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151.	If A is set of natural numbers, B is set of odd natural numbers and C is set of even natural numbers, then find A-B.(a) A(b) B(c) C(d) B-CI had been asked this question in a job interview.My question is based upon Operation on Sets-2 in section Sets of Mathematics – Class 11
Answer» Correct CHOICE is (c) C For explanation I would say: Natural number which is not odd is EVEN. A-B means set of natural NUMBERS EXCLUDING odd natural numbers so, A-B is set of even natural numbers Hence, A-B=C.

152.	If n(A)=10, n(B)=20, c=5 in the given Venn diagram. Find a and b.(a) a=10 and b=15(b) a=5 and b=15(c) a=15 and b=10(d) a=15 and b=5This question was addressed to me in exam.Question is taken from Venn Diagrams in division Sets of Mathematics – Class 11
Answer» Correct option is (b) a=5 and b=15 The EXPLANATION: From the GIVEN diagram, a + C = 10 => a+5=10 => a=5 and b + c = 20 => b+5=20 => b=15

153.	If set A={Φ} then P(A) is ___________(a) {Φ}(b) {{Φ}}(c) {Φ, {Φ}}(d) ΦThe question was asked during an online interview.My doubt stems from Power Sets topic in section Sets of Mathematics – Class 11
Answer» CORRECT answer is (C) {Φ, {Φ}} To EXPLAIN I would SAY: Set A={Φ} => Set A has one element Φ so, SUBSETS of set A are Φ, {Φ}. So, P(A) = {{Φ, {Φ}}.

154.	If A⊆B then what is A ∪B, where A and B are two sets?(a) A(b) B(c) Null Set(d) Universal SetThis question was addressed to me in an internship interview.I need to ask this question from Subsets topic in portion Sets of Mathematics – Class 11
Answer» Right ANSWER is (b) B Best explanation: Union of TWO SETS incorporates all elements of both A and B HENCE B will BET the union of A and B since B is the superset of A.

155.	Let X be the set of letters of the word ALLOY and Y be the set of letters of the word LOYAL. Are the sets equal?(a) True(b) FalseThis question was addressed to me during an online exam.Question is taken from Equal Sets topic in chapter Sets of Mathematics – Class 11
Answer» Right ANSWER is (a) True Easiest explanation: X={A,L,O,Y}and Y={L,O,Y,A} . SINCE both SETS have same elements so they are EQUAL.

156.	Equal sets _______ number of elements.(a) Must have same(b) May have same(c) Can’t have same(d) Shouldn’t have differentThe question was asked during a job interview.My query is from Equal Sets topic in portion Sets of Mathematics – Class 11
Answer» Correct OPTION is (a) MUST have same Easy explanation: Equal SETS are the sets having same number of ELEMENTS with value of each element SET A and B to be equal.

157.	Which of the following is a null set?(a) {x : x is a natural number and x^2=4}(b) {x : x is a rational number and x^2=2}(c) {x : x is an even prime number}(d) {x : x is name of the day of week}I have been asked this question in an interview.The origin of the question is The Empty Set in section Sets of Mathematics – Class 11
Answer» Correct ANSWER is (b) {x : x is a rational number and x^2=2} Explanation: x^2=4 => x=2,-2 where 2 is a NATURAL number so X={2}. X={2} for even prime number. Also we have SEVEN days of the WEEK so they cannot form null set. x^2=2 => x=√2, -√2 they both are irrational so, it is a null set.

