*** Following collection are sets or not.
1) The collection of all vowels in the English alphabet. Y/N
2) The collection of all even natural numbers less than 10, Y/N
3) the collection of all prime number less than 20, Y/N
4) the collection of all beautiful girls of India. Y/N.
5) the collection of all the days of a week. Y/N
6) the collection of all the months of year beginning with the letter M.
Y/N
7) a collection of 11 best Indian hockey players. Y/N.
8) the collection of all rich persons of Delhi. Y/N.
9) The collection of all persons of Chennai whose assessed annual income exceeds ₹ 10 lakhs. Y/N
10) the collection of all Books on mathematics. Y/N
11) Collection of all interesting books. Y/N.
12) the collection of all students of your class. Y/N
13) the collection of short boys of your class. Y/N.
14) the collection of all planets of the solar system. Y/N
15) The collection of five most talented writers of India. Y/N.
16) The collection of all interesting dramas written by Shakespeare. Y/N.
17) the collection of all letters of the English alphabet which precedes K. Y/N
18) The collection of fat boys of your locality. Y/N.
19) the collection of all those students of your class whose age exceeds 15 years. Y/N
*** Describe the following sets in Roster form:
20) (x:x is a letter before e in the English alphabet).
A) {a,b,c,d}. B){b,c,d} C){b,c} D) {b}
21) {x ∈N: x²< 25}.
A) {1,4,9,16} B){1,2,3,4}.
C) {1,4,9,16,25} D) {1,2,3,4,5}
22) {x ∈ N : is a prime number, 10<x< 20}.
A) {11,13,17,19}. B) {10,11,12,13}
C) {10, 13,17,19} D) {11,12,13,14}
23) { x∈N : x= 2n, n ∈N}.
A) {2,4,6,8,..}. B) {1,2,3,4}
C) {2,4,6,8} D) none
24) {x ∈R : x > x}.
A) φ. B) {0} C) {1} D) none
25) {x: x is a prime number which is a divisor of 60}.
A) {2,3,5}.
B) {1,2,3,4,5,6,10,12,15,30,60}
C) {10,12,15,30,60} D) none
26) {x : x is a two-digit number such that the sum of its digits is 8}.
A) {17,26,35,44,53,62,71,80}.
B) {1,2,3,4,5,6,6,7,8}
C) {1,2,3,4} D) none
27) the set of all letters in the word 'Trigonometry'.
A) {T,R,I,G,O,N,M,E,Y}.
B) {T,R,G,N,M,R}
C) {I,O,E} D) None
28) The set of all letters in the word 'Better'
A) {B,E,T,R} B) {B,e,t,r}
C) {B,E,T,E,R} D) none
29) {x: x+5=5, n∈Z}.
A) { } B) {0}. C) {φ} D) none
30) {x: x is a prime natural number and a divisor of 10}.
A) {1,2,5} B){2,5}. C) {1,2,5,10} D)n
31) {x: x is a natural number and divisor of 10}.
A){1,2,5,10} B){2,5} C){2,5,10} D)n
32) {x:x is a letter of the word "RAJASTHAN'}.
A) {A,H,J,R,S,T,N}.
B) {H,J,R,S,T,N}
C) {A,H,J,R,S,T,} D) n
33) {x:x² - 25= 0}.
A){-5,5,10} B) {5,-5}.
C) {1,5,-5,10} D) {0,-5,5}
34) {x:x is a letter of the word "APPLE"}.
A) {A,P,L,E}. B) {A,P,P,L,E}
C) {A,E} D) none
*** Describes the following shapes in set builder form:
35) A={1,2,3,4,5,6}.
A) {x:x ∈N,x<7}. B) {x:x ∈N,x≤7}
C) {x:x ∈I,x<7} D) none
36) B={1, 1/2,1/3,1/4,1/5,...}.
A) {x:x= 1/n², x∈N}
B) {x:x= 1/n, x∈N}.
C) {x:x= n, x∈N} D) none
37) C={0,3,6,9,12}
A) {x: x=3n, n∈N }.
B) {x:x= n, x∈N}
C) {x:x= 1/n², x∈N}
D) {x:x= n², x∈N}
38) D={10,11,12,13,14,15}.
