Class 11th Math - Sets - MERIT YARD
Class 11th Math - Sets - MERIT YARD
1 / 40Which of the following is an Empty Set?
A) \( \{0\} \)
B) \( \{\phi\} \)
C) \( \{x : x \in \mathbb{N}, x < 1\} \)
D) \( \{x : x \text{ is an even prime number}\} \)
2 / 40If a set \( A \) has \( n \) elements, then the number of subsets of \( A \) is:
A) \( 2^n \)
B) \( n^2 \)
C) \( 2n \)
D) \( 2^n - 1 \)
3 / 40The Roster form of the set \( \{x : x \in \mathbb{Z} \text{ and } -2 < x < 3\} \) is:
A) \( \{-2, -1, 0, 1, 2\} \)
B) \( \{0, 1, 2\} \)
C) \( \{-1, 0, 1, 2\} \)
D) \( \{-1, 0, 1\} \)
4 / 40The set builder form of \( \{2, 4, 6, 8\} \) is:
A) \( \{x : x = 2n, n \in \mathbb{Z}\} \)
B) \( \{x : x = 2n, n \in \mathbb{N}, n \le 4\} \)
C) \( \{x : x = n^2, n \in \mathbb{N}\} \)
D) \( \{x : x \text{ is prime}\} \)
5 / 40A set containing exactly one element is called:
A) Null set
B) Equal set
C) Finite set
D) Singleton set
6 / 40For any set \( A \), the value of \( A \cup A' \) is:
A) \( U \)
B) \( A \)
C) \( \phi \)
D) \( A' \)
7 / 40For any set \( A \), the value of \( A \cap A' \) is:
A) \( A \)
B) \( \phi \)
C) \( U \)
D) \( A' \)
8 / 40The number of proper subsets of a set containing \( n \) elements is:
A) \( 2^n \)
B) \( n^2 - 1 \)
C) \( 2^n - 1 \)
D) \( 2n \)
9 / 40If \( A = \{1, 2, 3\} \), then the number of elements in Power Set \( P(A) \) is:
A) \( 6 \)
B) \( 8 \)
C) \( 9 \)
D) \( 3 \)
10 / 40The number of elements in \( P(\phi) \) is:
A) \( 1 \)
B) \( 0 \)
C) \( 2 \)
D) Infinite
11 / 40If \( A \subset B \), then \( A \cup B \) is equal to:
A) \( A \)
B) \( \phi \)
C) \( B \)
D) \( U \)
12 / 40If \( A \subset B \), then \( A \cap B \) is equal to:
A) \( B \)
B) \( A \)
C) \( \phi \)
D) \( U \)
13 / 40De-Morgan's Law states that \( (A \cup B)' \) is equal to:
A) \( A' \cup B' \)
B) \( A \cap B \)
C) \( A' - B' \)
D) \( A' \cap B' \)
14 / 40De-Morgan's Law states that \( (A \cap B)' \) is equal to:
A) \( A' \cup B' \)
B) \( A' \cap B' \)
C) \( A \cup B \)
D) \( A - B \)
15 / 40The interval \( \{x : x \in \mathbb{R}, -4 \le x < 6\} \) is written as:
A) \( (-4, 6] \)
B) \( (-4, 6) \)
C) \( [-4, 6) \)
D) \( [-4, 6] \)
16 / 40Sets \( A \) and \( B \) are Disjoint sets if:
A) \( A \cup B = \phi \)
B) \( A \cap B = \phi \)
C) \( A = B \)
D) \( A \subset B \)
17 / 40If \( A = \{1, 2, 3\} \) and \( B = \{3, 4, 5\} \), then \( A \cup B \) is:
A) \( \{3\} \)
B) \( \{1, 2\} \)
C) \( \{1, 2, 3, 4, 5\} \)
D) \( \{4, 5\} \)
18 / 40If \( A = \{1, 2, 3\} \) and \( B = \{3, 4, 5\} \), then \( A \cap B \) is:
A) \( \{3\} \)
B) \( \{1, 2\} \)
C) \( \phi \)
D) \( \{1, 2, 3, 4, 5\} \)
19 / 40Difference of sets \( A - B \) is defined as elements which belong to \( A \) but:
A) Belong to \( U \)
B) Do not belong to \( B \)
C) Belong to \( B \)