158.	How to define Wavy Curve Method f(x)?(a) (x-a1)^n1 / (x-a2)^n2 / (x-a3)^n3 …………… / (x-ak)^nk * (x-b1)^m1 / (x-b2)^m2 / (x-b3)^m3 …….. /(x-bp)^mp(b) (x-a1)^n1 + (x-a2)^n2 +(x-a3)^n3 …………… + (x-ak)^nk / (x-b1)^m1 + (x-b2)^m2 + (x-b3)^m3 …….. + (x-bp)^mp(c) (x-a1)^n1 (x-a2)^n2 (x-a3)^n3 …………… (x-ak)^nk / (x-b1)^m1 (x-b2)^m2 (x-b3)^m3 …….. (x-bp)^mp(d) (x-a1)^n1 – (x-a2)^n2 – (x-a3)^n3 …………… – (x-ak)^nk / (x-b1)^m1 – (x-b2)^m2 – (x-b3)^m3 ……..- (x-bp)^mpI had been asked this question during a job interview.I'm obligated to ask this question of Sets and their Representations in chapter Sets of Mathematics – Class 11
Answer» The correct answer is (c) (x-a1)^n1 (x-a2)^n2 (x-A3)^n3 …………… (x-ak)^nk / (x-b1)^m1 (x-b2)^m2 (x-b3)^m3 …….. (x-bp)^mp The best EXPLANATION: The method of intervals {or WAVY CURVE} is used for solving INEQUALITIES of the form f(x) = (x-a1)^n1 (x-a2)^n2 (x-a3)^n3 …………… (x-ak)^nk / (x-b1)^m1 (x-b2)^m2 (x-b3)^m3 …….. (x-bp)^mp > 0 (< 0, ≤ 0, or ≥ 0) where, n1, n2, ,n3, …….. nk and m1, m2, m3, …….. , mp are natural numbers . a1, a2, a3, ……..ak and b1, b2, b3, …….. bp are any real numbers such that ai ≠ bj where i = 1, 2, 3, ……. , k and j = 1, 2, 3, ….. , p.

159.	Write the set \({\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}}\) in set builder form.(a) {x: \(x=\frac{n}{n+1}\) where n is a natural number less than 6}(b) {x: \(x=\frac{n+1}{n+2}\) where n is a natural number less than 6}(c) {x: \(x=\frac{n+1}{n}\) where n is a natural number less than 6}(d) {x: \(x=\frac{n}{n+1}\) where n is a natural number less than 5}The question was posed to me in an interview.My question comes from Sets and their Representations in portion Sets of Mathematics – Class 11
Answer» The correct option is (a) {x: \(x=\frac{n}{n+1}\) where n is a NATURAL NUMBER less than 6} EXPLANATION: Since denominator is one more than numerator and only 5 TERMS are present.So, the above set can be written as {x : \(x=\frac{n}{n+1}\) where n is a natural number less than 6}.

160.	Which of the following statement is correct?(a) A is subset of B(b) B is subset of A(c) U is subset of A and B(d) A and B are subsets of UI have been asked this question during an internship interview.I'd like to ask this question from Venn Diagrams in section Sets of Mathematics – Class 11
Answer» The correct option is (d) A and B are subsets of U For explanation: SINCE set A and set B lie COMPLETELY INSIDE set U as GIVEN in diagram so they are subsets of set U and set U is SUPERSET of set A and B.

161.	The number of subsets of a set containing 5 elements is?(a) 5(b) 25(c) 32(d) 64I got this question in semester exam.This question is from Subsets in section Sets of Mathematics – Class 11
Answer» The correct choice is (c) 32 The best explanation: The TOTAL NUMBER of subsets is given by 2^N where n is the number of ELEMENTS, HENCE a total number of subsets is 2^5=32.

162.	How will you define Union of two sets A and B?(a) {x: x € A or x € B}(b) {x: x € A or x € B (or both)}(c) {x: x € A and B}(d) {x: x € A – B}This question was addressed to me in an interview for internship.My question is based upon Sets and their Representations topic in portion Sets of Mathematics – Class 11
Answer» Correct answer is (b) {x: x € A or x € B (or both)} To elaborate: Union of two or more sets is the set of all elements that BELONGS to any of these sets. The symbol used for this union of sets is ‘∪‘. If A = {1, 2, 3, 4} and B = {2, 4, 5, 6} and C = {1, 2, 6, 8} Then, A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}.

163.	Let X={1,2,3,4,5,6}. Insert appropriate symbol in 9 ________ X.(a) =(b)
Answer» Right OPTION is (d) ∉ To explain: Here, 9 is not an ELEMENT of set X. So, 9 does not belongs to set A. 9∉X.

164.	Which of the following is true for set A = {1,2,3,5,7,10}?(a) 0 ∈ A(b) 2 ∈ A(c) 3 ∉ A(d) 5 ∉ AThis question was posed to me in quiz.The doubt is from Sets and their Representations topic in division Sets of Mathematics – Class 11
Answer» Right CHOICE is (B) 2 ∈ A Best explanation: Here 2 is GIVEN in the SET A THEREFORE 2 ∈ A.

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