A) {x: x∈ N, 9≤ x<16}
B) {x: x∈ N, 9< x≤16}
C) {x: x∈ N, 9< x<16}.
D) {x: x∈ N, 9≤ x≤16}
39) E={0}.
A) {x: x=0}. B) {x: x<0}
C) {x: x>0} D) none
40) {1,4,9,16,...100}.
A) {x²: x ∈N, 1≤ x<10}
B) {x²: x ∈N, 1≤ x≤ 10}.
C) {x²: x ∈N, 1< x≤ 10}
D) {x²: x ∈N, 1< x< 10}
41) {2,4,6,8,...}.
A) {x: x=2n, n∈N}.
B) {x: x=n², n∈N}
C) {x: x=n²-1, n∈N}
D) {x: x=n³, n∈N}
42) {5,25,125,625}.
A) {5ⁿ: n∈N, 1≤n≤4}.
B) {5ⁿ: n∈N, 1<n≤4}
C) {5ⁿ: n∈N, 1≤n<4}
D) {5ⁿ: n∈N, 1<n<4}
*** List all the elements of the following sets:
43) A={x: x²≤ 10, x∈ Z}.
A={0,±1,±2,±3}. B) {0,1,2,3}
C) {5,10} D) {1,5,10}
44) B={x: x= 1/(2n -1) , 1≤n≤5}.
A) B={1, 1/3,1/5,1/7,1/9}.
B) B={1/2, 1/3,1/5,1/7}
C) B={1/2, 1/3,1/4,1/5,1/6} D) n
45) C={x: x is an integer, -1/2<x<9/2}.
A) C={1,2,3,4}
B) C={0,1,2,3}
C) C={0,1,2,3,4}.
D) C={0,1,2,3,4,5}
46) D={ x:x is a vowel in the word 'EQUATION'}.
A) {A,E,I,O,U}. B) {Q,T,N}
C) {A,E,I,N,O,Q,T} D) none
47) E={x:x is a month of a year not having 31 days}.
A)E={Feb, April, June, Sept, November}.
B) {Jan, March, May, June, July, August, December}
C){Jan, March, June, August}
D) {February} E) none
48) F={x:x is a letter of the word 'MISSISSIPPI'}.
A) F={M,I,S,P}. B) F={M,S,P}
C) F=M,I,S,P D) F=(M,I,S,P)
49) Write the set of all vowels in the English alphabet which precedes q.
A) {a,e,i} B) {a,e,i,o}.C){a,e,i,o,u} D) n
50) Write the set of all positive integers whose cube is odd.
A) {2n+1: n∈Z, n ≥ 0}.
B) {1³,2³,3³,4³}
C) {1³,2³,3³,4³........} D) none
51) write the set {1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50} in the set builder form.
A) {n/(n²+1) : n∈N, n ≤7}.
B) {n/(n²+1) : n∈N, n <7}
C) {n/(n²+1) : n∈N, n >7}
D) {n/(n²+1) : n∈N, n >7}
*** Rewrite the following statements, using set notations:
52) a is an element of set A.
A) a∈A. B) a= A C) a≠ A D) n(A)= a
53) b is not an element of A.
A) b ψ A. B) a= A C) a≠ A D) n(A)= a
54) A is an empty set and B is a non empty set.
A) A= φ and B ≠ φ.
B) A≠ φ and B = φ
C) A≠ φ and B ≠ φ
D) A= φ and B = φ
55) number of element in A is 6.
A) n(A)= 6. B) A∈6 C) A ≠ 6 D) A=6
e) 0 is a whole number but not a natural number.
A) 0∈W but 0 ψ N
B) 0∈N but 0 ψ W
C) 0∈W but 0 ψ W
D) 0∈N but 0 ψ N
*** State the type of set
56) A= Set of all in triangles in a plane.
A) finite set B) Infinite set.
C) empty set D) Singleton set
57) B= set of all points on the circumference of a circle.
A) finite set B) Infinite set.
C) empty set D) Singleton set
58) C= set of all lines parallel to the y-axis.
A) finite set B) Infinite set.
C) empty set D) Singleton set
59) D= set of all leaves on a tree.
