{"id":13817,"date":"2024-03-30T15:19:20","date_gmt":"2024-03-30T09:49:20","guid":{"rendered":"https:\/\/gstguntur.com\/?p=13817"},"modified":"2024-04-03T16:41:13","modified_gmt":"2024-04-03T11:11:13","slug":"sets-functions-and-relations-ca-foundation-maths-study-material","status":"publish","type":"post","link":"https:\/\/gstguntur.com\/sets-functions-and-relations-ca-foundation-maths-study-material\/","title":{"rendered":"Sets, Functions and Relations \u2013 CA Foundation Maths Study Material"},"content":{"rendered":"

This Sets, Functions and Relations \u2013 CA Foundation Maths Study Material<\/a>\u00a0is designed strictly as per the latest syllabus and exam pattern.<\/p>\n

Sets, Functions and Relations \u2013 CA Foundation Maths Study Material<\/h2>\n

Previous Year Exam Questions<\/strong><\/p>\n

Question 1.
\nOut of 20 members in a family, 11 like to take tea and 14 like coffee. Assume that each one likes atleast one of the two drinks. F ind how many like both coffee and tea: [1 Mark, Nov. 2006]
\n(a) 2
\n(b) 3
\n(c) 4
\n(d) 5
\nAnswer:
\n(d) Given That n(T)= 11 ;n(C) = 14
\nand n(T \u222a C) =20
\nn(T \u2229 C) = n(T) + n(c) – n(T \u222a C)
\n= 11 + 14 – 20 = 5
\n(d) is correct<\/p>\n

Question 2.
\nIn a group of 70 people, 45 speak Hindi, 33 speak English and 10 speak neither Hindi nor English. Find how many can speak both English as well as Hindi: [1 Mark, Feb. 2007]
\n(a) 13
\n(b) 19
\n(c) 18
\n(d) 28.
\nAnswer:
\n(c) n(H) = 45 ; n(E) = 33
\nn(H \u222a E)’= 10 \u21d2 n(H \u222a E) = 70 – 10 = 60
\n\u2234 (H \u222a E) = n(H) + n(E) – n(H \u222a E)
\n= 45 + 33 – 60= 18
\n(c) is correct<\/p>\n

Question 3.
\nLet R is the set of real numbers, such that the function f: R \u2192 R and g : R \u2192 R are defined by f(x) = x2<\/sup> + 3x + 1 and g(x) = 2x – 3. Find (fog) : [1 Mark, Feb. 2007]
\n(a) 4x2<\/sup> + 6x + 1
\n(b) x2<\/sup> + 6x + 1
\n(c) 4x2<\/sup> – 6x +1
\n(d) x2<\/sup> – 6x + 1.
\nAnswer:
\n(c) f(x) = x2<\/sup> + 3x + 1
\ng (x) = 2x – 3
\nfog = f{g(x)}
\n= f (2x – 3)
\n= (2x – 3)2<\/sup> + 3(2x – 3) + 1
\n= 4x2<\/sup> – 2.2x3<\/sup> + 9 + 6x – 9 + 1
\n= 4x2<\/sup> – 6x +1
\n(c) is correct<\/p>\n

\"Sets,<\/p>\n

Question 4.
\nIn a survey of 300 companies, the number of companies using different media – Newspapers (N), Radio (R) and Television (T) are as follows:
\nn(N) = 200, n(R) = 100, n(T) = 40, n(N \u2229 R) = 50, n(R \u2229 T) = 20, n(N \u2229 T) = 25 and n(N \u2229 R \u2229 T) = 5.
\nFind the numbers of companies using none of these media: [1 Mark, May 2007]
\n(a) 20 companies
\n(b) 250 companies
\n(c) 30 companies
\n(d) 50 companies.
\nAnswer:
\n(d) n(N \u222a R \u222a T) = n(N) + n(R) + n(T) – n(N \u2229 R) – n(N \u2229 T) – n(R \u2229 T) + n(N \u2229 R \u2229 T)
\n= 200 + 100 + 40 – 50 – 20 – 25 + 5
\n= 250
\nNo. of Companies using no media = 300 – n(N \u222a R \u222a T)
\n= 300 – 250 = 50
\n(d) is correct<\/p>\n

Question 5.
\nIf R is the set of real numbers such that the function f : R \u2192 R is defined by f(x) = (x + 1)2<\/sup>, then find (fof). [1 Mark, May 2007]
\n(a) (x + 1)2<\/sup> + 1
\n(b) x2<\/sup> + 1
\n(c) {(x + 1)2<\/sup> + 1}2<\/sup>
\n(d) None
\nAnswer:
\n(c) f(x) = (x + 1)2<\/sup>
\nfof = f {f(x)} = f{(x + 1)2<\/sup>}
\n= {(x + 1)2<\/sup> + 1}2<\/sup>
\n(c) is correct<\/p>\n

Question 6.
\nIf f: R \u2192 R, f(x) = 2x + 7, then the inverse of f is : [1 Mark, Aug. 2007]
\n{a) f-1<\/sup>(x) = (x – 7)\/2
\n(b) f-1<\/sup>(x) = (x + 7)\/2
\n(c) f-1<\/sup>(x) = (x – 3)\/2
\n(d) None.
\nAnswer:
\n(a)
\nLet y = f(x) = 2x + 7
\nor 2x = y – 7
\nor x = \\(\\frac{y-7}{2}\\)
\nf-1<\/sup>(x) = \\(\\frac{x-7}{2}\\)<\/p>\n

Question 7.
\nIn a town of20,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families which buy A only is : [1 Mark, Nov. 2007]
\n(a) 6600
\n(b) 6300
\n(c) 5600
\n(d) 600.
\nAnswer:
\n(a) Given
\nn(A) = 40% ; n(B) = 20% ; n(C) = 10% n(A \u2229 B) = 5%; n(B \u2229 C) = 4% n(\u2229) = 4 %; n(A \u2229 B \u2229 C) = 2%
\nNo. of families which buy only A
\n= n(A) – n(A \u2229 B) – n(A \u2229 C) + n(A \u2229 B \u2229 C)
\n= 40 – 5 – 4 + 2 = 33%
\n= 20,000 \u00d7 33% = 6600
\n\u2234 (a) is correct<\/p>\n

