Tiêu đề 1.SETS.pdf ✅

SETS - MCQS TYPE (1.) If AB, and C are three sets such that A B A  = C and A B A C  =  , then [AIEEE-2009] (a.) A C= (b.) B C= (c.) A B  = (d.) A B = (2.) Let X = 1,2,3,4,5 . The number of different ordered pairs (Y Z, ) that can be formed such that Y X Z X   , and Y Z  is empty, is [AIEEE-2012] (a.) 5 3 (b.) 5 2 (c.) 3 5 (d.) 2 5 (3.) In a class of 140 students numbered 1 to 140 , all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is [JEE (Main)-2019] (a.) 1 (b.) 38 (c.) 102 (d.) 42 (4.) Let S =  1, 2,3, ,100 . The number of nonempty subsets A of S such that the product of elements in A is even is [JEE (Main)-2019] (a.) 100 2 1− (b.) 50 2 1+ (c.) ( ) 50 50 2 2 1− (d.) 50 2 1− (5.) Let Z be the set of integers. If ( )( )   2 2 5 6 1 : 2 + − + = =  x x x A x Z and B x Z x =  −  −  { : 3 2 1 9} , then the number of subsets of the set A B , is [JEE (Main)-2019] (a.) 15 2 (b.) 12 2 (c.) 18 2 (d.) 10 2 (6.) Two newspapers A and B are published in a city. It is known that 25% of the city population reads A and 20% reads B while 8% reads both A and B . Further, 30% of those who read A but not B look into advertisements and 40% of those who read B but not A also look into advertisements, while 50% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisements is [JEE (Main)-2019] (a.) 13.9 (b.) 13 (c.) 12.8 (d.) 13.5 (7.) Let AB, and C be sets such that     A B C . Then which of the following statements is not true? [JEE (Main)-2019] (a.) B C   (b.) (C A C B C    = ) ( ) (c.) If (A C B − ) , then A B  (d.) If ( A B C − ) , then A C  (8.) Let A B C , , and D be four non-empty sets. The contrapositive statement of "If A B  and B D  , then A C   is [JEE (Main)-2020]
(a.) If A C Ø , then A B  and B D  (b.) If A C Ø , then A B Ø and B D  (c.) If A C Ø , then A B Ø or B D Ø (d.) If A C  , then B A  or D B  (9.) If A x R x =   { : 2} and B x R x =  −   : 2 3 ; then [JEE (Main)-2020] (a.) A B− = − 1, 2) (b.) A B R  = − (2,5) (c.) B A R − = − −( 2,5) (d.) A B  = − − ( 2, 1) (10.) Consider the two sets : A m R =   : both the roots of ( ) 2 x m − +1 x m+ + =4 0 are real } and B = − 3,5) . Which of the following is not true? [JEE (Main)-2020] (a.) A B  = − 3 (b.) B A − = −( 3,5) (c.) A B R  = (d.) A B− = − −  (   , 3 5, ) ( ) (11.) A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B . If x% of the people read both the newspapers, then a possible value of x can be [JEE (Main)-2020] (a.) 37 (b.) 55 (c.) 29 (d.) 65 (12.) Let 50 1 1 n i i i i X Y T = = = = , where each ANY Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets ' Xi s and exactly 6 of sets ' Ysi , then n is equal to [JEE (Main)-2020] (a.) 50 (b.) 15 (c.) 30 (d.) 45 (13.) A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be [JEE (Main)-2020] (a.) 63 (b.) 36 (c.) 38 (d.) 54 (14.) In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement? (a.) Q and R (b.) P and Q (c.) P and R (d.) None of these 17th Mar M( )
(15.) Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K cannot belong to the set: (a.) 84,87,90,93 (b.) 84,86,88,90 (c.) 79,81,83,85 (d.) 80,83,86,89 (16.) The number of elements in the set { : 3 x R x  − ( ) x + = 4 6} is equal to : [JEE (Main)-2021] (a.) 4 (b.) 2 (c.) 1 (d.) 3 (17.) Let A x R x =  +  { : 1 2} and B x R x =  − { : 1 ∣ ∣ 2} . Then which one of the following statements is NOT true? [JEE (Main)-2022] (a.) A B− = −( 1,1) (b.) B A R − = − −( 3,1) (c.) A B  = − − ( 3, 1 (d.) A B R  = −1,3) (18.) Let     3 1 6,3 2,2 : 0 2     + − =  − − −      −   x S x x and   2 T x x x =  − +  Z : 7 9 0 . Then the number of elements in S T  is [JEE (Main)-2022] (a.) 7 (b.) 5 (c.) 4 (d.) 3 (19.) A bag contains 6 white and 4 black balls. A die is rolled once and the number of ball equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is [15 APRIL 2023 (MORNING)] (a.) 1 4 (b.) 9 50 (c.) 11 50 (d.) 1 5 (20.) An organization awarded 48 medals in event ' A ', 25 in event ' B ' and 18 in event ' C '. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events ? [11 APRIL 2023 (MORNING)] (a.) 15 (b.) 9 (c.) 21 (d.) 10
SETS - INTEGER TYPE (21.) Set A has m elements and Set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B , then the value of m n − is [JEE (Main)-2020] (22.) Let X n N n =     :1 50 . If A n X n =  { : is a multiple of 2 } and B n X n =  { : is a multiple of 7 } , then the number of elements in the smallest subset of X containing both A and B is [JEE (Main)-2020] (23.) The sum of all the elements in the set { 1, 2, ,100 n   ∣ H.C.F. of n and 2040 is 1 } is equal to 22nd Jul (E) (24.) Let   2 A n N n n B k k =   + = +  ∣ ∣ 10,000 , {3 1 N} and C k k N =  2 ∣  , then the sum of all the elements of the set A B C  − ( ) is equal to 27nd Jul (E) (25.) If   2 A { : 2 1},B : 3 1 =  −  =  −  x x x x R R , C : 4 2 =  −  x x R  and Z is the set of all integers, then the number of subsets of the set ( )   C A B C Z is 27th Aug (M) (26.) Let S = 1, 2,3, 4,5,6,9 . Then the number of elements in the set T {A S: A =   and the sum of all the elements of A is not a multiple of 3 } is 27th Aug (E) (27.) Let A n =  { : N H.C.F. (n, 45 1} ) = and Let B k ={2 : 1, 2, ,100 } k     . Then the sum of all the elements of A B  is [JEE (Main)-2022] (28.) Let A a a a =  1, , ,77 1 2 18  be a set of integers with 1 2 18 1 77     a a a . Let the set A A + = x y x y A +  : ,  contain exactly 39 elements. Then, the value of a a a 1 2 18 + ++ is equal to [JEE (Main)-2022] (29.) Let A = 1, 2,3, 4,5,6,7 . Define B = {T A  : either 1T or 2 } T and C T A T =  { : the sum of all the elements of T is a prime number}. Then the number of elements in the set B C  is [JEE (Main)-2022] (30.) Total numbers of 3 -digit numbers that are divisible by 6 and can be formed by using the digits 1,2,3,4,5 with repetition, is [13 APRIL 2023 (EVENING)]