Practice Test

Q1) The set of intelligent students in a class is Show Answer

Q2) Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then Show Answer

Q3) Which of the following is not null set? Show Answer

Q4) Which of the following is an equal set? Show Answer

Q5) 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. Show Answer

Q6) 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, Show Answer

Q7) 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 Show Answer

Q8) 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 Show Answer

Q9) 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 Show Answer

Q10) Which of the following is a singleton set? Show Answer

Q11) If P(A) = P(B) , then Show Answer

Q12) 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 Show Answer

Q13) 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 Show Answer

Q14) 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. Show Answer

Q15) 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 Show Answer

Q16) 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 Show Answer

Q17) The number of students passed in English and Mathematics but not in Science is Show Answer

Q18) The number of student only passed in Mathematics is Show Answer

Q19) The number of students only passed in more than one subject is Show Answer

Q20) 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 Show Answer

Q21) Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A, is Show Answer

Q22) 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 Show Answer

Q23) Let R be a relation on N defined by x + 2y = 8. The domain of R is Show Answer

Q24) 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 Show Answer

Q25) The domain and range of the function f given by f(x) = 2 - |x - 5| is Show Answer

Q26) The graph of the function y = f(x) is symmetrical about the line x = 2, then Show Answer

Q27) The example of relation which are reflexive and transitive but not symmetric of Show Answer

Q28) 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 Show Answer

Q29) Which of the following is empty set Show Answer

Q30) 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 Show Answer

Q31) 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 Show Answer

Q32) In rule method the null set is represented by Show Answer

Q33) Which set is the subset of all given sets Show Answer

Q34) The number of non empty subset of the set {1,2,3,4} is Show Answer

Q35) Let A and B be two sets . then Show Answer

Q36) For any two sets A and B , A -(A-B) equals Show Answer

Q37) If A is any set , then Show Answer

Q38) 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 Show Answer

Q39) 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 Show Answer

Q40) 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 Show Answer

Q41) 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 Show Answer

Q42) 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 Show Answer

Q43) 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 Show Answer

Q44) Let A and B be subset of a set X. Then Show Answer

Q45) Let A and B be two sets in the universal set. Then A-B equals Show Answer

Q46) 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 Show Answer

Q47) 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 Show Answer

Q48) 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 Show Answer

Q49) If the set A contain 5 elements, then the number of elements in the power set P(A) is equal to Show Answer

Q50) 25 people for programme A, 50 people for programme B, 10 people for both So, the number of employee employed only A is Show Answer

Q51) Let S ={ 1,2,3,4} the total number of unordered pairs of disjoint subsets of S is equal to Show Answer

Q52) In a college of 300 students , every student read 5 and every newspaper is read by 60 students . the no. of newspaper is
Show Answer

Q53) Let A={1,2,3} and B ={2,3,4} , then which of the following relation is a function from A to B Show Answer

Q54) The relation R defined on the set of natural number as {(a,b):a differ from b by 3}, is given by Show Answer

Q55) A relation from P to Q is Show Answer

Q56) 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 Show Answer

Q57) The relation "is subset of" on the power set P(A) of a set A is Show Answer

Q58) If A={x,y} then the power of set A is Show Answer

Q59) Which of is a true statement Show Answer

Q60) Let R and S be two relation on a set A. then Show Answer

Q61) 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 Show Answer

Q62) Let R be an equivalent relation on a finite set A having n elements . Then the number of ordered pairs in R is Show Answer

Q63) Let X be family of set and R be a relation on X define by ' A is disjoint from B' . Then R is Show Answer

Q64) 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 Show Answer

Q65) An integer m is said to be related to another integer n if m is a multiple of n . then relation is Show Answer

Q66) 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 Show Answer

Q67) 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 Show Answer

Q68) Let R be a reflexive relation on finite set A having n-element and let there be m ordered pairs in R . Then Show Answer

Q69) Let R be a reflexive relation on a set A and I be the identity relation on A . Then Show Answer

Q70) Let S be the set of all real numbers .Then the relation R={a,b):1+ab>0} on S is Show Answer

Q71) Let R= {(a,a)} be a relation on a set A . then R is Show Answer

Q72) The void on set A is Show Answer

Q73) Which one of the following relation on r is an equivalence relation Show Answer

Q74) In order that a relation R is defined on a non empty set A is an equivalence relation sufficient , if R Show Answer

Q75) The relation "congruence modulo m" is Show Answer

Q76) If (24,92)=24m+92n, then(m,n) is Show Answer

Q77) 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 Show Answer

Q78) 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 , Show Answer

Q79) 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 , Show Answer

Q80) 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 Show Answer

Q81) 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 Show Answer

Q82) The maximum equivalence relation on the set A={1,2,3} are Show Answer

Q83) If, A={1,2,3} and consider the relation R = {(1,1),(2,2), (3,3), (1,2),(2,3), (1,3)} Show Answer

Q84) 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 Show Answer

Q85) 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 Show Answer

Q86) With reference to a universal set , the inclusion of a subset in another , is relation , which is Show Answer