Question 8.
\nLet f: R \u2192 R be such that f(x) = 2x<\/sup>, then f(x + y) equals: [1 Mark, Nov. 2007]
\n(a) f(x) + f(y)
\n(b) f(x). f(y)
\n(c) f(x) \u00f7 f(y)
\n(d) None of these
\nAnswer:
\n(b) f(x) = 2x<\/sup>
\nf(x+y) = 2x+y<\/sup> = 2x<\/sup>.2y<\/sup> = f(x).f(y)
\n\u2234 (b) is correct<\/p>\n

Question 9.
\nOut of total 150 students, 45 passed in Accounts, 30 in Economics and 50 in Maths, 30 in both Accounts and Maths, 32 in both Maths and Economics, 35 in both Accounts and Economics, 25 students passed in all the three subjects. Find the numbers who passed atleast in anyone of the subjects: [1 Mark, Feb. 2008]
\n(a) 63
\n(b) 53
\n(c) 73
\n(d) None.
\nAnswer:
\n(b) Total students = 150
\nn(A) = 45 ; n(E) = 30 ; n(M) = 50;
\nn(A \u2229 M) = 30;n(M \u2229 E) = 32 n(A \u2229 M) = 35; n(M \u2229 E \u2229 M) = 25
\n\u2234 n(A \u222a E \u222a M) = 45 + 30 + 50 – 30 – 32 – 35 + 25 = 53
\n\u2234 (b) is correct<\/p>\n

\"Sets,<\/p>\n

Question 10.
\nIf f(x) = \\(\\frac{2+x}{2-x}\\), then f-1<\/sup>(x):
\n(a) \\(\\frac{2(x-1)}{x+1}\\)
\n(b) \\(\\frac{2(x+1)}{x-1}\\)
\n(c) \\(\\frac{x+1}{x-1}\\)
\n(d) \\(\\frac{x-1}{x+1}\\)
\nAnswer:
\n(a)
\n\u2235 f(x) = \\(\\frac{2+x}{2-x}\\) = y(let)
\n2 + x = 2y – xy
\nor x + xy = 2y – 2
\nor x(1 + y) = 2 (y – 1)
\nor x = \\(\\frac{2(y-1)}{1+y}\\)
\nf-1<\/sup>(x) = \\(=\\frac{2(x-1)}{x+1}\\); (a) is correct<\/p>\n

Question 11.
\nIf A = {1, 2, 3, 4,} ; B = {2, 4, 6, 8,} f(1) = 2, f(2) = 4, f(3) = 6 and f(4) = 8, And f: A \u2192 B then f-1<\/sup> is : [1 Mark, Dec. 2008]
\n(a) {(2, 1), (4, 2), (6, 3), (8, 4)}
\n(b) {(1, 2), (2, 4), (3; 6), (4, 8)}
\n(c) {(1, 4), (2, 2), (3, 6), (4, 8)}
\n(d) None of these
\nAnswer:
\n(a)
\n\"Sets,
\nf-1<\/sup> = {(2, 1) (4, 2), (6, 3) (8, 4)}
\n(a) is correct.<\/p>\n

Question 12.
\nIf f (x) = x2<\/sup> + x – 1 and 4f(x) = f(2x) then find \u2018x’. [1 Mark, Dec. 2008]
\n(a) 4\/3
\n(b) 3\/2
\n(c) -3\/4
\n(d) None of these
\nAnswer:
\n(b) f(x) = x2<\/sup> + x – 1
\nand 4f(x) = f (2x)
\nor 4(x2<\/sup> + x – 1) = (2x)2<\/sup> +2x – 1
\nor 4x2<\/sup> + 4x – 4 = 4x2<\/sup> + 2x – 1
\nor 4x – 2x = 4 – 1
\nor 2x = 3 x = 3\/2
\n\u2234 (b) is correct<\/p>\n

Question 13.
\nIf A = {p, q, r, s}, B = {q, s, t}, C = {m, q, n} Find C – (A \u2229 B). [1 Mark, Dec. 2008]
\n(a) {m, n}
\n(b) {p, q}
\n(c) {r, s}
\n(d) {p, r}
\nAnswer:
\n(a)
\nC – (A \u2229 B) = { m, q, n} – ({p, q, r, s} \u2229 {q, s, t}
\n= {m, q, n} – {q, s}
\n= {m; n}
\n\u2234 (a) is correct.<\/p>\n

Question 14.
\nX = {x, y, w, z} y = {l,2,3,4}; H = {(x, 1); (y, 2); (y, 3); (z, 4); (x, 4. [1 Mark, Dec. 2009]
\n(a) H is a function from x to y
\n(b) H is not a function from x to y
\n(c) H is a relation from y to x
\n(d) None of these
\nAnswer:
\n(b) H is not a function from x to y because x has 2 images 1 & 4
\n(b) is correct<\/p>\n

Question 15.
\nGiven the function f(x) = (2x + 3), then the value of f(2x) – 2f(x) +3 will be : [1 Mark, Dec. 2009]
\n(a) 3
\n(b) 2
\n(c) 1
\n(d) 0
\nAnswer:
\n(d) \u2235 f(x) = 2x + 3
\nf(2x) – 2 f(x) + 3
\n= 2(2x) + 3 – 2(2x + 3) + 3
\n= 4x + 3 – 4x – 6 + 3 = 0
\n\u2234 (d) is correct<\/p>\n

Question 16.
\nIf f(x) = 2x + h then find f(x + h) – 2f(x). [1 Mark, Dec. 2009]
\n(a) h – 2x
\n(b) 2x – h
\n(c) 2x + h
\n(d) None of these
\nAnswer:
\n(a) f(x) = 2x + h
\nf(x + h) – 2f(x)
\n= 2(x + h) + h – 2(2x + h)
\n= 2x + 2h + h – 4x – 2h
\n= h – 2x
\n\u2234 (a) is correct<\/p>\n

Question 17.
\nIf A = {X :X2<\/sup> – 3X + 2 = o]
\nB = {X :X2<\/sup> – 4X + 12 = o),
\nThen B – A is equal to: [1 Mark, June 2010]
\n(a) {-6}
\n(b) {1}
\n(c) {1, 2}
\n(d) {2, -6}
\nAnswer:
\n(a) \u2235 x2<\/sup> – 3x + 2 = 0
\nor x2<\/sup> – 2x – x + 2 = 0
\nor x(x – 2) -1 (x – 2) = 0
\nor (x- 2) (x – 1) = 0
\n\u2235 x = 1 ;2
\nA = {1, 2}
\nAnd x2<\/sup> + 4x – 12 = 0
\nor x2<\/sup> + 6x – 2x – 12 = 0
\nor x(x +6) -2 (x + 6) = 0
\nor (x + 6) (x – 2) = 0
\nx = -6 ; 2
\n\u2235 B = {-6 ; 2}
\nB – A = {-6 ; 2} – {1 ; 2}
\n= {-6}
\n(a) is correct<\/p>\n

