{"id":17437,"date":"2022-05-25T21:00:29","date_gmt":"2022-05-25T15:30:29","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=17437"},"modified":"2022-05-17T11:07:12","modified_gmt":"2022-05-17T05:37:12","slug":"mcq-questions-for-class-11-maths-chapter-1","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/mcq-questions-for-class-11-maths-chapter-1\/","title":{"rendered":"MCQ Questions for Class 11 Maths Chapter 1 Sets with Answers"},"content":{"rendered":"

Students can access the NCERT MCQ Questions for Class 11 Maths Chapter 1 Sets with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 11 Maths with Answers<\/a> during preparation and score maximum marks in the exam. Students can download the Sets Class 11 MCQs Questions with Answers from here and test their problem-solving skills. Clear all the fundamentals and prepare thoroughly for the exam taking help from Class 11 Maths Chapter 1 Sets Objective Questions.<\/p>\n

Sets Class 11 MCQs Questions with Answers<\/h2>\n

Students are advised to solve the Sets Multiple Choice Questions of Class 11 Maths to know different concepts. Practicing the MCQ Questions on Sets Class 11 with answers will boost your confidence thereby helping you score well in the exam.<\/p>\n

Explore numerous MCQ Questions of Sets Class 11 with answers provided with detailed solutions by looking below.<\/p>\n

Question 1.
\nIf f(x) = log [(1 + x)\/(1 – x), then f(2x )\/(1 + x\u00b2) is equal to
\n(a) 2f(x)
\n(b) {f(x)}\u00b2
\n(c) {f(x)}\u00b3
\n(d) 3f(x)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 2f(x)
\nGiven f(x) = Log [(1 + x)\/(1-x)]
\nNow, f{(2x )\/(1 + x\u00b2)} = Log [{(1 + (2x )\/(1 + x\u00b2))}\/{(1 – (2x )\/(1 + x\u00b2))}]
\n\u21d2 f{(2x )\/(1 + x\u00b2)} = Log [{(1 + x\u00b2 + 2x )\/(1 + x\u00b2))}\/{(1 + x\u00b2 – 2x )\/(1 + x\u00b2))}]
\n\u21d2 f{(2x )\/(1 + x\u00b2)} = Log [(1 + x\u00b2 + 2x )\/{(1 + x\u00b2 – 2x )]
\n\u21d2 f{(2x )\/(1 + x\u00b2)} = Log [(1 + x)2 \/{(1 – x)2]
\n\u21d2 f{(2x )\/(1 + x\u00b2)} = Log [(1 + x)\/{(1 – x)]2
\n\u21d2 f{(2x )\/(1 + x\u00b2)} = 2 \u00d7 Log [(1 + x)\/{(1 – x)]
\n\u21d2 f{(2x )\/(1 + x\u00b2)} = 2 f(x)<\/p>\n<\/details>\n

\n

Question 2.
\nThe smallest set a such that A \u222a {1, 2} = {1, 2, 3, 5, 9} is
\n(a) {3, 5, 9}
\n(b) {2, 3, 5}
\n(c) {1, 2, 5, 9}
\n(d) None of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) {3, 5, 9}
\nGiven, a set A such that A \u222a {1, 2} = {1, 2, 3, 5, 9}
\nNow, smallest set A = {3, 5, 9}
\nSo, A \u222a {1, 2} = {1, 2, 3, 5, 9}<\/p>\n<\/details>\n

\n

Question 3.
\nLet R= {(x, y) : x, y belong to N, 2x + y = 41}. The range is of the relation R is
\n(a) {(2n – 1) : n belongs to N, 1 \u2264 n \u2264 20}
\n(b) {(2n + 2) : n belongs to N, 1 < n < 20}
\n(c) {2n : n belongs to N, 1< n< 20}
\n(d) {(2n + 1) : n belongs to N , 1 \u2264 n \u2264 20}<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) {(2n – 1) : n belongs to N, 1 \u2264 n \u2264 20}
\nGiven,
\n2x + y = 41
\n\u21d2 y = 41 – 2x
\nx : 1 2 3 ………………20
\ny : 39 37 35 ……………..1
\nSo, range is
\n{(2n – 1) : n belongs to N, 1 \u2264 n \u2264 20}<\/p>\n<\/details>\n

\n

Question 4.
\nEmpty set is a?
\n(a) Finite Set
\n(b) Invalid Set
\n(c) None of the above
\n(d) Infinite Set<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) Finite Set
\nIn mathematics, and more specifically set theory, the empty set is the unique set having no elements and its size or cardinality (count of elements in a set) is zero.
\nSo, an empty set is a finite set.<\/p>\n<\/details>\n