Q87) Let R and S be two non - void relation on a set A. which of the following statement is false
Show Answer

Q88) The example of relation which are reflexive and transitive but not symmetric of Show Answer

Q89) 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 Show Answer

Q90) 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 Show Answer

Q91) Let R be an equivalent relation on a finite set A having n elements . Then the number of ordered pairs in R is Show Answer

Q92) Let X be family of set and R be a relation on X define by ' A is disjoint from B' . Then R is Show Answer

Q93) 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 Show Answer

Q94) An integer m is said to be related to another integer n if m is a multiple of n . then relation is Show Answer

Q95) 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 Show Answer

Q96) 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 Show Answer

Q97) Let R be a reflexive relation on finite set A having n-element and let there be m ordered pairs in R . Then Show Answer

Q98) Let R be a reflexive relation on a set A and I be the identity relation on A . Then Show Answer

Q99) Let S be the set of all real numbers .Then the relation R={a,b):1+ab>0} on S is Show Answer

Q100) Let R= {(a,a)} be a relation on a set A . then R is Show Answer

Q101) The void on set A is Show Answer

Q102) Which one of the following relation on R is an equivalence relation Show Answer

Q103) In order that a relation R is defined on a non empty set A is an equivalence relation sufficient , if R Show Answer

Q104) The relation "congruence modulo m" is Show Answer

Q105) If (24,92)=24m+92n, then(m,n) is Show Answer

Q106) 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 Show Answer

Q107) 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 , Show Answer

Q108) 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 , Show Answer

Q109) 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 Show Answer

Q110) 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 Show Answer

Q111) The maximum equivalence relation on the set A={1,2,3} are Show Answer

Q112) If, A={1,2,3} and consider the relation R = {(1,1),(2,2), (3,3), (1,2),(2,3), (1,3)} Show Answer

Q113) 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 Show Answer

Q114) 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 Show Answer

Q115) With reference to a universal set , the inclusion of a subset in another , is relation , which is Show Answer

Q116) Let R and S be two non - void relation on a set A. which of the following statement is false
Show Answer

Q117) The relation "less than" in the set of natural number is Show Answer

Q118) The number of reflexive relation of a set with four element is equal to Show Answer

Q119) Let R and S be two equivalence relation on a set A. Then Show Answer

Q120) 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 Show Answer

Q121) Let A and B be two non-empty subsets of set X such that A is not a subset of B , then Show Answer

Q122) 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 Show Answer

Q123) 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 Show Answer

Q124) 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 Show Answer

Q125) 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 Show Answer

Q126) 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 Show Answer

Q127) Let A = {2, 4, 6, 8} and define R = {(2, 4), (4, 2), (4, 6), (6, 4)} then R is Show Answer

Q128) Let A = {p ,q, r, s} and B = {1, 2, 3} which of the following relations from A to B is not a function. Show Answer

Q129) Let A = {p, q, r} which of the following is an equivalence relation on A? Show Answer

Q130) In the set X = {a, b, c, d} which of the following relations is a function? Show Answer

Q131) If A = {2, 3, 4, 5}, then which of the following relations is a function from A to itself Show Answer

Q132) If a set X = {a, b, c, d} which of the following is a function on X? Show Answer

Q133) 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. Show Answer

Q134) Let A = {p, q, r, s}, B = {1, 2, 3} which of the following relations from A to B is not a function. Show Answer

Q135) Let A = {1, 2, 3, 4} and B = {1, 2}. Then the number of onto functions from A onto B is Show Answer

Q136) The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is Show Answer

Q137) The number of bijective functions from the set A to itself, if A contains 108 elements is Show Answer

Q138) Let A be a set containing 10 distinct elements, then the total number of distinct functions from A to A is Show Answer

Q139) 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 Show Answer

Q140) The number of bijective functions (one-one, onto) from the set A onto itself, when n (A) = 108, is Show Answer

Q141) The number of functions from the set A into the set B, when n (A) = 7 and n (B) = 5 is Show Answer

Q142) If n (A) = 15 and n (B) = 10, then the number of injective (one-one) mapping from A into B is Show Answer

Q143) The domain of the function f (x) = cot 5 x is Show Answer

Q144) The domain of the function f (x) = tan 3 x is Show Answer

Q145) 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) = Show Answer

Q146) A survey shows that 65% of the Americans like cheese whereas 79% like Oranges. If x% of the Americans like both, then Show Answer

Q147) If A = {1, 2, 3, 4, 5, 6} then how many subsets of A contain the elements 2, 3 and 5? Show Answer

Q148) 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 = Show Answer

Q149) The number of equivalence relation that can be defined on {a, b, c} is Show Answer

Q150) The relation 'is not equal to' is defined on R, is Show Answer

Q151) If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is Show Answer

Q152) 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 Show Answer

Q153) Which of the following functions from Z into Z is a bijection? Show Answer

Q154) If a set has n elements than the total number of subsets of A is Show Answer