Question 18.
\nIf F: A \u2192 R is a real-valued function defined by f(x) = \\(\\frac{1}{x}\\) then: [1 Mark, June 2010]
\n(a) R
\n(b) R-{1}
\n(c) R-{o}
\n(d) R-N
\nAnswer:
\n(c)
\nf(x) = \\(\\frac{1}{x}\\) is defined at all x \u2208 R except x = 0
\nA = R – { 0}
\n\u2234 (c) is correct<\/p>\n

\"Sets,<\/p>\n

Question 19.
\nIn the set N of all natural numbers the relation R defined by a R b \u201cif and only if, a divide b\u201d, then the relation R is: [1 Mark, June 2010]
\n(a) Partial order relation
\n(b) Equivalence relation
\n(c) Symmetric relation
\n(d) None of these.
\nAnswer:
\n(a) It is transitive relation, i.e. partial order relation<\/p>\n

Question 20.
\nFor any two sets A and B, A \u2229 (A’ \u222a B) = _______, where A\u2019 represent the compliment of the set A. [1 Mark, Dec. 2010]
\n(a) A \u2229 B
\n(A) A \u222a B
\n(c) A \u222a B
\n(d) None of these
\nAnswer:
\nTricks : Take an example and then decide the answer
\nLet U = {0, 1, 2, 3, 4, 5}
\nA = {0, 1, 2, 3}
\nB = {2, 3, 4, 5}
\nA’ = U – A
\n= (4; 5}
\nA\u2018 \u222a S = {4, 5} \u222a {2, 3, 4, 5}
\n= {2, 3, 4, 5}
\n\u2234 A \u2229 (A\u2019 \u222a B)
\n= {0, 1, 2, 3} \u2229 {2, 3, 4, 5}
\n= {2, 3}
\n= A \u2229 B
\n\u2234 (a) is correct
\nIInd method = (A \u2229 A’) \u222a (A \u2229 B) = { } \u222a (A \u2229 B) = A \u2229 B<\/p>\n

Question 21.
\nIf f : R \u2192 R, f(x) = x + 1, g :R \u2192 R g(x) = x2<\/sup> + 1 then fog(-2) equals to : [1 Mark, Dec. 2010]
\n(a) 6
\n(b) 5
\n(c) -2
\n(d) None
\nAnswer:
\n(a) f(x) = x + 1
\ng(x) = x2<\/sup> + 1. \u21d2 g(-2) = (-2)2<\/sup> + 1 = 5
\nfog(-2) = f{g(-2)} = f(5)
\n= 5 + 1 = 6
\n\u2234 (a) is correct<\/p>\n

Question 22.
\nIf A \u2282 B, then following is true: [1 Mark, Dec. 2010]
\n(a) A \u2229 B = B
\n(b) A \u222a B = B
\n(c) A \u2229 B = A’
\n(d) A \u2229 B
\nAnswer:
\n(b)<\/p>\n

Question 23.
\nIf f(x – 1)= x2<\/sup> – 4x + 8, then f(x + 1) = . [1 Mark, Dec. 2010]
\n(a) x2<\/sup> + 8
\n(b) 2<\/sup> + 7
\n(c) x2<\/sup> + 4
\n(d) x2<\/sup> – 4x
\nAnswer:
\n(c); f(x – 1) = x2<\/sup> – 4x + 8
\n= (x – 1 + 1)2<\/sup> – 4 (x – 1+ 1) + 8
\nf(x + 1) = (1 + 1 + 1)2<\/sup> – 4(x + 1 + 1) + 8
\n= (x + 2)2<\/sup> – 4 (x + 2) + 8 = x2<\/sup> + 4x + 4 – 4x – 8 + 8
\n= x2<\/sup> +4
\n\u2234 (c) is correct.<\/p>\n

Question 24.
\nThere are 40 students, 30 of them passed in English, 25 of them passed in Maths and 15 of them passed in both. Assuming that every Student has passed atleast in one subject. How many student\u2019s passed in English only but not in Maths. [1 Mark, June 2011]
\n(a) 15
\n(b) 20
\n(c) 10
\n(d) 25
\nAnswer:
\n(a) Total students = 40
\nn(E) = 30 ;
\nn(M) = 25 (E \u2229 M) = 15
\nNo. of stds. passed in English only n(E) – n(E \u2229 M)
\n= 30 – 15 = 15
\n\u2234 (a) is correct<\/p>\n

Question 25.
\nIf A = {\u00b12,\u00b13} B = -{1, 4, 9} AND F = {(2, 4) (-2, 4) (3, 9) (-3, 4)} then \u2018F\u2019 is defined as: [1 Mark, June 2011]
\n(a) One to one function from A into B
\n(b) One to one function from A onto B
\n(c) Many to one function from A onto B.
\n(d) Many to one function from A into B.
\nAnswer:
\n(c)
\n\"Sets,<\/p>\n

\"Sets,<\/p>\n

Question 26.
\nIf f(x) = \\(\\frac{x}{\\sqrt{1+x^2}}\\) and g(x) = \\(\\frac{x}{\\sqrt{1-x^2}}\\) Find fog ? [1 Mark, June 2011]
\n(a) x
\n(b) \\(\\frac{1}{x}\\)
\n(c) \\(\\frac{x}{\\sqrt{1-x^2}}\\)
\n(d) x\\(\\sqrt{1-x^2}\\)
\nAnswer:
\n(a)
\n\"Sets,
\n\u2234 (a) is correct<\/p>\n

Question 27.
\nf(x) = 3 + x, for -3 < x < 0 and 3 – 2x for 0 < x < 3, then value of f(2) will be: [1 Mark, Dec. 2011]
\n(a) -1
\n(b) 1
\n(c) 3
\n(d) 5
\nAnswer:
\n(a) is correct
\nf(x) = 3 + 2x ; when -3 < x < 0
\n= 3 – 2x ; when 0 < x < 3
\nf(x = 2) = 3 – 2 \u00d7 2 = -1
\n\u2234 2 lies in 2nd condition<\/p>\n