D) Do not belong to \( A \)
20 / 40If \( U = \{1, 2, 3, 4, 5\} \) and \( A = \{1, 3\} \), then \( A' \) is:
A) \( \{1, 3\} \)
B) \( \phi \)
C) \( \{2, 4, 5\} \)
D) \( U \)
21 / 40Complement of Universal set \( U' \) is:
A) \( \phi \)
B) \( U \)
C) \( A \)
D) \( \{0\} \)
22 / 40Complement of Empty set \( \phi' \) is:
A) \( \phi \)
B) \( U \)
C) \( A' \)
D) \( 0 \)
23 / 40The value of \( A \cup \phi \) is always:
A) \( \phi \)
B) \( U \)
C) \( A \)
D) \( A' \)
24 / 40The value of \( A \cap U \) is always:
A) \( U \)
B) \( A \)
C) \( \phi \)
D) \( A' \)
25 / 40For any set \( A \), the double complement \( (A')' \) is equal to:
A) \( U \)
B) \( \phi \)
C) \( A' \)
D) \( A \)
26 / 40If \( n(A) = 20, n(B) = 30 \) and \( n(A \cap B) = 10 \), then \( n(A \cup B) \) is:
A) \( 50 \)
B) \( 40 \)
C) \( 30 \)
D) \( 20 \)
27 / 40If \( n(A) = 15 \) and \( n(B) = 20 \) and \( A \cap B = \phi \), then \( n(A \cup B) \) is:
A) \( 15 \)
B) \( 20 \)
C) \( 35 \)
D) \( 5 \)
28 / 40If \( A = \{1, 2, 3, 4\} \) and \( B = \{3, 4, 5, 6\} \), then \( A - B \) is:
A) \( \{1, 2\} \)
B) \( \{5, 6\} \)
C) \( \{3, 4\} \)
D) \( \phi \)
29 / 40Two sets are equivalent if they have the same:
A) Elements
B) Subsets
C) Cardinal Number
D) Union
30 / 40If \( A = \{x : x \text{ is a letter in SCHOOL}\} \), then \( n(A) \) is:
A) \( 6 \)
B) \( 5 \)
C) \( 4 \)
D) \( 7 \)
31 / 40Which of the following is an Infinite Set?
A) Set of months in a year
B) Set of even numbers less than 100
C) Set of prime numbers
D) Set of vowels
32 / 40Idempotent Law states that \( A \cup A \) is equal to:
A) \( \phi \)
B) \( U \)
C) \( A \)
D) \( A' \)
33 / 40If \( n(A) = 4 \), then the number of subsets of \( A \) is:
A) \( 8 \)
B) \( 12 \)
C) \( 16 \)
D) \( 4 \)
34 / 40The number of subsets of the set \( \{1\} \) is:
A) \( 0 \)
B) \( 1 \)
C) \( 2 \)
D) \( 4 \)
35 / 40Every set is considered to be a subset of:
A) \( \phi \)
B) Proper set
C) Itself
D) Infinite set
36 / 40If \( A \cap B = A \), it implies that:
A) \( B \subset A \)
B) \( A = \phi \)
C) \( A \subset B \)
D) \( A \) and \( B \) are disjoint
37 / 40The set builder form of the interval \( [2, 5] \) is:
A) \( \{x : 2 < x < 5\} \)
B) \( \{x : 2 \le x < 5\} \)
C) \( \{x : 2 \le x \le 5\} \)
D) \( \{x : 2 < x \le 5\} \)
38 / 40Two sets \( A \) and \( B \) are said to be equal if and only if:
A) \( A \cap B = \phi \)
B) \( A \subset B \text{ and } B \subset A \)
C) \( A \cup B = U \)
D) \( n(A) = n(B) \)
39 / 40In a group of 50 people, 30 like Cricket, 25 like Football. How many like both?
A) \( 10 \)
B) \( 5 \)
C) \( 15 \)
D) \( 20 \)
40 / 40If \( A = \phi \), then the number of proper subsets is:
A) \( 1 \)
B) \( 2 \)
C) \( 0 \)
D) Not defined
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