A) finite set. B) Infinite set
C) empty set D) Singleton set
60) E= set of all positive integers greater than 500.
A) finite set B) Infinite set.
C) empty set D) Singleton set
61) F={x ∈ R: 0<x < 1}
A) finite set B) Infinite set.
C) empty set D) Singleton set
62) G={x ∈ Z: x < 1}
A) finite set B) Infinite set.
C) empty set D) Singleton set
63) H={x ∈ Z : -15 < x < 15}
A) finite set. B) Infinite set
C) empty set D) Singleton set
64) I={x:x ∈ N and x² < 36}
A) finite set. B) Infinite set
C) empty set D) Singleton set
65) J={x: x ∈ Z and x < 10}
A) finite set B) Infinite set.
C) empty set D) Singleton set
66) K={x: x ∈ N and x is prime}.
A) finite set B) Infinite set.
C) empty set D) Singleton set
67) L={x:x ∈ N and x is even}.
A) finite set B) Infinite set.
C) empty set D) Singleton set
68) set of numbers which are multiple of 5.
A) finite set B) Infinite set.
C) empty set D) Singleton set
69) set of animals living on earth.
A) finite set. B) Infinite set
C) empty set D) Singleton set
70) M={x: x ∈ N and x >100}.
A) finite set B) Infinite set.
C) empty set D) Singleton set
71) N={x: x ∈ N and x < 1000}.
A) finite set. B) Infinite set
C) empty set D) Singleton set
72) A{x:x²-3= 0 and x is rational} is
A) finite B) infinite C) empty D) singleton set
73) B={x:x is an even prime number}
A) finite B) infinite C) empty D) singleton set
74) C={x:4<x<5, x∈N}
A) finite B) infinite C) empty D) singleton set
75) M={x:x²= 25, and x is an odd integers}
A) finite B) infinite C) empty D) singleton set
76) set of all odd natural numbers divisible by 5.
A) finite B) infinite C) empty D) singleton set
77) set of all odd prime numbers.
A) finite B) infinite C) empty D) singleton set
78) set of all even prime numbers
A) finite B) infinite C) empty D) singleton set
79) S={x∈N, 2x+5= 6}
A) finite B) infinite C) empty D) singleton set
80) B={x|x ∈N, 1< x ≤2}
A) finite B) infinite C) empty D) singleton set
81) X={x|x is prime, 90< x ≤96}
A) finite B) infinite C) empty D) singleton set
81) B={x|x N, x² +4= 0}
A) finite B) infinite C) empty D) singleton set
82) K={0}
A) finite B) infinite C) empty D) singleton set
83) which of the following sets are equal ?
i) A={1,2,3}
ii) B={x∈ R: x²- 2x+1= 0}
iii) C={1,2,2,3}
iv) D={x∈ R: x³-6x² +11x-6= 0}
A) i and ii B) ii and iii
C) iii and iv D) i and iii and iv.
84) which of the following sets are equal ?