Question 28.
\nIf A = (1, 2, 3, 4, 5), B = (2, 4) and C = (1, 3, 5) then (A – C) \u00d7 B is: [1 Mark, Dec. 2011]
\n(a) {(2, 2)(2, 4)(4, 2)(4, 4)(5, 2) (5, 4)}
\n(b) {(1, 2) (1, 4) (3, 2) (3, 4) (5, 2) (5, 4)}
\n(c) {(2, 2) (4, 2) (4, 4) (4, 5)}
\n(d) {(2, 2) (2, 4) (4, 2) (4, 4)}
\nAnswer:
\n(d) is correct
\n(A – C) \u00d7 B = {2, 4} \u00d7 {2, 4} = {(2, 2), (2, 4); (4 ;2) ; (4 ; 4)}<\/p>\n

Question 29.
\nFor any two sets A and B the set (A \u222a B\u2019)’ is Equal to (where\u2019 denotes compliment of the set): [1 Mark, Dec. 2011]
\n(a) B – A
\n(b) A – B
\n(c) A\u2019 – B\u2019
\n(d) B\u2019 – A\u2019
\nAnswer:
\n(a) is correct
\nTricks: Let U = {0, 1, 2, 3, 4, 5}
\nA = {0, 1, 2} ; B = {1, 2, 3}
\nB’ = U – B = {0, 4, 5)
\nA \u222a B’ = (0, 1, 2, 4, 5)
\n(A \u222a B’)’ = \u222a – (A \u222a B’) = {3}
\nThen Go by choices
\nFor (a) B – A = {1, 2, 3} – {0, 1, 2} = {3}
\n(A \u222a B’)’ = \u222a – (A \u222a B’) = {3}
\nII nd method (A \u222a B’)’
\n= A’ \u2229 (B’)’
\n= A’ \u2229 B = B – A \u2229 B = B – A<\/p>\n

Question 30.
\nThe number of proper sub-set of the set {3, 4, 5, 6, 7} is: [1 Mark, June 2012]
\n(a) 32
\n(b) 31
\n(c) 30
\n(d) 25
\nAnswer:
\n(b) No. of proper subsets = 2n<\/sup> – 1 = 25<\/sup> – 1 = 31<\/p>\n

Question 31.
\nOn the set of lines, being perpendicular is a : [1 Mark, June 2012]
\n(a) Reflexive
\n(b) Symmetric
\n(c) Transitive
\n(d) None of these
\nAnswer:
\n(b) is correct
\nIt is symmetric relation Because it x is perpendicular to y
\nThen y is also perpendicular to x<\/p>\n

Question 32.
\nThe range of the function f :N \u2192 N; f(x) = (-1)x-1<\/sup>, is: [1 Mark, June 2012]
\n(a) {0, -1}
\n(b) {1,-1}
\n(c) {1, 0}
\n(d) {1, 0, -1}
\nAnswer:
\n(b) is correct
\nf(x) = (-1)x-1<\/sup>
\nIf x = odd No. f(x) = 1
\nIt x = 0; even No. f(x) = -1
\n\u2234 Range = {1 ; -1}
\nDomain = {any real No.}<\/p>\n

\"Sets,<\/p>\n

Question 33.
\nFor a group of 200 persons, 100 are interested in music, 70 in photography and 40 in swimming, Further more 40 are interested in both music and photography, 30 in both music and swimming, 20 in photography and swimming and 10 in all the three. How many are interested in photography but not in music and swimming ? [1 Mark, Dec. 2012]
\n(a) 30
\n(b) 15
\n(c) 25
\n(d) 20
\nAnswer:
\n(d) is correct
\nLet A = No. of persons interested in Music
\nB = No. of persons interested in photography
\nC = No. of persons interested in Swimming
\nn(A) = 100; n(B) = 70 ; n(C) = 40; n( A \u2229 B) = 40; n( A \u2229 C) = 30; n(B \u2229 C) = 20; n(A \u2229 B \u2229 C) = 10.
\n\u2234 n(B \u2229 A’ \u2229 C’) = n(B) – n(B \u2229 A) – n(B \u2229 C) + n(A \u2229 B \u2229 C)
\n= 70 – 40 – 20 + 10
\n= 20<\/p>\n

Question 34.
\nIf f : R \u2192 R is a function, defined by f(x) = 10x – 7, if g(x) = f-1<\/sup>(x), then the value of g(x) is equal to: [1 Mark, Dec. 2012]
\n(a) \\(\\frac{1}{10 x-7}\\)
\n(b) \\(\\frac{1}{10 x+7}\\)
\n(c) \\(\\frac{x+7}{10}\\)
\n(d) \\(\\frac{x-7}{10}\\)
\nAnswer:
\n(c) is correct
\nLet y = f(x) = 10x – 7
\nor 10x = y + 7
\n\u2234 x = \\(\\frac{y+7}{10}\\)
\n\u2234 f-1<\/sup>(x) = \\(\\frac{x+7}{10}\\)
\n\u2234 g(x) = \\(\\frac{x+7}{10}\\)<\/p>\n

Question 35.
\nThe No. of elements in range of constant function is: [1 Mark, Dec. 2012]
\n(a) One
\n(b) Zero
\n(c) Infinite
\n(d) None
\nAnswer:
\n(a) is correct
\nLet f(x) = c (where c= constant)
\n\"Sets,
\nDomain = {x\/x \u2208 R}
\nRange = {c}<\/p>\n

Question 36.
\nIf f(x) = x + 2, g(x) = 7x<\/sup> then go f(x) = _______. [1 Mark, June 2013]
\n(a) 7x<\/sup>.x + 2.7x<\/sup>
\n(b) 7x+2<\/sup>
\n(c) (7x<\/sup>) + 2
\n(d) none
\nAnswer:
\nf(x) = x+2 ; g(x) =7x<\/sup>
\ngof (x) = g{f(x)} = g(x + 2) = 7x+2<\/sup>
\n\u2234 (b) is correct<\/p>\n

Question 37.
\nIf f(x) = log\\(\\left(\\frac{1+x}{1-x}\\right)\\) then f\\(\\left(\\frac{2 x}{1+x^2}\\right)\\). [1 Mark, June 2013]
\n(a) f(x)
\n(b) 2 f(x)
\n(c) 3 f(x)
\n(d) -f(x)
\nAnswer:
\n\"Sets,
\n(b) is correct<\/p>\n

