Practice Test


1) The set of intelligent students in a class is


2) Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then


3) Which of the following is not null set?


4) Which of the following is an equal set?


5) Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The value of m and n are, respectively.


6) Let S = set of points inside the square, T = the set of points inside the triangle and C = the set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then,


7) In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. The number of people speak atleast one of these two languages is


8) In a class of 60 students, 25 students play Cricket and 20 students play Tennis, and 10 students play both the games. Then ,the number of students who play neither is


9) In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 read both. Then the number of persons who read neither is


10) Which of the following is a singleton set?


11) If P(A) = P(B) , then


12) There are 100 families in a society, 40 families buy newspapers A, 30 families buy newspapers B, 30 families buy newspapers C, 1 families buy newspaper A and B , 8 families buy newspaper A and C. 3 families buy newspaper A,B and C, then the number of families who do not buy and newspaper is


13) In a survey of 200 students of a school, it was found that 120 study Mathematics, 90 study Physics, and 70 study Chemistry, 40 study mathematics and Physics, 30 study Physics and Chemistry, 50 study Chemistry and mathematics and 20 none of these subjects. The number of students who study all the three subjects is


14) Let U be the set of all the boys and girls in a school, G be the set of all the girls in the school, B be the set of all the boys in the school and S be the set of all students in the school who take swimming, but not all the students in the school take swimming.


15) From 50Students taking examinations in mathematics, Physics, and Chemistry, each of the student has passed in atleast6 one of the subject, 37 passed mathematics, 24 passed in Physics, and 43 in Chemistry. Atmost 19 passed mathematics and Physics, atmost 29 mathematics and Chemistry and atmost 20 Physics and Chemistry. The largest possible number that could have passed all three examination is


16) In a group of 50 students studying French, English, Sanskrit were found to be as follows
French = 17, English = 13, Sanskrit = 15
French and English = 09, English and Sanskrit = 4
French and Sanskrit = 5, English, French and Sanskrit = 3. The number of students who study


17) The number of students passed in English and Mathematics but not in Science is


18) The number of student only passed in Mathematics is


19) The number of students only passed in more than one subject is


20) If two sets A and B are having 99 element in common, then the number of elements common to each of the sets A x B and B x A are


21) Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A, is


22) Let n(A) = m and n(B) = n. Then, the total number of non-empty relations that can be defined from A to B is


23) Let R be a relation on N defined by x + 2y = 8. The domain of R is


24) If R is a relation from a set A to the set B and S is a relation from B to C, then the relation SoR


25) The domain and range of the function f given by f(x) = 2 - |x - 5| is


26) The graph of the function y = f(x) is symmetrical about the line x = 2, then


27) The example of relation which are reflexive and transitive but not symmetric of


28) Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. The relation is


29) Which of the following is empty set


30) In a town of 10,000 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 newspaper, then number of families which buy A only is


31) In the class of 55 students, the number of students studying different are 23 in mathematics, 24 in physics,19 in chemistry, 12 in mathematics and physics, 9 in mathematics and chemistry and 4 in all the three subjects . The number of students who have taken exactly one subject is


32) In rule method the null set is represented by


33) Which set is the subset of all given sets


34) The number of non empty subset of the set {1,2,3,4} is


35) Let A and B be two sets . then


36) For any two sets A and B , A -(A-B) equals


37) If A is any set , then


38) A class has 175 students. The following data shows that number of students obtaining one or more subjects. mathematics 100, physics 70, and chemistry 40; mathematics and physics 30, mathematics and chemistry 28, physics and chemistry 23; mathematics physics and chemistry 18. How many students have offered mathematics alone


39) In a battle 70% combatants lost one eye ,80% an ear, 75% an arm 85% a leg,x% lost all four limbs. The minimum value of x is


40) Out of 800 boys in school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all three games. The number of students who did not play any games is


41) A survey shows that 63 % of Americans like cheese where as 76% of them like apple If x% of the Americans like both cheese and apple


42) Of the member of three athletic teams in school 21 are in the cricket team, 26 are in the hockey team and 29 are in football team. Among them 14 play hockey and cricket, 15 play hockey and football and 12 play football and cricket. Eight play all three games. The total number of member in the three athletic team is


