Practice Test

Q1) If I is the set of isosceles triangles and E is the set of equilateral triangles, then Show Answer

Q2) In a group of 20 persons, 8 drink tea but not coffee and 13 drink tea. Then number of persons who drink coffee but not tea is Show Answer

Q3) In a population of 50000 of a town, 28000 read newspaper X and 23000 read Y while 4000 read both. Then the number of persons who read neither X nor Y is Show Answer

Q4) If set Q = {1,2,3 } and PxQ = {(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(6,1),(6,2),(6,3)}, then: set P is Show Answer

Q5) The number of non-empty subsets of set {0,1,2,3} is Show Answer

Q6) If A={0,1,2,3,4} , then the number of proper subset of A is Show Answer

Q7) Which of the following is the empty set? Show Answer

Q8) Two finite have m and n elements. If the first set has 56 more subsets than the second set, then Show Answer

Q9) A-(A-B)= Show Answer

Q10) The set of intelligent students in a class is Show Answer

Q11) In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. If everyone speaks at least one of the two languages, then the number of people who can speak both Hindi and Bengali is? Show Answer

Q12) In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. If everyone speaks at least one of the two languages, then the number of people who can speak only Hindi? Show Answer

Q13) In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. If everyone speaks at least one of the two languages, then the number of people who can speak only Bengali? Show Answer

Q14) In a class of 100 students, 60 play Cricket, 50 play Hockey and 30 play both. Then the number of students who play only one of the two games is Show Answer

Q15) In a class of 100 students, 60 play Cricket, 50 play Hockey and 30 play both. Then the number of students who play none of the two games? Show Answer

Q16) In a class of 100 students, 55 students passed in Maths and 67 in stats. Then the number of students who passed in stats only is Show Answer

Q17) In a college of 300 students, every student reads 5 newspaper and every newspaper is ready by 60 students. then the number of newspapers is Show Answer

Q18) The null set is represented by Show Answer

Q19) If A = {2, 5, 6, 8}, then n (A) is Show Answer

Q20) If A = {1, 2, 3}, then P (A) is, Show Answer

Q21) If A = {a, b, c}, then n (p(A)) is Show Answer

Q22) If A= ( a b c d} list the element of power set P(A) Show Answer

Q23) If N is the set of natural numbers and I is the set of positive integers, then Show Answer

Q24) The set of squares of positive integers is Show Answer

Q25) Equal sets are- Show Answer

Q26) If cardinal number of two finite sets is same, then the sets are- Show Answer

Q27) The range set of a constant function is a- Show Answer

Q28) The number of subsets of a set containing n elements is Show Answer

Q29) A set containing 4 elements have- Show Answer

Q30) The number of subsets of the set {2, 3, 5} is Show Answer

Q31) Let A = {a,b}. Set of subsets of A is called power set of A denoted by P(A). Now n(P(A)) is Show Answer

Q32) If E={1,2,3,4,5,6,7,8,9}, the subset of E satisfying 5 + x >10 is Show Answer

Q33) If R is the set of positive rational number and E is the set of real numbers then Show Answer

Q34) What is the relationship between the following sets?
A={x:x is a letter in the word flower}
B={x:x is a letter in the world flow}
C = {x:x is a letter in the world wolf}
D ={x:x is a leter in the word follow}
Show Answer

Q35) E is a set of positive even number and O is a set of positive odd numbers, then E U O is a Show Answer

Q36) If A = {1 2 3 4} B ={2 3 7 9} and C = {1 4 7 9} then Show Answer

Q37) If S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, P = {0, 2, 4, 6, 8}, and Q = {1, 2, 3, 4, 5}, then P' is Show Answer

Q38) If S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, P = {0, 2, 4, 6, 8}, and Q = {1, 2, 3, 4, 5}, then Q' is Show Answer

Q39) A'is Show Answer

Q40) The set B' is Show Answer

Q41) The set C' is Show Answer

Q42) The set (A')' is Show Answer

Q43) The set (B')' is Show Answer

Q44) A - B is Show Answer

Q45) If n (P) = 3 and n (Q) = 4, then n (P x Q) is Show Answer

Q46) If the set P has 6, Q has 5 and R has 2 elements then the set P×Q×R contains Show Answer

Q47) If A = {1, 2} and B = {2,3} then A × B is equal to- Show Answer

Q48) If A = {1, 2, 3}, B = {4, 5}, then A × B is Show Answer

Q49) If A = (1,2,3,5,7) and B= (1,3,6,10,15) then cardinal number of A - B is Show Answer

Q50) When 5 X < 24 and X belongs to set of natural numbers then the solution set is Show Answer