\"Sets,<\/p>\n

Question 38.
\nIf A= {1,2,3} then the relation R={(1,1), (2,3), (2,2), (3,3), (1,2)} on A is: [1 Mark, June 2013]
\n(a) Reflexive
\n(b) Symmetric
\n(c) Transitive
\n(d) Equivalence
\nAnswer:
\n(a) is correct.
\nReflexive Relation.
\nxRx ; (x ; x) \u2208 R
\nHere (1,1), (2, 2), (3, 3) \u2208 R
\nSo; It is Reflexive<\/p>\n

Question 39.
\nOf the 200 candidates who were interviewed for a position at call center, 100 had a two wheeler, 70 had a credit card and 140 had a mobile phone 40 of them had both a two wheeler and a credit card, 30 had both a credit card and mobile phone, 60 had both a two wheeler and a mobile phone and 10 had all the three. How many candidates had none of them ? [1 Mark, Dec. 2013]
\n(a) 0
\n(b) 20
\n(c) 10
\n(d) 18
\nAnswer:
\n(c) is correct
\nLet n(A) = No. of Candidates having two wheeler
\nn(B) = No. of candidates having credit cards
\nn(C) = No. of candidates having mobile phone.
\nGiven
\nn(A) = 100 ; n(B) = 70 ; n(c) = 140
\nn(A \u2229 B) = 40; n(B \u2229 C) = 30; n(C \u2229 A) = 60 n(A \u2229 B \u2229 C) = 10.
\n\u2234 n(A \u222a B \u222a C) = 100 + 70 + 140 – 40 – 30 – 60 + 10 = 190
\nNo. of candidates having none = 200 – 190 = 10<\/p>\n

Question 40.
\nIf f(x) = \\(\\frac{x^2-25}{x-5}\\) then f(5). [1 Mark, Dec. 2013]
\n(a) 0
\n(b) 1
\n(c) 10
\n(d) Undefined
\nAnswer:
\n(d) is correct
\nf(5) = \\(\\frac{x^2-25}{x-5}=\\frac{5^2-25}{5-5}=\\frac{0}{0}\\)
\n\u2234 Undefined<\/p>\n

Question 41.
\nf(x) = (a – xn<\/sup>)1\/n<\/sup>, a > 0 and n is positive integer then f'[f(x)]. [1 Mark, Dec. 2013]
\n(a) x
\n(b) a
\n(c) x1\/n<\/sup>
\n(d) a1\/n<\/sup>
\nAnswer:
\n(a) is correct
\nf{f(x)} = f{a-nn<\/sup>)1\/n<\/sup>]
\n\"Sets,<\/p>\n

Question 42.
\nIn a class of 50 students 35 opted for Maths, 37 opted for commerce. The number of such student who opted for both maths and commerce is: [1 Mark, June 2014]
\n(a) 13
\n(b) 15
\n(c) 22
\n(d) 28
\nAnswer:
\n(c) is correct
\nn(M) = No. of students opted for Maths = 35
\nn(C) = No. of Student opted for Commerce = 37
\nSo;(M \u222a C) = 50
\nn(M \u2229 C) = 35 + 37 – 50 = 22<\/p>\n

\"Sets,<\/p>\n

Question 43.
\nThe range of the relation {(1,0) (2, 0) (3, 0) (4, 0) (0, 0)} is: [1 Mark, June 2014]
\n(a) (1,2, 3, 4,0}
\n(b) {0}
\n(c) {1,2, 3, 4}
\n(d) None
\nAnswer:
\n(b) is correct
\nRange = {0}<\/p>\n

Question 44.
\nIf A = {1, 2, 3} and B = {4, 6, 7} then the relation R = {(2, 4) (3, 6)} is: [1 Mark, June 2014]
\n(a) A function
\n(b) A function from A to B
\n(c) Both (a) and (b)
\n(d) Not a function
\nAnswer:
\n(d) is correct.
\nNote:- 1 has no image<\/p>\n

Question 45.
\nA = (2, 3), B = (4, 5), C = (5, 6) then A \u00d7 (B \u2229 C). [1 Mark, Dec. 2014]
\n(a) [(5, 2), (5, 3)]
\n(b) [(2, 5), (3, 5)]
\n(c) [(2, 4), (5, 3)
\n(d) [(3, 5), (2, 6)]
\nAnswer:
\n(b) is correct
\nB \u2229 C = {4, 5} \u2229{5, 6} = {5}
\n\u2234 A \u00d7 (B\u2229 C) – {2, 3} \u00d7 {5}
\n= {(2,5); (3, 5)}<\/p>\n

Question 46.
\nIf a relation S = ((1,1), (2,2), (1,2), (2,1)) is symmetric and .[1 Mark, Dec. 2014]
\n(a) Reflexive but not transitive
\n(b) Reflexive as well as transitive
\n(c) Transitive but not reflexive
\n(d) Neither transitive nor reflexive
\nAnswer:
\nIf S = {1, 2, 3} then
\nThen relation {(1,1); (2,2); (1,2); (2,1)} is symmetric and transitive but not Reflexive.<\/p>\n

Question 47.
\nIf f(x) = \\(\\frac{x}{x-1}\\), then \\(\\frac{f(x \/ y)}{f(y \/ x)}\\) = _______. [1 Mark, Dec. 2014]
\n(a) x\/y
\n(b) y\/x
\n(c) -x\/y
\n(d) -y\/x
\nAnswer:
\nf(x) = \\(\\frac{x}{x-1}\\)
\n\"Sets,<\/p>\n

Question 48.
\nLet N be the set of all Natural number; E be the set of all even natural numbers then the function f: N \u2192 E defined as f(x) =2x ; \u2200 x \u2208 N is : [1 Mark, Dec. 2014]
\n(a) One-one into
\n(b) One-one onto
\n(c) Many-one into
\n(d) Many-one onto
\nAnswer:
\n(b) is correct
\nN = {1, 2, 3, …………. ;n}
\nE = {2, 4, 6, …………. ;2n}
\n\"Sets,
\nClearly it is one-one onto mapping<\/p>\n

Question 49.
\nWhich of these is a function from A \u2192 B; A= {x, y, z}; B = {a, b, c, d}. [1 Mark, Dec. 2015]
\n(a) {(x, a) (x, b) (y, c)}
\n(b) {(x, a) (x, b) (y, c) (z, d)}
\n(c) {(x, a) (y, b) (z, d)}
\n(d) {(a, x) (b, z) (c, y)}
\nAnswer:
\n(c) is correct.
\n\"Sets,<\/p>\n