43) In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in physics. Then the number of students who have passed in physics only is


44) Let A and B be subset of a set X. Then


45) Let A and B be two sets in the universal set. Then A-B equals


46) There are 100 students in a class. In examination, 50 of then failed in mathematics, 45 failed in physics, 40 failed in biology and, 32 failed in in exactly two subjects. Only one student passed in all three subjects. Then the number of students failing in all the three subjects


47) In a class of 80 students numbered 1 to 80, all odd number students opt for Cricket , students who's number are divisible by 5 opt for Football and those number are divisible by 7 opt for Hockey . the number of students who do not play any of the three games, is


48) In a class of 30 pupils, 12 take needle work , 16 physics and 18 take history. If all the 30 students take at least one subject and no one take all three then the number of pupils taking 2 subject is


49) If the set A contain 5 elements, then the number of elements in the power set P(A) is equal to


50) 25 people for programme A, 50 people for programme B, 10 people for both So, the number of employee employed only A is


51) Let S ={ 1,2,3,4} the total number of unordered pairs of disjoint subsets of S is equal to


52) In a college of 300 students , every student read 5 and every newspaper is read by 60 students . the no. of newspaper is


53) Let A={1,2,3} and B ={2,3,4} , then which of the following relation is a function from A to B


54) The relation R defined on the set of natural number as {(a,b):a differ from b by 3}, is given by


55) A relation from P to Q is


56) If A is the set of even natural numbers less than 8 is B is the set of prime number less than 7 then the number of relation from A to B is


57) The relation "is subset of" on the power set P(A) of a set A is


58) If A={x,y} then the power of set A is


59) Which of is a true statement


60) Let R and S be two relation on a set A. then


61) Let X={1,2,3,4,5} and Y={1,3,5,7,9}. which of the following is / are relation from X to Y


62) Let R be an equivalent relation on a finite set A having n elements . Then the number of ordered pairs in R is


63) Let X be family of set and R be a relation on X define by ' A is disjoint from B' . Then R is


64) If R is a relation from set A to a set B and S is a relation from B to set C, then the relation SoR


65) An integer m is said to be related to another integer n if m is a multiple of n . then relation is


66) Let A ={a,b,c} and B={1,2}. consider a relation R defined from set A to set B . Then R is equal to set


67) On the set N of all natural numbers define the relation R by a R b if and only if the G.C.D. of a and b is 2 then R is


68) Let R be a reflexive relation on finite set A having n-element and let there be m ordered pairs in R . Then


69) Let R be a reflexive relation on a set A and I be the identity relation on A . Then


70) Let S be the set of all real numbers .Then the relation R={a,b):1+ab>0} on S is


71) Let R= {(a,a)} be a relation on a set A . then R is


72) The void on set A is


73) Which one of the following relation on r is an equivalence relation


74) In order that a relation R is defined on a non empty set A is an equivalence relation sufficient , if R


75) The relation "congruence modulo m" is


76) If (24,92)=24m+92n, then(m,n) is


77) Two finite sets have m and n elements . The number of sunsets of the first set is 112 more than that of the second set . The value of m and n are , respectively


78) Let S = set of points inside the square ,T= set of points inside the triangle and C= set of points inside the circle If the triangle and circle intersect each other and are contained in a square . Then ,


79) If R be the set of points inside a rectangle of sides a and b (a,b>1) with two sides along the positive direction of
x -axis and y-axis Then ,


80) In a town of 840 person , 450 person read hindi , 300 read english and 200 read both . then , the number of person who read neither is


81) A survey shows that 63% of the person watch a new channel whereas 76% watch another channel . If x% of the people who watch both channel then


82) The maximum equivalence relation on the set A={1,2,3} are


83) If, A={1,2,3} and consider the relation R = {(1,1),(2,2), (3,3), (1,2),(2,3), (1,3)}


84) Let R={(3,3),(6,6),(9,9),(12,12), (6,12),(3,9),(3,12),(3,6)} be a relation on the set A ={3,6,9,12}. The relation is


85) Let R ={1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is


86) With reference to a universal set , the inclusion of a subset in another , is relation , which is


87) Let R and S be two non - void relation on a set A. which of the following statement is false


88) The example of relation which are reflexive and transitive but not symmetric of


89) Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. The relation is


90) Let X={1,2,3,4,5} and Y={1,3,5,7,9}. which of the following is / are relation from X to Y


91) Let R be an equivalent relation on a finite set A having n elements . Then the number of ordered pairs in R is


92) Let X be family of set and R be a relation on X define by ' A is disjoint from B' . Then R is


93) If R is a relation from set A to a set B and S is a relation from B to set C, then the relation SoR


94) An integer m is said to be related to another integer n if m is a multiple of n . then relation is


95) Let A ={a,b,c} and B={1,2}. consider a relation R defined from set A to set B . Then R is equal to set


96) On the set N of all natural numbers define the relation R by a R b if and only if the G.C.D. of a and b is 2 then R is


97) Let R be a reflexive relation on finite set A having n-element and let there be m ordered pairs in R . Then


98) Let R be a reflexive relation on a set A and I be the identity relation on A . Then


99) Let S be the set of all real numbers .Then the relation R={a,b):1+ab>0} on S is


100) Let R= {(a,a)} be a relation on a set A . then R is


101) The void on set A is


102) Which one of the following relation on R is an equivalence relation


103) In order that a relation R is defined on a non empty set A is an equivalence relation sufficient , if R


104) The relation "congruence modulo m" is


105) If (24,92)=24m+92n, then(m,n) is


106) Two finite sets have m and n elements . The number of subsets of the first set is 112 more than that of the second set . The value of m and n are , respectively


107) Let S = set of points inside the square ,T= set of points inside the triangle and C= set of points inside the circle If the triangle and circle intersect each other and are contained in a square . Then ,


108) If R be the set of points inside a rectangle of sides a and b (a,b>1) with two sides along the positive direction of
x -axis and y-axis Then ,


109) In a town of 840 person , 450 person read hindi , 300 read english and 200 read both . then , the number of person who read neither is


110) A survey shows that 63% of the person watch a news channel whereas 76% watch another channel . If x% of the people who watch both channel then


111) The maximum equivalence relation on the set A={1,2,3} are


112) If, A={1,2,3} and consider the relation R = {(1,1),(2,2), (3,3), (1,2),(2,3), (1,3)}


113) Let R={(3,3),(6,6),(9,9),(12,12), (6,12),(3,9),(3,12),(3,6)} be a relation on the set A ={3,6,9,12}. The relation is


114) Let R ={1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is


115) With reference to a universal set , the inclusion of a subset in another , is relation , which is


116) Let R and S be two non - void relation on a set A. which of the following statement is false


117) The relation "less than" in the set of natural number is


118) The number of reflexive relation of a set with four element is equal to


119) Let R and S be two equivalence relation on a set A. Then


120) Two finite sets have M and N elements . the total numbers of subsets of second set is 56 more than the total number of element


121) Let A and B be two non-empty subsets of set X such that A is not a subset of B , then


122) Given the relation R = {(1,2),(2,3)} on the set A={1,2,3}, the minimum number of ordered pairs which when added to R make it an equivalence relation is


123) In a group of 75 persons every one takes either tea or coffee. If 45 take tea and 35 take coffee, then the number of persons who take tea only and not coffee is


124) Two finite sets A and B have m and n elements. Number of subsets of A is 56 more than that of B. The values of m and n are


125) Let A = {a, b, c} and R = {(a, a), (b, b), (a, b), (b, a), (b, c)} be a relation on A, then R is


126) Let X = {1, 2, 3} and R = {(1, 1), (2, 2), (3, 3), (2, 3)} be a relation on X. Then which one is not true


127) Let A = {2, 4, 6, 8} and define R = {(2, 4), (4, 2), (4, 6), (6, 4)} then R is


128) Let A = {p ,q, r, s} and B = {1, 2, 3} which of the following relations from A to B is not a function.


129) Let A = {p, q, r} which of the following is an equivalence relation on A?


130) In the set X = {a, b, c, d} which of the following relations is a function?


131) If A = {2, 3, 4, 5}, then which of the following relations is a function from A to itself


132) If a set X = {a, b, c, d} which of the following is a function on X?


133) Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following relation from A to B is a function from A into B.