\n

Question 5.
\nTwo finite sets have M and N elements. The total number of subsets of the first set is 56 morethan the total number of subsets of the second set. The values of M and N are respectively.
\n(a) 6, 3
\n(b) 8, 5
\n(c) none of these
\n(d) 4, 1<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 6, 3
\nLet A and B be two sets having m and n numbers of elements respectively
\nNumber of subsets of A = 2m<\/sup>
\nNumber of subsets of B = 2n<\/sup>
\nNow, according to question
\n2m<\/sup> – 2n<\/sup> = 56
\n\u21d2 2n<\/sup>( 2m-n<\/sup> – 1) = 2\u00b3(2\u00b3 – 1)
\nSo, n = 3
\nand m – n = 3
\n\u21d2 m – 3 = 3
\n\u21d2 m = 3 + 3
\n\u21d2 m = 6<\/p>\n<\/details>\n

\n

Question 6.
\nIf the number of elements in a set S are 5. Then the number of elements of the power set P(S) are?
\n(a) 5
\n(b) 6
\n(c) 16
\n(d) 32<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 32
\nGiven, the number of elements in a set S are 5
\nThen the number of elements of the power set P(S) = 25<\/sup> = 32<\/p>\n<\/details>\n

\n

Question 7.
\nEvery set is a ___________ of itself
\n(a) None of the above
\n(b) Improper subset
\n(c) Compliment
\n(d) Proper subset<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) Improper subset
\nAn improper subset is a subset containing every element of the original set.
\nA proper subset contains some but not all of the elements of the original set.
\nEx: Let a set {1, 2, 3, 4, 5, 6}. Then {1, 2, 4} and {1} are the proper subset while {1, 2, 3, 4, 5} is an improper subset.
\nSo, every set is an improper subset of itself.<\/p>\n<\/details>\n

\n

Question 8.
\nIf x \u2260 1, and f(x) = x + 1 \/ x – 1 is a real function, then f(f(f(2))) is
\n(a) 2
\n(b) 1
\n(c) 4
\n(d) 3<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 3
\nGiven f(x) = (x + 1)\/(x \u2013 1)
\nNow, f(2) = (2 + 1)\/(2 \u2013 1) = 3
\nNow since f(2) is independent of x
\nSo, f(f(f(2))) = 3<\/p>\n<\/details>\n

\n

Question 9.
\nIn 3rd Quadrant?
\n(a) X < 0, Y < 0 (b) X > 0, Y < 0
\n(c) X < 0, Y > 0
\n(d) X < 0, Y > 0<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) X < 0, Y < 0
\n\"MCQ
\nIn the 3rd quadrant,
\nX < 0, Y < 0<\/p>\n<\/details>\n

\n

Question 10.
\nIF A \u222a B = A \u222a C and A \u2229 B = A \u2229 C, THEN
\n(a) none of these
\n(b) B = C only when A I C
\n(c) B = C only when A ? B
\n(d) B = C<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) B = C
\nIf A \u222a B = A \u222a C and A \u2229 B = A \u2229 C
\nThen B = C<\/p>\n<\/details>\n

\n

Question 11.
\nA set is known by its _______.
\n(a) Elements
\n(b) Values
\n(c) Members
\n(d) Letters<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) Elements
\nA set is known by its elements.<\/p>\n<\/details>\n

\n

Question 12.
\nIf the set has P elements, B has q elememts then number of elements in A \u00d7 B is
\n(a) pq
\n(b) p + q
\n(c) p + q + 1
\n(d) p\u00b2<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) pq
\nGiven the set A has p elements, B has q elements.
\nthen number of elements in A \u00d7 B = pq<\/p>\n<\/details>\n

\n

Question 13.
\nWhich from the following set has closure property w.r.t multiplication?
\n(a) {0, -1}
\n(b) {1, -1}
\n(c) {-1}
\n(d) {-1,-1}<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) {1, -1}
\nThe set {1, -1} has closure property w.r.t multiplication.
\nThis is because -1 \u00d7 1 = -1 which is an element in the given set.<\/p>\n<\/details>\n