Question 50.
\nf(x) = 2x + 2, g(x) = x2<\/sup>, fog(4) = ? [1 Mark, Dec. 2015]
\n(a) 100
\n(b) 10
\n(c) 34
\n(d) None of these
\nAnswer:
\n(c) is correct
\nfog(x) = f{g(x)}
\n= f(x2<\/sup>) = 2.x2<\/sup> + 2
\nfog (4) = 2 \u00d7 42<\/sup> + 2 = 34<\/p>\n

Question 51.
\nIn a class of 80 students, 35% play only cricket, 45% only Tennis, How many play Cricket? [1 Mark, Dec. 2015]
\n(a) 86
\n(b) 54
\n(c) 36
\n(d) 44
\nAnswer:
\n(d) is correct
\nGiven n(C-T) = n(C) – n(C \u2229 T) = 35%
\nn(T – C) = n(T) – n(C \u2229 T) = 45%
\nn(CUT) = n(C) + n(T) – n(C \u2229 T) = 100
\nor; 35 + n(C \u2229 T) + 45 + n(C \u2229 T) – n(C \u2229 T) = 100
\nor 80 + n(C \u2229 T) = 100 n(C \u2229 T) = 20%
\nn(C) = 35 + n(C \u2229 T) = 35 + 20 = 55%
\n= 80 \u00d7 55% = 44<\/p>\n

\"Sets,<\/p>\n

Question 52.
\nIf Set A = {x: \\(\\frac{x}{2}\\) \u2208 Z, 0 \u2264 x \u2264 10}
\nB = {x : x is one digit prime number} and
\nC = {x : \\(\\frac{x}{3}\\) \u2208 N, x \u2264 12} then A \u2229 (B \u2229 C) = .[1 Mark, June 2016]
\n(a) \u03a6
\n(b) Set A
\n(c) Set B
\n(d) Set C
\nAnswer:
\n(a)
\nA = {2, 4, 6, 8, 10}
\nB = {2, 3, 5, 7}
\nC = {3, 6, 9, 12}
\nA \u2229(B \u2229 C)
\n= A \u2229 (B \u2229 C) = \u03a6
\nNo Common element in all 3 sets.<\/p>\n

Question 53.
\nThe domain (D) and range (R) of the function: [1 Mark, June 2016]
\nf (x) = 2 – |x + 1| is
\n(a) D = Real numbers, R = (2, \u221e)
\n(b) D = Integers, R = (0, 2)
\n(c) D = Integers, R = (- \u221e, \u221e)
\n(d) D = Real numbers, R = (- \u221e, 2)
\nAnswer:
\n(d) is correct, let y = f(x) = 2 – |x + 1l
\nFor any real values of x; f (x) is defined.
\n\u2234 Domain = D Real numbers
\nMinimum value of |x + 1| is Zero
\nMaximum value of Range = 2 – 0 = 2
\n\u2234 Range = – \u221e < y < 2
\n= (- \u221e; 2]<\/p>\n

Question 54.
\nLet A be the set of the squares of natural numbers and x \u2208 A, y \u2208 A . Then [1 Mark, June 2016]
\n(a) x + y \u2208 A
\n(b) x – y \u2208 A
\n(c) \\(\\frac{x}{y}\\) \u2208 A
\n(d) xy \u2208 A
\nAnswer:
\n(d) is correct.
\nA = {x \/ x is the squares of natural Nos.}= {1, 4, 9, 16, 25, …………..}
\nTricks: then Go by Choices let x = 1; y = 4 \u2208 A.
\nx + y = 1 + 4 = 5 \u2209 A.
\nx – y = 1 – 4 = -3 \u2209 A.
\n\\(\\frac{x}{y}=\\frac{1}{4}\\) = \u2209 A.
\nBut xy = 1 \u00d7 4 = 4 \u2208 A.
\n\u2234 (d) is correct.<\/p>\n

Question 55.
\nThe number of sub-sets formed from the letters of the word \u201cALLAHABAD\u201d. [1 Mark, June 2016]
\n(a) 128
\n(b) 16
\n(c) 32
\n(d) None
\nAnswer:
\n(C) is correct.
\nLet X = {Letters of word ALLAHABAD}
\n= {A, L, H, B, D }
\nNo. of sub-sets = 25<\/sup> = 32<\/p>\n

Question 56.
\nIf f(x)=100 A then f-1<\/sup>(x) = .[1 Mark, June 2016]
\n(a) \\(\\frac{x}{100}\\)
\n(b) \\(\\frac{1}{100 x}\\)
\n(c) \\(\\frac{1}{100}\\)
\n(d) None of these
\nAnswer:
\n(a) is correct
\nLet y = f(x) = 100x
\nx = \\(\\frac{y}{100}\\); So, f-1<\/sup>(x) = \\(\\frac{x}{100}\\)<\/p>\n

Question 57.
\nf : R \u2192 R is defined by f (x) = 2x<\/sup> then f is [1 Mark, June 2016]
\n(a) One – one and onto
\n(b) One – one and into
\n(c) Many to one
\n(d) One to many
\nAnswer:
\n(B) is correct.<\/p>\n

Question 58.
\nIn a class, 80 students speak Hindi, 60 students speak English and 40 students speak both Hindi and English then the number of students in the class is _______. [1 Mark, June 2017]
\n(a) 100
\n(b) 120
\n(c) 140
\n(d) 180
\nAnswer:
\nLet H = Students speak Hindi
\nE = Students speak English
\nGiven
\nn(H) = 80 ; n (E) = 60
\nand n (H \u2229 E) = 40
\nn(H \u222a E) = n(H) + n(E) – n(H \u2229 E)
\n= 80 + 60 – 40 = 100.
\nOption (a) is correct<\/p>\n

Question 59.
\nIf f(x) = \\(\\frac{x-1}{x}\\) and g(x) = \\(\\frac{1}{1-x}\\) then fog(x) = \u222a
\n(a) x – 1
\n(b) x
\n(c) 1 – x
\n(d) – x
\nAnswer:
\n\"Sets,
\nOption (b) is correct<\/p>\n