Q51) For 3X + 1 <= 16 and X belongs to set of natural number, the solution set is - Show Answer

Q52) If the universal set E = {x|x is a positive integer < 25}, A = {2,6,8,14,22}, B = {4,8,10,14} then Show Answer

Q53) Re-write the following sets in a set builder form :- A={a, e, l, o, u} B={1, 2, 3, 4 ……} C is a set of integers between - 15 and 15. Show Answer

Q54) In a group of 20 children, 8 drink tea but not coffee and 13 like tea. The number of children drinking coffee but not tea is Show Answer

Q55) In a group of 40 children 16 like cricket but not movie and 26 like cricket. The number of children like movie but not cricket are Show Answer

Q56) Out of total 150 students 45 passed in Accounts, 50 in Maths, 30 in Costing, 30 in both Accounts and Maths, 32 in both Maths and Costing, 35 in both Accounts and Costing. 25 students passed in all the three subjects. Find the number who passed at least in any one of the subjects. Show Answer

Q57) A survey shows that 68% of women like apples, 74% of women like orange. What percentage like both Show Answer

Q58) A survey shows that 74% of the Indians like grapes, whereas 68% like bananas. What % of Indians like both grapes and bananas? Show Answer

Q59) In a class 30 students, 20 students like maths, 18 like science and 12 like both the subject. Find the number of student who likes no subject. Show Answer

Q60) At a certain conference of 100 people there are 29 Indian women and 23 Indian men. Out of these Indian people 4 are doctors and 24 are either men or doctors. There are no foreign doctors. The number of women doctors attending the conference is Show Answer

Q61) Find how many could not get any of these Show Answer

Q62) Find how many of them did only one of these. Show Answer

Q63) Find how may failed in all the three papers. Show Answer

Q64) How many passed in all the three papers? Show Answer

Q65) Find the number having all the three. Show Answer

Q66) Find the number having tea and cocoa but not coffee. Show Answer

Q67) Find the number having only coffee. Show Answer

Q68) Determine the complaints about all the three. Show Answer

Q69) Determine the complaints about two or more than two. Show Answer

Q70) Find out how many failed in all the three Show Answer

Q71) How many failed in the aggregate but not in group-II? Show Answer

Q72) How many failed in group-I but not in the aggregate. Show Answer

Q73) How many failed in group-II but not in group-I? Show Answer

Q74) How many failed in the aggregate or group-II but not in group-I? Show Answer

Q75) How many failed in the aggregate but not in group-I and group-II? Show Answer

Q76) List the winning coalitions. Show Answer

Q77) List the blocking conditions. Show Answer

Q78) List the losing conditions. Show Answer

Q79) n(A') is Show Answer

Q80) How many buy B grade? Show Answer

Q81) How many buy C grade if any only if they do not buy B grade? Show Answer

Q82) How many buy C and B grades but not the A grade? Show Answer

Q83) On a survey of 100 boys it was found that 50 used white shirt 40 red and 30 blue. 20 were habituated in using both white and red shirts 15 both red and blue shirts and 10 blue and white shirts. Find the number of boys using all the colours. Show Answer

Q84) If a relation R = {(1,1), (2,2), (1,2), (2,1)} is symmetric on A = {1,2,3} then R is Show Answer

Q85) If A={1,2,3} and B={4,6,7} then the
Relation R={(2,4) (3,6)} is .
Show Answer

Q86) A function is invertible if and only if f is- Show Answer

Q87) A function f(x) is an even function if Show Answer

Q88) The domain of {(1,7), (2,6)} is Show Answer

Q89) The range of {(3,0),(2,0),(1,0),(0,0)} is Show Answer

Q90) The range of { (1,6),(2,7)} is- Show Answer

Q91) Let the domain of x be the set {0,1}. Which of the following functions are equal to 1 Show Answer

Q92) Which of the diagram are graph of a function Show Answer

Q93) "Is equal to" over the set of all rational numbers is Show Answer

Q94) "Is smaller than" over the set of eggs in a box is Show Answer

Q95) "Is greater than" over the set of all natural number if known as Show Answer

Q96) The relation "is parallel to" on the set of all straight lines in a plane is- Show Answer

Q97) "is perpendicular to" over the set of straight lines in a given plane is Show Answer

Q98) is the reciprocal of '………. over the set of non zero real numbers is Show Answer

Q99) "Is the square of" over n set of reai numbers is Show Answer

Q100) "has the same father as" ……..over the set of children Show Answer

Q101) If A = { 1,2,3} then R = {(1,1),(2,2) ,(3,3) ,(1,2)} is Show Answer

Q102) If a = {1,2,3} then a relation {(1,1),(2,2),(3,3)} is- Show Answer

Q103) In inverse relation R - Show Answer

Q104) Out of 20 members in a family, 11 like to take tea and 14 like coffee, Assume that each one likes at least one of the two drinks, find how many like both coffee and tea: Show Answer