Q155) The number of non empty subsets of the set {1, 2, 3, 4} is Show Answer

Q156) 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 Show Answer

Q157) 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 Show Answer

Q158) Which of the following function is an even function? Show Answer

Q159) Which one of the following is the bijective function on the set of real numbers? Show Answer

Q160) Which of the following is not periodic? Show Answer

Q161) A set of A has 5 element. Then the maximum number of relations on A (including empty relation) is Show Answer

Q162) Let R be an equivalence relation defined on a set containing 6 elements. The minimum number of ordered pairs that R should contain is Show Answer

Q163) The number of non-one and onto mapping from A to B where n (A) = 6 and n (B) = 7 is Show Answer

Q164) 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 Show Answer

Q165) The function which map [-1, 1] to [0, 2] are Show Answer

Q166) Which of the four statements given below is different from others Show Answer

Q167) Which of the following function is invertible? Show Answer

Q168) Domain and Range are equal for the Show Answer

Q169) Which of the following real valued functions is/are not even functions? Show Answer

Q170) 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 Show Answer

Q171) If equation of the curve remain unchanged by replacing x and y from y and x respectively, then the curve is Show Answer

Q172) Which relation is a function? Show Answer

Q173) Which of the following functions are periodic? Show Answer

Q174) A function whose graph is symmetrical about the origin is given by Show Answer

Q175) Which of the following functions is are injective map(s)? Show Answer

Q176) 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 Show Answer

Q177) 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 Show Answer

Q178) In the set Z of all integers, which of the following relation R is not an equivalence relation? Show Answer

Q179) Which of the following function is a polynomial function? Show Answer

Q180) Which of the following functions is periodic? Show Answer

Q181) 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 Show Answer

Q182) Let S = {0, 1, 5, 4, 7}. Then the total number of subsets of S is Show Answer

Q183) 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 Show Answer

Q184) 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 Show Answer

Q185) 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 Show Answer

Q186) 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 Show Answer

Q187) 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 Show Answer

Q188) 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 " Show Answer

Q189) 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 ? Show Answer

Q190) 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 Show Answer

Q191) Which of the following cannot be the number of elements in the power set of any finite set?
Show Answer

Q192) The relation ‘is subset of’ on the power set P(A) of a set A is Show Answer

Q193) 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 Show Answer

Q194) 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 Show Answer

Q195) The void relation on a set A is
Show Answer

Q196) In the above question, the number of families which buy none of A, B and C is Show Answer

Q197) 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 Show Answer

Q198) 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 Show Answer

Q199) 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? Show Answer

Q200) 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 Show Answer

Q201) 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? Show Answer

Q202) Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is Show Answer

Q203) 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 Show Answer

Q204) 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 Show Answer

Q205) 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 Show Answer

Q206) 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 Show Answer

Q207) If A = {1, 2, 3}, then the relation R = { (1, 1), (2, 2), (3, 1), (1, 3) } is Show Answer

Q208) 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? Show Answer

Q209) Let X be a family of sets and R be a relation on X defined by 'A is disjoint from B'. Then, R is Show Answer

Q210) If A = {x, y}, then the power set of A is Show Answer

Q211) Which of the following is true? Show Answer

Q212) If A and B are two sets, then A - ( A - B ) is equal to
Show Answer

Q213) If A = {1, 2, 3, 4}, then the number of subsets of A that contain the element 2 but not 3, is Show Answer

Q214) The relation “is a factor of” on the set N of all natural numbers is not Show Answer

Q215) 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 Show Answer

Q216) The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
Show Answer

Q217) Set builder form of the relation R = {(−2, −7), (−1, −4), (0, −1), (1, 2), (2, 5)} is Show Answer

Q218) 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 Show Answer

Q219) 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? Show Answer

Q220) If A = {x, y, z}, then the relation R = {(x, x), (y, y), (z, z), (z, x), (z, y)} is Show Answer

Q221) If A = {a, b, c, l, m, n}, then the maximum number of elements in any relation on A is
Show Answer

Q222) 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? Show Answer

Q223) 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 Show Answer

Q224) Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following relations is a function from A to B? Show Answer

Q225) Which one is not periodic? Show Answer

Q226) Let n(A) = 4 and n(B) = 6. The number of one to one functions from A to B is Show Answer

Q227) Which of the following functions is inverse of itself? Show Answer

Q228) The number of bijective functions from set A to itself when A contains 106 elements is Show Answer

Q229) The number of onto mappings from the set A = {1, 2, ...., 100} to set B = {1, 2} is Show Answer

Q230) The number of reflexive relations of a set with four elements is equal to Show Answer

Q231) 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
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Q232) Which of the following functions is one-to-one? Show Answer

Q233) If f(x) is defined on [0, 1], then the domain of definition of f(tan x) is Show Answer

Q234) Which of the following functions is not an are not an injective map(s)? Show Answer

Q235) Which of the following functions is (are) not an injective map(s)? Show Answer