\"Sets,<\/p>\n

Question 60.
\nThe Range of the function f is defined by f(x) = \\(\\frac{x}{x^2+2}\\) is _______.[1 Mark, June 2017]
\n\"Sets,
\nAnswer:
\nLet y = \\(\\frac{x}{x^2+2}\\) = f(x)
\nor ; yx2<\/sup> + 2y = x
\nor yx2<\/sup> – x + 2y = 0
\nIt is a quadratic equation in terms of x.
\nDiscriminant = D = b2<\/sup> – 4ac
\n= (-1)2<\/sup> – 4. y ,2y = 1 – 8y2<\/sup>
\nTo be Real solutions ;
\nD \u2265 0 \u21d2 1 – 8y2<\/sup> \u2265 0
\nor 1 \u2265 8y2<\/sup> \u21d2 8y2<\/sup> \u2264 1
\n\"Sets,
\n(c) is correct.<\/p>\n

Question 61.
\nIn a class of 35 students, 16 students play football and 24 students play cricket. Assume that each one play atleast one game, then number of students who play both the games is :
\n(a) 5
\n(b) 11
\n(c) 12
\n(d) 17
\nAnswer:
\nn(F \u2229 C) = n(F) + n(C) – n(F \u222a C)
\n= 16 + 24 – 35 = 5
\noption (a) is correct.<\/p>\n

Question 62.
\nIf f(x) = \\(\\frac{x+1}{x+2}\\) = then f[f\\(\\left(\\frac{1}{x}\\right)\\)] = _______. [1 Mark, Dec. 2017]
\n(a) \\(\\frac{2 x+3}{3 x+5}\\)
\n(b) \\(\\frac{2 x+5}{3 x+2}\\)
\n(c) \\(\\frac{3 x+2}{5 x+3}\\)
\n(d) \\(\\frac{5 x+2}{2 x+3}\\)
\nAnswer:
\n(c)
\n\"Sets,<\/p>\n

Question 63.
\nIf A = {\u03a6, {\u03a6}} then the Power Set of A is: [1 Mark, June 2018]
\n(a) {\u03a6},{0}
\n(b) {\u03a6, {\u03a6}, {{\u03a6}}, A}
\n(c) A
\n(d) {A}, {\u03a6}
\nAnswer:
\n(b)
\nA= {\u03a6;{\u03a6}}
\np(A)={{}}; {\u03a6};{{\u03a6}}; {\u03a6; {\u03a6}}
\n= {\u03a6; {\u03a6};{{\u03a6}}; A}}<\/p>\n

Question 64.
\nIf A = {x \/ x =3n<\/sup> – 2n – 1, where n \u2208 N}, B = {x\/x = 4(n – 1), where n \u2208 N}. Then
\n(A) A \u2282 B
\n(b) B \u2282 A
\n(c) A = B
\n(d) None
\nAnswer:
\n(a)
\nPutting n = 1, 2, 3, ……….. ; we get
\nA = {x \/ x = 3n<\/sup> – 2n -1}
\n= {0 ; 4 ; 20 ; ……………..}
\nB = {A \/ x = 4 (n – 1)}
\n= {0 ; 4 ; 8 ; 12 ; 16 ; 20 ; …………}
\nClearly; A \u2282 B<\/p>\n

Question 65.
\nThe range of the function \\(\\frac{x^6}{x^{12}+1}\\) is: [1 Mark, June 2018]
\n(a) (0, \u221e)
\n(b) [0,
\n(c) (-\u221e, 0) \u222a [2, \u221e)
\n(d) (0, \\(\\frac{1}{2}\\))
\nAnswer:
\n(b)
\nLet y = \\(\\frac{x^6}{x^{12}+1}\\)
\nor yx12<\/sup> + y = x6<\/sup>
\nlet z = x6<\/sup>
\nyz2<\/sup> + y = z \u21d2 yz2<\/sup> – z + y = 0
\nIt is a Quadratic Eqn. in terms of Z. for real solns.
\nD = b2<\/sup> – 4ac = (-1)2<\/sup> – 4.y.y
\n= 1 – 4 y2<\/sup>
\nD > 0
\nor; 1 – 4y2<\/sup> \u2265 0 \u21d2 1 \u2265 4y2<\/sup>
\nor ; 4y2<\/sup> \u2264 1
\nor y2<\/sup> \u2264 \\(\\frac{1}{4}\\) If y2<\/sup> = \\(\\frac{1}{4}\\) \u21d2 y \u00b1 \\(\\frac{1}{2}\\)
\n–\\(\\frac{1}{2}\\) \u2264 y \u2264 \\(\\frac{1}{2}\\)
\nFromQts. 0, [\u2235 y is always positive.]<\/p>\n

Question 66.
\nLet N be the set of all natural numbers; E be the set of all even natural numbers then the function; [1 Mark, May 2018]
\n(a) One – one – into
\n(b) Many – one – into
\n(c) One – one – one
\n(d) Many – one – onto
\nAnswer:
\n(c)
\n\u2235 N = set of Natural Numbers
\n= {1, 2, 3, ………….}
\nf{x} = 2x ; \u2200 X \u2208 N
\nSo; f(1) = 2 \u00d7 1 = 2
\nf(2) = 2 \u00d7 2 = 4
\nf(3) = 2 \u00d7 3 = 6
\nSo;
\n\"Sets,
\nClearly ; It is one-one and onto mapping.<\/p>\n

\"Sets,<\/p>\n

Question 67.
\nIn a town of 20,000 families it was found that 40% families buy newspaper. A, 20% families buy newspaper B and 10% families buy newspaper C. 5% families buy A and B, 3% buy B and C and 4% buy A and C if 2% families buy all the three newspapers, then the number of families which buy A only is : [1 Mark, May 2018 ]
\n(a) 6600
\n(b) 6300
\n(c) 5600
\n(d) 600
\nAnswer:
\n(a)
\n\"Sets,
\nn(A) = 40% ; n(B) = 20% n(c) = 10% ;
\nn(A \u2229 B) = 5% n(B \u2229 C) = 3% ;
\nn(C \u2229 A)=4% n(A \u2229 B \u2229 C) = 2%
\nn(A \u2229 B\u0304 \u2229 C\u0304) = Only A
\n= n(A) – n(A \u2229 B) – n(A \u2229 C)+ n(A \u2229 B \u2229 C)
\n= 20000 \u00d7 33%
\n= 6600.<\/p>\n

Question 68.
\nThe numbers of proper sub-sets of the set {3, 4, 5, 6, 7} is : [1 Mark, May 2018]
\n(a) 32
\n(b) 31
\n(c) 30
\n(d) 25
\nAnswer:
\n(b)
\nFormula
\nNo. of proper sub-sets = 2n<\/sup> – 1 = 25<\/sup> – 1 = 31.<\/p>\n