Q105) In a group of 70 people who speak Hindi, 33 speak English and 10 speak neither Hindi nor English. Find how many can speak both English as well as Hindi: Show Answer

Q106) In a town of 20,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families but 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, the the number of families which buy A only is: Show Answer

Q107) If A = {p, q, r, s}
B = {q, s, t}
C = {m, q, n}
Find C - (A B). Show Answer

Q108) X = {x, y, w, z} , y = {1, 2, 3, 4} H = {(x, 1), (y, 2), (y, 3), (z, 4), (x, 4)} Show Answer

Q109) If the set N of natural numbers the relation R defined by a R b "if and only if, a divide b" , then the relation R is Show Answer

Q110) The number of proper sub set of the set {3, 4, 5, 6, 7} is Show Answer

Q111) On the set of lines, being perpendicular is a _______ relation. Show Answer

Q112) For 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? Show Answer

Q113) The number of element in range of constant function is: Show Answer

Q114) Of the 200 candidates who were interviewed for a position at call centre, 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 credit card and a mobile phone, 60 had both a two wheeler and mobile phone, and 10 had all three. How many candidates had none of the three? Show Answer

Q115) In a class of 50 students, 35 opted for Mathematics and 37 opted for Commerce. The number of such students who opted for both Mathematics and Commerce are: Show Answer

Q116) The range of {(1, 0), (2, 0), (3, 0), (4, 0), (0, 0)} is: Show Answer

Q117) In a class of 80 students, 35 % students can play only cricket, 45% students can play only table tennis and the remaining students can play both the games, in all how many students can play cricket? Show Answer

Q118) The number of subset of the set formed by the word Allahabad is: Show Answer

Q119) In a group of students 80 can speak Hindi, 60 can speak English and 40 can speak English and Hindi both, then number of students is: Show Answer

Q120) In a class of 35 students, 24 like to play cricket and 16 like to play football. Also each students likes to play at least one of the two games. How many students like to play both cricket and football? Show Answer

Q121) The number of proper sub set of the set {3, 4, 5, 6,7} is: Show Answer

Q122) If A = {1, 2} and B = {3, 4}. Determine the number of relations from A and B: Show Answer

Q123) Identify the function from the following: Show Answer

Q124) The no. of subsets of the set {3,4,5} is: Show Answer

Q125) If A={a, b, c, d}; B={p, q, r,s} which of the following relation is a function from A to B Show Answer

Q126) Two finite sets respectively have x and y number of elements. The total number of subsets of the first is 56 more than the total number of subsets of the 2nd. The value of x and y respectively. Show Answer

Q127) The number of items in the set A is 40; in the set B is 32; in the set C is 50; in both A and B is 4, in both A and C is 5; in both B and C is 7 in all the sets 2. How many are in only one set? Show Answer

Q128) The set of cubes of the natural number is: Show Answer

Q129) In the set of all straight lines on a plane which of the following is Not 'TRUE'? Show Answer

Q130) Out of a group of 20 teachers in a school, 10 teach mathematics, 9 teach Physics and 7 teach Chemistry. 4 teach Mathematics and Physics but none teach both mathematics and chemistry. How many teach chemistry and physics; how many teach only physics? Show Answer

Q131) If a is related to b if and only if the difference in a and b is an even integer. This relation is Show Answer

Q132) Two finite sets have x and y number of elements. The total number of subsets of first is 56 more than the total number of subsets of second. The value of x and y is: Show Answer

Q133) The number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7 is
Show Answer

Q134) Let A=1,2,3 and consider the relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}. Then r is Show Answer

Q135) The number of subsets of the set (0,1,2,3) is: Show Answer

Q136) Given the relation R={(1,2), (2,3)} on the set A={1, 2, 3}, the minimum number of ordered parts which when added to R make it Equivalence relation is:
Show Answer

Q137) A survey shows that 74% of the Indian like grapes, whereas 68% like bananas.What percentage of the Indian like both grapes and bananas if everybody likes either fruit? Show Answer

Q138) In a survey of 100 boys it was found that 50 used white shirts, 40 red shirts and 30 blue shirts.20 were habituated in using both white and red shirts.15 were using both red and blue shirts and 10 were using blue and white shirt.Find the number of boys who are using all colours;
Show Answer

Q139) If B={1, 2, 3, 4, 5}, then the number of proper subsets of B is:
Show Answer