i) A={x:x is a letter in the word reap}
ii) B={x:x is a letter in the word paper}
iii) C={x:x is a letter in the word rope}
A) ii and iii B) i and iii
C) i and ii D) i≠ ii≠ iii
85) A={1,2,3}; B={x,y,z} both set are
A) equal B) equivalent C) empty D) none
86) A={t,o,q,r,s}; B={a,e,i,o,u} both set are
A) equal B) equivalent C) empty D) none
87) A={2,3};
B={x:x is a solution of {x²+5x+6=0} both set are
A) equal B) equivalent C) empty D) none
88) A={x:x is a letter of the word 'WOLF'}
B={x:x is a letter of the word 'FOLLOW'}
A) equal B) equivalent C) empty D) none
89) A={1,2,3,4};
B={3,1,2,4} both set are
A) equal B) equivalent C) empty D) none
90) A={4,8,12};
B={8,4,12} both set are
A) equal B) equivalent C) empty D) none
91) A={0,a};
B={1,0} both set are
A) equal B) equivalent C) empty D) none
*** If A={1,2,3,4,5}; B={4,5,6,7,8}
C={7,8,9,10,11} D={9,11,12,13,14}
then find
92) AUB
A) {1,2,3,4,5}; B {4,5,6,7,8 B)
C) {1,2,3,4,5,6,7,8} D) none
93) AUC
A) {1,2,3,4,5,6,7,8}
B) {1,2,3,4,5,6,7,8,9,10}
C) {1,2,3,4,5,6,7,8,9,10,11}
D) {1,2,3,4,5,7,8,9,10,11}
94) BU C
A) {1,2,3,4,5,6,7,8}
B) {5,6,7,8,9,10}
C) {1,2,3,4,5,6,7,8,9,10,11}
D) {4,5,6,7,8,9,10,11}
95) B U D
A) {1,2,3,4,5,6,7,8}
B) {4,5,6,7,8,9,10,11,12}
C) {1,2,3,4,5,6,7,8,9,10,11,12,13,}
D) {4,5,6,7,8,9,11,12,13,14}
96) A U B U C
A) {1,2,3,4,5,6,7,8}
B) {1,2,3,4,5,6,7,8,9,10}
C) {1,2,3,5,6,7,8,9,10,11}
D) {1,2,3,4,5,6,7,8,9,10,11}
97) A U BU D
A) {1,2,3,4,5,6,7,8,9,10}
B) {1,2,3,4,5,6,7,8,9,10,11,12}
C) {1,2,3,4,5,6,7,,9,10,11,12,13,}
D) {1,2,3,4,5,6,7,8,10,11,12,13,14}
98) B U CU D
A) {1,2,3,4,5,6,7,8}
B) {3,4,5,6,7,8,9,10,11,12}
C) {4,5,6,7,8,9,10,11,12,13,14}
D) {1,2,3,4,5,7,8,9,10,11,12,13,14}
99) A∩(B UC)
A) {1,2,3}
B) {4,5}
C) {1,2,3,4,5,6,7,8,9,10,11}
D) {1,2,3,4,5,7,8,9,10,11}. E) none
100) (A ∩B) ∩(B ∩C)
A) {1,2,3}
B) {4,5}
C) {1,2,3,4,5,6,7,8,9,10}
D) null set
101) (A UB) ∩(B UC)
A) {1,2,3} B) {4,5}
C) {1,2,3,4,5,6,7,8,9,10} D) null set
*** Let A={x:x∈ N}
B={x:x= 2n, n∈ N}
C={x:x= 2n-1, n∈ N}
D={x:x is a prime natural number} then find
102) (A ∩B)
A) A B) B. C) C D) D E) null set
103) (A ∩ C)
A) A B) B C) C. D) D E) null set
104) (A ∩ D)
A) A B) B C) C D) D. E) null set
105) (B∩ C)
A) A B) B. C) C D) D E) null set.
106) (B ∩ D)
A) {1} B) {2}. C) {1,2} D) A E) null
**If A={3,6,12,15,18,21}
B={4,812,16,20}
C={2,4,6,8,10,12,14,16} D={5,10,15,20}
then find
107) A - B
A) {3,6,8,15}; B) {3,15,18}
B) {3,15,18,21} D) null set
108) A - C
A) {3,6,8,15} B) {3,15,18}
B) {3,15,18,21} D) null set
109) A - D