134) Let A = {p, q, r, s}, B = {1, 2, 3} which of the following relations from A to B is not a function.


135) Let A = {1, 2, 3, 4} and B = {1, 2}. Then the number of onto functions from A onto B is


136) The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is


137) The number of bijective functions from the set A to itself, if A contains 108 elements is


138) Let A be a set containing 10 distinct elements, then the total number of distinct functions from A to A is


139) If the set A has 3 elements and the set B has 4 elements, then the number of injections (one-one) that can be defined from A to B is


140) The number of bijective functions (one-one, onto) from the set A onto itself, when n (A) = 108, is


141) The number of functions from the set A into the set B, when n (A) = 7 and n (B) = 5 is


142) If n (A) = 15 and n (B) = 10, then the number of injective (one-one) mapping from A into B is


143) The domain of the function f (x) = cot 5 x is


144) The domain of the function f (x) = tan 3 x is


145) Two finite sets have m and n elements. The number of elements is the power set of first set is 48 more than the power set of second set. Then (m, n) =


146) A survey shows that 65% of the Americans like cheese whereas 79% like Oranges. If x% of the Americans like both, then


147) If A = {1, 2, 3, 4, 5, 6} then how many subsets of A contain the elements 2, 3 and 5?


148) In an election, two persons A and B contested x% of the total voter voted for A and (x + 20)% for B. If 20% of the voters did not vote, then x =


149) The number of equivalence relation that can be defined on {a, b, c} is


150) The relation 'is not equal to' is defined on R, is


151) If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is


152) If a set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mapping from A to B is


153) Which of the following functions from Z into Z is a bijection?


154) If a set has n elements than the total number of subsets of A is


155) The number of non empty subsets of the set {1, 2, 3, 4} is


156) Let, R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {(1, 2, 3, 4)}. Then the relation R is


157) In a city 20 percent of the population travel by car, 50 percent travel by bus and 10 percent travels by both car and bus. The persons traveling by car and bus in


158) Which of the following function is an even function?


159) Which one of the following is the bijective function on the set of real numbers?


160) Which of the following is not periodic?


161) A set of A has 5 element. Then the maximum number of relations on A (including empty relation) is


162) Let R be an equivalence relation defined on a set containing 6 elements. The minimum number of ordered pairs that R should contain is


163) The number of non-one and onto mapping from A to B where n (A) = 6 and n (B) = 7 is


164) The number of functions that can be formed from the set A = {a, b, c, d} into the set B = {1, 2, 3} is equal to


165) The function which map [-1, 1] to [0, 2] are


166) Which of the four statements given below is different from others


167) Which of the following function is invertible?


168) Domain and Range are equal for the


169) Which of the following real valued functions is/are not even functions?


170) The set A has 4 elements and the set B has 5 elements then the number of injective mappings that can be defined from A to B is


171) If equation of the curve remain unchanged by replacing x and y from y and x respectively, then the curve is


172) Which relation is a function?


173) Which of the following functions are periodic?


174) A function whose graph is symmetrical about the origin is given by


175) Which of the following functions is are injective map(s)?


176) A college awarded 38 medals in Football, 15 in Basketball and 20 to Cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports. The number of students who received medals in exactly two of the three sports is


177) In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then persons traveling by car or bus is


178) In the set Z of all integers, which of the following relation R is not an equivalence relation?


179) Which of the following function is a polynomial function?


180) Which of the following functions is periodic?


181) In a class of 55 students, the number of students studying different subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is


182) Let S = {0, 1, 5, 4, 7}. Then the total number of subsets of S is


183) 20 teachers of a school either teach mathematics or physics. 12 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching physics only is


184) Given two finite sets A and B such that n(A) = 2, n(B) = 3. Then total number of relations from A to B is


185) If R is a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is


186) Let A = {1, 2, 3, 4} and R be a relation in A given by R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)}. Then R is


187) In a class of 35 students, 17 have taken Mathematics, 10 have taken Mathematics but not Economics. If each student has taken either Mathematics or Economics or both, then the number of students who have taken Economics but not Mathematics is


188) Let A be the set of all students in a school. A relation R is defined on A as follows:
"aRb iff a and b have the same teacher "


189) In a class, 70 students wrote two tests viz; test-I and test-II. 50% of the students failed in test-I and 40% of the students in test-II. How many students passed in both tests ?


