , ii) Write the power set of A., , (1), (2), , b) Out of 25 members in an office 17 like to, , 21. Consider the sets A = 2,3,5, 7 and, , B = 1, 2,3, 4, 6,12 ., a) Find A  B, b) Find A − B, B − A and hence show that, , take tea, 16 like to take coffee. Assume, , ( A  B )  ( A − B )  ( B − A) = A  B, , that each takes at least one of the two, , (3), (1), , IMPROVEMENT 2013, , Both coffee and tea?, , ii) Only tea and not coffee?, , (1), , c) Write the power set of A  B ., , drinks. How many like:, i), , (3), , (2), , 22. If A and B are two sets such that A  B ,, a), , A  B is ……………, , (1), , MARCH 2015, , b) Draw the Venn diagram of B − A, , 19. Let A = {x : x  W , x  5} and, , c) In a committee, 60 people speak English,, , (2), , B = {x : x is a prime number less than 5}, , 30speak Hindi and 15 speak both English and, , U = {x : x is an integer, 0  x  6} ,, , Hindi. How many speak atleast one of these, , a) Write A, B in roster form., b) Find ( A − B )  ( B − A ), , c) Verify that ( A  B ) = A  B, IMPROVEMENT 2014, , (1), , two languages?, , (2), , (2), , MARCH 2013, , (2), , 23. Let U = 1, 2,3, 4,5, 6, 7,8,9 ; A = 1, 2, 4, 7, and B = 1,3,5, 7, a) Find A  B, , (1), , 20. a) If two sets A and B are disjoint, which one, Teaching Mathematics since 1990, , | [email protected]

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Remesh’s, Mathematics, , [XI MATHEMATICS QUESTION BANK], , A =  x : x is a prime number  10, , b) Find A , B and hence show that, , c), , ( A  B ) ' = A ' B ' ., The power set P ( A  B ), , (2), has, , ………elements., , (1), , IMPROVEMENT 2012, , B =  x : x is a natural number which divides 12, a) Write A and B in the roster form., , (2), , b) Find A  B and B − A ., , (2), , c) Verify that ( A  B ) − A = B − A ., , (1), , 24. i) How many elements has P ( A ) ,, , if A = 1, 2,3 ?, , (1), , ii) U = 1, 2,3, 4,5, 6, 7 ; A = 1, 4, 6, 7 ; and, , IMPROVEMENT 2010, 28. Which among the following is a finite set?, , B = 1, 2,3. Find A ', B ', A ' B ', A  B ., , a), , Hence show that ( A  B ) ' = A ' B ' ., , b), , iii) If A and B are two sets such that A  B, then what is A  B ?, , (3), (1), , c), d), , MARCH 2012, 25. Let A =  x : x is an integer,, , B = 2,3, 4, , 1, 7, x , 2, 2, , a) Write A in the roster form., b) Find the power set of A  B ., c) Verify that ( A − B )  ( A  B ) = A, , , , (1), (2), (2), , 26. Let U =  x : x is a integer , − 4  x  4 be the, , A =  x : x is a integer , 0  x  3 and, , , , , , and U = 1 , 2 , 3 ,1, 2,3 , then find, a), , A B ., , (1), , b) B  C, c), , (1), , n ( A  B )  ( B  C ) , , , , (2), , 30. Consider, , B =  x : x is a integer , − 3  x  1 are the subset, , c) Write the power set of A  B ., , , , MARCH 2010, , universal set., , b) Verify ( A  B ) ' = A ' B ' ., ,  x : x is an integer less than 1,  x : x is an integer, which is divisible by 7,  x : x is a prime number less than 910 ,  x : x R  Q; R, set of real numbers, Q,set of rational numbers, , 29. If A =  1 , B = 1 , 2 , C = 1 ,3, , IMPROVEMENT 2011, , of U., a) Write A and B in the roster form., , (2), (2), (1), , A =  x : x is a natural number , 2  x  6, , B =  x : x is a prime number , x  7, , C =  x : x 2 − 5 x + 6 = 0, , a) Write A,B,C in the roster form., (3), A, , B, , C, =, A, , B, , C, b) Verify that (, ), (, ) (2), , MARCH 2011, , IMPROVEMENT 2009, , 27. Consider the set A and B given by, , 31. Let A = x : x  R, x 2 − 5 x + 6 = 0, , , , , , B = {x : x  R, x 2 = 9}, Teaching Mathematics since 1990, , (1), , | [email protected]

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Remesh’s, Mathematics, , [XI MATHEMATICS QUESTION BANK], , a) Write A and B in roster form, , (1), , b) Find A  B and A  B, , (1), , c) Find A − B , B − A and verify that, , ( A − B )  ( B − A) = ( A  B ) − ( A  B ), , (2), , MARCH 2009, 32. Let U= 1, 2,3, 4,5, 6, 7,8 , A = 2, 4, 6,8, and B = 2, 4,8, a) Find A and B , , (1), , b) Also find ( A  B ), , (1), , c) Verify ( A  B ) = A  B, , (2), , MARCH 2008, 33. i) If X = a, b, c, d  and Y =  f , b, d , g  ,, , then find X − Y and X  Y ., , (2), , ii) State whether the following is True or, False: If A  B then A  B = B., , Teaching Mathematics since 1990, , (2), , | [email protected]