A) {3,6,8,12,15} B) {3,6,12,18,21}
C) {3,15,18,21} D) null set
110) B - A
A) {3,6,8,15} B) {4,8,16}
C) {4,8,16,20} D) null set
111) C - A
A) {2,4,8,10,14,16} B) {3,15,18}
C) {3,15,18,21} D) null set
112) D - A
A) {5,15} B) {2,5,15,18}
C) {5,10,15} D) null set
113) B - C
A) {3,6,8,15} B) {3,15,18}
C) {3,15,18,21} D) null set E){20}
114) B - D
A) {4,8,12,16} B) {4,8,12,18}
C) {3,15,18,21} D) null set
***If A={1,2,3,4,5,6,7,8,9}
B={1,2,3,4}
C={2,4,6,8} D={3,4,5,6}
then find
115) A'
A) {5,6,7,8} B) {5,6,7,8,9}
C) {3,4,5,7,8,9} D) null set
116) B'
A) {1,5,6,7,8} B) {5,6,7,8,9}
C) {1,3,5,7,9} D) null set
117) (A∩ C)
A) {1,5,6,7,8} B){5,6,7,8,9}
C) {1,2,5,6,7,8,9} D) null set
118) (A U B)'
A) {1,5,6,7,8} B) {5,6,7,8,9}
C) {5,7,9} D) null set
119) (A')'
A) {1,5,6,7,8} B) {5,6,7,8,9}
C) {13,5,7,9} D) A E) null set
120) (B - C)'
A) {1,3,4,5,6,7,9} B {1,3,5,6,7,8,9}
C) {13,5,7,9} D) null set E){4}
*** If A={a,b,c,d,e,f}
B={c,e,g,h}
C={a,e,m,n} then find
121) AU B
A) {a,b,d,e,f,g,m} B={a,b,c,d,e,f,g}
C={a,b,c,d,e,f,g,h} D={a,b,c} E) n
122) B U C
A) {a,b,d,e,f,g,m} B={a,b,c,d,e,f,g}
C={a,c,e,f,g,h,m,n} D={a,b,c} E) n
123) A U C
A) {a,b,c,d,e,f,m,n}. B={a,b,c,d,e,f,g}
C={a,b,c,d,e,f,g,h} D={a,b,c} E) n
124) B ∩ C
A) {a,b,c,d,e,f,m,n} B={a,b,c,d,e,f,g}
C={a,b,c,d,e,f,g,h} D={a,b,c} E) {e}
125) C ∩ A
A) {a,b,c,d,e,f,m,n} B={a,b,c,d,e,f,g}
C={a,c} D={a,b,c} E) {e}
126) A ∩ B
A) {a,b,c,d,e,f,m,n} B={c,e}
C={a,b,c,d,e,f,g,h} D={a,b,c} E) {e}
**If A={1,2,3,4,5}
B={4,5,6,7,8}
C={7,8,9,10} D={10,11,12,13,14}
then find
127) A U B
A) {1,2,3,4,5,6,7,8} B) {5,6,7,8,9}
C) {3,4,5,7,8,9} D) null set
128) AU BU C
A) {1,2,3,4,5,6,7,8,9,10,11}
B) {5,6,7,8,9}
C) {3,4,5,7,8,9} D) null set
**If A={2,4,6,8,10,12}
B={3,4,5,6,7,8,10} then find
129) (A-B) U(B- A)
A) {5,6,7,8} B) {5,6,7,8,9}
C) {2,3,5,7,12} D) null set
**If A={a,b,c,d,e}; B={a,c,e,g}
C={b,e,f,g} Then find
130) A∩(B - C)
A) {a,c} B) {a,b,c}
C) {a,b,c,d,e} D) null set
131) A - (B U C)
A) {a} B){a,c} C) {a,b,c}
D) {a,b,c,d,e} E) null set
132) A - (B∩C)
A) {a} B){a,b} C) {a,b,c}
D) {a,b,c,d} E) null set
***If A={1/x:x∈ N and x< 8}
B={1/2x:x∈ N and x≤4}. Then find
133) A UB
A) {1,1/2,1/3,1/4,1/5,1/6}
B) {1,1/2,1/3,1/4,1/5,1/6,1/7}
C) {1,1/2,1/3,1/4,1/5,1/6,1/7,1/8}
D) {,1/2,1/3,1/4,1/5,1/61/7,1/8}
134) A ∩ B
A) {1,1/2,1/3,1/4} B) {1/2,1/3,1/4}
C) {1/2,1/4,1/6,}
D) {1/2,1/3,1/4,1/5,1/6,1/7,1/8}
135) A - B
A) {1,1/2,1/3,1/4,1/5,1/6}
B) {1,1/2,1/3,1/4}
C) {1,1/3,1/5}
D) {1,1/3,1/5,1/7}
136) B - A
A) {1} B) {1/4} C) {1/6} D) {1/8}.