\n

Question 14.
\nConsider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of containing all determinants with value 1. Let C be the subset of containing all determinants with value -1 then
\n(a) B has many elements as C
\n(b) A = B \u222a C
\n(c) B has twice as many elements as C.
\n(d) C is empty<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) B has many elements as C
\nThe matrix C is not empty because
\n|1 0 0|
\n|1 0 1| = -1
\n|1 1 0|
\nLet \u0394 \u2208 B
\nSo, \u0394 = 1
\nAgain let \u03941<\/sub> be the determinant obtained by interchanging any two rows and columns of \u0394
\nSo, \u03941<\/sub> = -1 \u21d2 n(B) \u2265 n(C)
\nSimilarly, we can show that n(C) \u2265 n(B)
\nSo, n(B) = n(C)<\/p>\n<\/details>\n

\n

Question 15.
\nIf A and B are two sets containing respectively M and N distinct elements. How many different relations can be defined for A and B?
\n(a) 2m + n<\/sup>
\n(b) 2m \/ n<\/sup>
\n(c) 2m – n<\/sup>
\n(d) 2mn<\/sup><\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 2mn<\/sup>
\nGiven A and B are two sets containing respectively m and n distinct elements.
\nThen number of different relations can be defined for A and B = 2mn<\/sup><\/p>\n<\/details>\n

\n

Question 16.
\nLet R be a relation N define by x + 2y = 8. The domain of R is
\n(a) {2, 4, 6, 8}
\n(b) {1, 2, 3, 4}
\n(c) {2, 4, 8}
\n(d) {2, 4, 6}<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) {2, 4, 6}
\nGiven R be a relation N define by x + 2y = 8
\n\u21d2 2y = 8 – x
\n\u21d2 y = 8\/4 – x\/2
\n\u21d2 y = 4 – x\/2
\nNow, the pair of x any satisfying the above equation is:
\n(2, 3), (4, 2),(6, 1)
\nSo R = {(2, 3), (4, 2),(6, 1)}
\nNow, Dom(R) = {2, 4, 6}<\/p>\n<\/details>\n

\n

Question 17.
\nIn 2nd quadrant?
\n(a) X < 0, Y < 0
\n(b) X < 0, Y > 0
\n(c) X > 0, Y > 0
\n(d) X > 0, Y < 0<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) X < 0, Y > 0
\n\"MCQ
\nIn the second quadrant,
\nX < 0, Y > 0<\/p>\n<\/details>\n

\n

Question 18.
\nA survey shows that 63% of the americans like cheese whereas 76% like apples. If X% of the americans like both cheese and apples, then we have
\n(a) 39 \u2264 x \u2264 63
\n(b) x \u2264 63
\n(c) x \u2264 39
\n(d) none of these.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 39 \u2264 x \u2264 63
\nGiven,
\nNumber of americans who like cheese n(C) = 63
\nNumber of americans who like apple n(A) = 76
\nTotal number of person = 100 (since 100%)
\nNumber of americans who like both n(A \u2229 B) = x
\nNow, n(A \u222a B) = n(A) + n(B) – n(A \u2229 B)
\n\u21d2 100 = 63 + 76 – x
\n\u21d2 100 = 139 – x
\n\u21d2 x = 139 – 100
\n\u21d2 x = 39
\nThis is the minimum value of x
\nNow, let us look for the highest value of x, the intersection or the common portion
\nbetween A and C, it would be larger when one set takes in more of the other.
\nThus, when the smaller set gets completely absorbed into the larger and in that situation then x = 63
\nSo 39 \u2264 x \u2264 63<\/p>\n<\/details>\n

\n

Question 19.
\nWhich from the following set has closure property w.r.t addition?
\n(a) {0}
\n(b) {1}
\n(c) {1, 1}
\n(d) {1, -1}<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) {0}
\nA set is closed under addition if, when we add any two elements, we always get another element in the set.
\n(a) Closed under addition. The only possible way to add two numbers in the set is 0 + 0 = 0, which is in the set.
\n(b) Not closed under addition. For example, 1 + 1 = 2, which is not in the set.
\n(c) Not closed under addition. For example, 1 + 1 = 2, which is not in the set.
\n(d) Not closed under addition. For example, 1 + (-1) = 0, which is not in the set.<\/p>\n<\/details>\n

\n

Question 20.
\nA’ will contain how many elements from the orginal set A
\n(a) 0
\n(b) All elements in A
\n(c) 1
\n(d) Infinite<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 0
\nA’ will contain zero many elements from the original set A.
\nLet A = {1, 2, 3, 4}, then |A| = 4
\nNow A\u2019 = {}, then |A| = 0<\/p>\n<\/details>\n

\n

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Students can access the NCERT MCQ Questions for Class 11 Maths Chapter 1 Sets with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 11 Maths with Answers during preparation and score maximum marks in the exam. Students can download …<\/p>\n

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