Question 69.
\nA is {1, 2, 3, 4} and B is {1, 4, 9, 16, 25} if a function f is defined from set A to B where f(x) = x2<\/sup> then the range of f is: [1 Mark, Nov. 2018]
\n(a) {1, 2, 3, 4}
\n(b) {1, 4, 9, 16}
\n(c) {1, 4, 9, 16, 25}
\n(d) None of these
\nAnswer:
\n(b)
\n\u2235 f(x) = x2<\/sup>
\n\"Sets,
\nRange = {1, 4, 9, 16}<\/p>\n

Question 70.
\nIf A = {1, 2} and B = {3, 4}. Determine the number of relations from A and B: [1 Mark, Nov. 2018]
\n(a) 3
\n(b) 16
\n(c) 5
\n(d) 6
\nAnswer:
\n(b)
\nNo. of Relations = 2n(A\u00d7B)<\/sup>
\n= 2(2\u00d72)<\/sup>
\n= 16.<\/p>\n

Question 71.
\nIf A = {1, 2, 3, 4, 5, 6, 7} and B = {2, 4, 6, 8}. Cardinal number of A – B is: [1 Mark, Nov. 2018]
\n(a) 4
\n(b) 3
\n(c) 9
\n(d) 7
\nAnswer:
\nA \u2229 B = {1, 2, 3, 4, 5, 6, 7} \u2229 {2,4, 6, 8}
\n= {2, 4, 6} \u21d2n(A \u2229 B) = 3
\nn(A – B) = n(A) – n(A \u2229 B)
\n= 7 – 3 = 4<\/p>\n

Question 72.
\nIdentify the function from the following: [1 Mark, Nov. 2018]
\n(a) {(1,1), (1,2), (1,3)}
\n(b) {(1,1), (2,1), (2,3)}
\n(c) {(1,2), (2,2), (3,2), (4,2)}
\n(d) None of these
\nAnswer:
\n(c)
\nGo by choices
\n\"Sets,<\/p>\n

\"Sets,<\/p>\n

Question 73.
\nIf A= {1, 2, 3, 4, 5, 6, 7, 8, 9}; B = {1, 3, 4, 5, 7, 8}; C = {2, 6, 8}. [1 Mark, June 2019]
\nThen find (A – B) \u222a C
\n(a) {2, 6}
\n(b) {2, 6, 8}
\n(c) {2, 6, 8, 9}
\n(d) None
\nAnswer:
\n(c)
\nA – B = A – (A \u2229 B)
\n= {1, 2, 3, 4, 5, 6, 7, 8, 9}
\n= {1, 3, 4, 5, 7, 8}
\n= {2, 6, 9}
\n(A – B) \u222a C = {2; 6; 9} \u222a{2; 6; 8}
\n= {2 ; 6 ; 8 ; 9}
\n(c) is correct.<\/p>\n

Question 74.
\nA= {1, 2, 3, 4 ………….. 10} a relation on A, R= {(x,y)\/x + y= 10, x \u2208 A, Y \u2208 A, x \u2265 Y} then domain of R-1<\/sup> is: [1 Mark, June 2019]
\n(a) {1,2, 3, 4, 5}
\n(b) {0,3, 5, 7, 9}
\n(c) {1, 2, 4, 5, 6, 7}
\n(d) None
\nAnswer:
\n(a)
\nGiven; A = {1, 2, 3, ………………10}
\nR={x; y)\/x + y = 10; X \u2208 A; Y \u2208 A; x > y}
\n\u21d2 R = (5 ; 5) ; (6 ; 4) ; (7 ; 3); (8 ; 2); (9 ; 1)
\n\u21d2 R-1<\/sup> = (5; 5);(4; 6) ; (3 ; 7); (2 ; 8); (1 ; 9)
\nDomain of R-1<\/sup> = (5 ; 4 ; 3 ; 2 ; 1)<\/p>\n

Question 75.
\nThe no. of sub-sets of the set {3, 4, 5} is :
\n(a) 4
\n(b) 8
\n(c) 16
\n(d) 32
\nAnswer:
\n(b)
\nNo. of sub-sets = 2n<\/sup> = 23<\/sup> = 8.<\/p>\n

Question 76.
\nIf f(x) = x2<\/sup> and g(x) = \u221ax then
\n(a) go f(3) = 3
\n(b) go f(-3) = 9
\n(c) go f(9) = 3
\n(d) go f(-9) = 3
\nAnswer:
\n(a)
\n\u2235 f(x) = x2<\/sup>; g(x)= \u221ax
\ngo f(x) = g {f(x)}
\n\\(\\sqrt{f(x)}=\\sqrt{x^2}\\)
\n= x
\ngof{ 3) = 3
\n(a) is correct.<\/p>\n

\"Sets,<\/p>\n

Question 77.
\nIf A = {a, b, c, d}; B = {p, q, r, s} which of the following relation is a function from A to B: [1 Mark, June 2019]
\n(a) R1<\/sub> = {(a, p), (b, q), (c, s)}
\n(b) R2<\/sub> = {(p, a), (b, r), (d, s)}
\n(c) R3<\/sub> = {(b, p), (c, s), (b, r)}
\n(d) R4<\/sub> = {(a, p), (b, r), (c, q), (d, s)}
\nAnswer:
\n(d)
\nGBC
\n(a) All have one and only one solution of A in B except d i.e. d has no solution in B
\n\u21d2 Clearly R, is not Function.
\nSimilarly (b) & (c) are not functions or mappings.
\n\"Sets,
\n\u2234 R4<\/sub> is a function or mapping from A to B.<\/p>\n","protected":false},"excerpt":{"rendered":"

This Sets, Functions and Relations \u2013 CA Foundation Maths Study Material\u00a0is designed strictly as per the latest syllabus and exam pattern. Sets, Functions and Relations \u2013 CA Foundation Maths Study Material Previous Year Exam Questions Question 1. Out of 20 members in a family, 11 like to take tea and 14 like coffee. Assume that …<\/p>\n

Sets, Functions and Relations \u2013 CA Foundation Maths Study Material<\/span> Read More »<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[160],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/posts\/13817"}],"collection":[{"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/comments?post=13817"}],"version-history":[{"count":3,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/posts\/13817\/revisions"}],"predecessor-version":[{"id":13839,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/posts\/13817\/revisions\/13839"}],"wp:attachment":[{"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/media?parent=13817"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/categories?post=13817"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gstguntur.com\/wp-json\/wp\/v2\/tags?post=13817"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}