** If A= {2,3,5,7,11} B={ } find
137) A U B
A) {2,3,5,7,11} B) {2,3,5,7}
C) {2,3,5} D) {2,3} E) {}
138) A ∩ B
A) {2,3,5,7,11} B) {2,3,5,7}
C) {2,3,5} D) {2,3} E) {}
*** If A = {a , b,c, d, e}, B={a,e,i,o,u} and C= {m,n,o,p,q,r,s,t,u} find
139) A∪B has _____ elements
i) 8 ii) 7 iii) 9 iv) 11
140) B∪C is equal to
i) {a,e,i,o,u,m,n,p,q,r,s,t}
ii) {a,e,i,r,s,t}
iii) {o,u,p,q,r,s} iv) none
141) A∪C is equal to
i) {d,e,f,p,q,r}
ii) {a,b,c,d,e,m,n,o,p,q,r,s,t,u}
iii) {a,b,c,s,t,u} iv) none
140) If A and B are two sets containing 4 and 7 distinct elements respectively, find the minimum possible number of and maximum possible number of elements A∪B
i) 5,10. ii) 4,12. iii) 7,11. iv) 8,13
141) If A, B, C are three sets in which n(A∩B∩C)= 8, n(A∩B)=15, n(A)=22, n(B∩C)=11, n(B)=19=n(C) , (A∩C)=10, then find A∪B∪C
i) 31. ii) 33. iii) 35. iv) 32
142) Set X, Y and Z are such that X={A:A²-5A+6=0};
Y={B: B²-8B+15=0} and
Z={C: C²-7C+10=0}. Find
(X∩Y∩Z)∩ (X∪Y∪Z)
a) { } b) {2,5}. c) {2,3,5}. d) {2,5}
143) At a party , 30% of people have only cocktail drinks and snacks, 20% have only food, and 70% have snacks. If nobody has all the three and everybody has something, then how many people (%) have food (given cocktail and snacks are not taken alone).
a) 60%. b) 50%. c) 70%. d) none
145) 2 sets M and N are defined as follows: M={S,T,R,A,N,D} and
N={S,T,A,N,D,A,R,D}. the above two set are:
A) equal. B) equivalent.
C) disjoint. D) none
7) A survey of a society whose residents are mainly gangsters shows that one-sixth of the society residents own bungalows, one-fourth own flats and one-eighth of those who own bungalows do not own flats.
A) what fraction of the society residents owns both a bungalow and a flat?
i) 7/12. ii) 7/48. iii) 7/16. iv) none
B) What fraction of the society residents owns either bungalow or a flat or both ?
i) 4/5. ii) 1/48. iii) 13/48 iv) 15/48
C) What fraction of the society residents owns neither a bungalow nor a flat?
i) 35/48. ii) 15/16. iii) 30/44 iv) n
8) Total students is 2800. English students only 650, Hindi students only 550, Bengali students 450 only, students took all the three subjects 100, students who took Hindi as well as English is 200, students who took Hindi as well as bengali is 400. Bengali as well as English is 300
A) find the number of Bengali students.
I) 950. ii) 1050. iii) 650. iv) 550
B) Find the number of students who didn't take any subject?
i) 450. ii) 2650. iii) 2550. iv) 550
C) Find the number of students take only one subject
i) 450 ii) 1100. iii) 1600. iv) 1650
D) find the number of students taking atleast two subjects.
i) 600. I) 400. iii) 700. iv) 500
E) The ratio of students taking Hindi to that of Bengali is:
i) 2:1 ii) 1:1. iii) 1:2. iv) 3:2
9) In the ISC Board examination last year. 53% passed in Economics, 61% passed in English, 60% in Mathematics, 24% in Economics and English. 35% in English and Mathematics, 27% in Economics and Mathematics and 5% none.
A) % of pass in all subjects
a) nil b) 7. c) 12. d) 10
B) If the number of students in the class is 200, how many passed in only one subject?
a) >50. b) 46. c) <40. d) 48
C) If the number of students in the class is 300, what will be the% change in the number of passes in only two subjects, if the original number of students is 200?
a) >50%. b) <50%. c) 50%. d) none
D) What is the ratio of% of passes in Economics and Mathematics but not English in relation to the% of passes in Mathematics and English but not economics?