190) In an office, every employee likes at least one of tea, coffee and milk. The number of employees who like only tea, only coffee, only milk and all the three are all equal. The number of employees who like only tea and coffee, only coffee and milk and only tea and milk are equal and each is equal to the number of employees who like all the three. Then a possible value of the number of employees in the office is


191) Which of the following cannot be the number of elements in the power set of any finite set?


192) The relation ‘is subset of’ on the power set P(A) of a set A is


193) In a class of 45 students, 22 can speak Hindi and 12 can speak English only. The number of students, who can speak both Hindi and English, is


194) In a class of 30 pupils 12 take chemistry work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three, then the number of pupils taking 2 subjects is


195) The void relation on a set A is


196) In the above question, the number of families which buy none of A, B and C is


197) In a set of ants in a locality, two ants are said to be related iff they walk on a same straight line, then the relation is


198) If A is a non-empty set, then which of the following is false?
p ∶ There is at least one reflexive relation on A
q ∶ There is at least one symmetric relation on A


199) In a rehabilitation program, a group of 50 families were assured new houses and compensation by the government. Number of families who got both is equal to the number of families who got neither of the two. The number of families who got new houses is 6 greater than the number of families who got compensation. How many families got houses?


200) In a certain town 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is


201) Let X = {1, 2, 3, 4, 5} and Y = {1, 3, 5, 7, 9}. Which of the following is/are not relations from X to Y?


202) Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is


203) X is the set of all residents in a colony and R is a relation defined on X as follows:
“Two persons are related iff they speak the same language” The relation R is


204) Let A = { ONGC, BHEL, SAIL, GAIL, IOCL } and R be a relation defined as “two elements of A are related if they share exactly one letter”. The relation R is


205) The finite sets A and B have m and n elements respectively. if the total number of subsets of A is 112 more than the total number of subsets of B, then the volume of m is


206) The relation R = { (1,3), (3,5) } is defined on the set with minimum number of elements of natural numbers. The minimum number of elements to be included in R so that R is an equivalence relation, is


207) If A = {1, 2, 3}, then the relation R = { (1, 1), (2, 2), (3, 1), (1, 3) } is


208) If A is a non-empty set, then which of the following is false?
p ∶ Every reflexive relation is a symmetric relation
q ∶ Every antisymmetric relation is reflexive
Which of the following is/are true?


209) Let X be a family of sets and R be a relation on X defined by 'A is disjoint from B'. Then, R is


210) If A = {x, y}, then the power set of A is


211) Which of the following is true?


212) If A and B are two sets, then A - ( A - B ) is equal to


213) If A = {1, 2, 3, 4}, then the number of subsets of A that contain the element 2 but not 3, is


214) The relation “is a factor of” on the set N of all natural numbers is not


215) In a set of teachers of a school, two teachers are said to be related if they “teach the same subject”, then the relation is


216) The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is


217) Set builder form of the relation R = {(−2, −7), (−1, −4), (0, −1), (1, 2), (2, 5)} is


218) Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then, the value of M and N are


219) Let R be a relation defined on S, the set of squares on a chess board such that xRy if x and y share a common side. Then, which of the following is false for R?


220) If A = {x, y, z}, then the relation R = {(x, x), (y, y), (z, z), (z, x), (z, y)} is


221) If A = {a, b, c, l, m, n}, then the maximum number of elements in any relation on A is


222) In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?


223) Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of the set of all determinants with value −1. Then


224) Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following relations is a function from A to B?


225) Which one is not periodic?


226) Let n(A) = 4 and n(B) = 6. The number of one to one functions from A to B is


227) Which of the following functions is inverse of itself?


228) The number of bijective functions from set A to itself when A contains 106 elements is


229) The number of onto mappings from the set A = {1, 2, ...., 100} to set B = {1, 2} is


230) The number of reflexive relations of a set with four elements is equal to


231) Let R ={(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. The relation is


232) Which of the following functions is one-to-one?


233) If f(x) is defined on [0, 1], then the domain of definition of f(tan x) is


234) Which of the following functions is not an are not an injective map(s)?


235) Which of the following functions is (are) not an injective map(s)?