a) 5:7. b) 4:5. c) 7:5. d) none
10) In an Institute, it was found that 48% preferred coffee, 54% liked iced tea and 64% smoked. Of the total 28% liked coffee and iced tea, 32% smoked and drank iced tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then:
A) The ratio of the number of students who like only coffee to the number who like only iced tea
a) 3:2. b) 2:3. c) 9:8. d) 8:9
B) The number of students who like coffee and smoking but not iced tea
a) 440. b) 240. c) 300. d) 270
C) The % of those who like coffee or iced tea but not smoking those who like atleast one of these?
a) >30%. b) <30%. c) < 25% d) n
D) The % of those who like atleast one of these is:
a) 94. b) nil. c) 91. d) 100
E) The two items having the ratio 1:2 are :
a) Iced tea only and iced tea and smoking only.
b) coffee and smoking only and iced tea only
c) coffee and tea but not smoking and smoking but not coffee and tea. d) none
F) The number of persons who like coffee and smoking only and the number who like coffee only bear a ratio.
a) 2:3. b) 3:2. c) 2:1. d) 1:2
G) Percentage of those who like iced tea and smoking but not coffee is:
a) 14.9 b) < 14
c) 14 d) more than 14
11) A & B are two sets such that n(A)=17, n(B)=23, n(A∪B)= 38, then (A∩B)= ?
A) 12. B) 2. C) 7. D) 9
12) In a club, all the members participate either in the Kambola or the Kete. 420 participate in the Kete, 350 participate in the Kambola and 220 participate in both. How many members does the club have ?
A) 1550. B) 550. C) 750. D) 960
13) There are 100000 people living in DLF Colony, New Delhi. Out of them 45000 subscribe to Start Gold Network and 60000 to Zoo TV Network. If 20000 subscribe to both, how many do not subscribe to any of the two?
A) 25000. b) 15000
c) 27000 d)25550
14) At the bachelor party of Sheri, 40 persons chose to kiss him and 25 chose to shake hands with him. 10 persons chose to both kiss him and shake hands with him. How many persons turned out at the party ?
A) 45. B) 55. C) 47. D) 53
15) Set X and Y had 6 and 12 elements respectively. What can be the minimum number of elements in (X∪Y) ?
A) 14. B) 16. C) 12. D) 18
16) In a class of 200 students, 110 students have passed in Economics and 134 students have passed in political science. Then the number of students who have passed in political science only is:
A) 66. B) 44. C) 90. D) 20
17) If A= {1,2,3}, B={3,4}, C={4,5,6}
Then (AXB)∩(BXC) = ?
A) { } B) {(3,4)}.
C) {(2,3)(3,2)(3,4)}. D) none
18) Let A={O,R,A,N,G,E} and
B={0,1,2,3,4,5}. The above two sets are :
A) equal. B) equivalent
C) disjoint. D) both B and C
19) There are 40 students in DI Class and 60 students in PS Class. Find the number of students which are either DI class or PS Class if the two classes meet at different hours and 20 students are enrolled in both the subjects.
A) 40. B) 20. C) 80. D) 60
20) The number of elements in the power set of a set containing "p" element is:
A) 2ᵖ⁻¹ B) 2ᵖ C) 2ᵖ⁺¹ D) 2ᵖ +1
21) 30 MBAs went to a B-school festival. 25 MBSs choose to irritate M. Techs while 20 chose to irritate M. Scs. How many chose to irritate both M. Techs and M. Scs ?
A) 20. B) 15. C) 5. D) 10
22) In the final of Miss India contest, between two contestants, half the number of judges voted for Miss Kolkata, one-fourth of them voted for Miss Kerala, 2 voted for both, whereas 8 did not vote for any one of them. How many judges were there in the panel?
A) 32 B) 24 C) 20 D) none
23) The number of non empty subsets of the {8,9,10,11,15} is:
A) 32. B) 31. C) 30. D) 33
24) O & M, a market research group Conducted a survey of 20000 consumers and reported that 17200 consumers liked product K and 14500 consumers liked product L. What is the least number that must have liked both the products ?
A) 20000. B) 17200
C) 14500. D) 7000
25) If the set A has M elements and set B had N elements then the number of elements in AxB is :
A) m+n B) mn. C) m - n. D) mⁿ
26) Out of 450 students who appeared at the BA Examination from a centre, 135 failed in A, 150 failed in M and 137 in C. Those who failed in both A and M were 93, in M and C were 98 and in A and C were 106. The number of students who failed in all the three subjects was 75. Assume that each student appeared in all the three subjects.
A) Find the number of students who failed in a least one of the three subjects.
a) 200 b) 210. c) 205. d) 250
B) Find the number of students who passed in all the three subjects.
a) 300. b) 350. c) 250. d) none
27) In a group of 400, each of whom is atleast accountant or management consultant or sales manager, it was found that 160 are only accountant, 220 are only management consultant and 260 are sales manager, 50 are accountant as well as sales manager, 20 are accountant as well as management consultant as well as sales manager. Find the number of those who are accountant as well as management consultant but not sales manager.
A) 45. B) 40. C) 30. D) 25
28) In a college there are 2500 students. It was revealed that 652 students played football, 405 played hockey and 820 played cricket. But only 212 played both football and hockey, 73 played hockey and cricket, and 87 both cricket and football. Also 76 students played all the three games. The number of students who didn't play at all is:
A) 430. B) 431. C) 429. D) 49
29) Set A and B has 3 and 6 elements respectively. What is the minimum of elements in A∪B ?
A) 18. B) 9. C) 6. D) 3
30) In a company X, 5 employees drink tea, coffee and milk, 4 employees drink tea and milk, 1 employee drinks tea and coffee. No employee takes only milk and coffee, 8 employees take only tea, 13 employees take only milk and 9 employees take only coffee. Similarly in company Y, 7 employees drink tea, coffee and milk, 4 employees drink only tea, 1 employee drinks only coffee and 12 employees drink only milk. There are 10 common employees in company X and Y who drink only milk.
i) What are the total number of employees in X and Y together?
A) 83. B) 73. C) 63. D) 93
ii) What is the ratio of number of employees of X taking milk to the number of employees of Y taking milk?
A) 13/12.B) 11/13.C)3/8.D) 22/15
31) A shop has only red, green and blue carpets. 60% of the carpets have red colour, 30% have green colour and 50% have blue colour. If no carpet has all the three colours, what percentage of the carpets have only one colour?
A) 40%. B) 60%. C) 70%. D) none
32) Two finite sets have p and q number of elements. The total number of subsets of the first set is eight times the total number of subsets of the second set. Find the value of p - q.
A) 2. B) 3. C) 4. D) none
33) Out of 1600 students in a college, 390 played Kho-Kho, 450 played Kabaddi, and 500 played cricket; 90 played both Kho-Kho and Kabaddi; 125 played Kabaddi and Cricket, and 155 played Kho-Kho and Cricket; 50 played all the three games.
A) how many students didn't play any game ?
i) 400. B) 500. C) 450. D) none
B) How many played only Kho-Kho ?
i) 295. B) 195. C) 95. D) 1000
C) How many played only one game?
A) 1030. B) 930 C) 750. D) 730
D) How many played only two games ?
i) 220. B) 320. C) 120 D) none
34) 85 children went to an amusement park where they could ride on the marry-go-round, roller coaster and Ferris wheel. It was known that 20 of them took all the three rides and 55 of them took atleast two of the three. Each ride cost Rs 1, and the total receipts of the amusement park was Rs145.
A) how many children didn't try any of the rides ?
i) 5. B) 15. C) 20. D) 10
B) how many children took exactly one ride ?
i) 5. B) 10. C) 15. D) 20
35) A survey of 235 families to find the type of heating used - gas, electricity or oil -- revealed the following-- 20 houses use oil, of which 8 use gas also and 10 use electricity as well as oil and two use both gas and electricity besides oil. In all 175 houses use either gas or electricity and 132 use electricity.
A) number of houses using is :
i) 90. B) 141. C) 41. D) none
B) number of houses using only electricity is :
i) 82. ii) 130. iii) 12. iv) none
C) Amongst the house using one type of heating, percentage, using electricity only is :
i) 46. B) 34. C) 36. D) none
D) number of houses using gas or oil is :
i) 150. ii) 153. iii) 175. D) none
E) Number of houses using two types of fuel, but not all the three is :
i) 50. B) 54. C) 45. D) none
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