Sets, Relations and Functions · Mathematics · NDA

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MCQ (Single Correct Answer)

1
Let X be the set of all persons living in Delhi. The persons a an b in X are said to be related, if the difference in their ages is almost 5 hr. The relation is
NDA 2015 Paper 2
2
If A = {x$$\in$$ R : x2 + 6x $$-$$ 7 < 0} and B = {x$$\in$$ R : x2 + 9x + 14 < 0}, then which of the following is/are correct?

1. (A $$\cap$$ B) = ($$-$$2, 1)

2. (A $$-$$ B) = ($$-$$7, $$-$$2)

Select the correct answer using the code given below
NDA 2015 Paper 2
3
A, B, C and D are four sets such that A $$\cap$$ B = C $$\cap$$ D = $$\phi$$.

Consider the following

1. A $$\cup$$ C and B $$\cup$$ D are always disjoint.

2. A $$\cap$$ and B $$\cap$$ D are always disjoint.

Which of the above statements is/are correct?
NDA 2015 Paper 2
4
In an examination, 70% students passed in Physics, 80% students passed in Chemistry, 75% students passed in Mathematics and 85% students passed in Biology, and x% students failed in all the four subjects. What is the minimum value of x?
NDA 2016 Paper 2
5
Let S be a set of all distinct numbers of the form $${p \over q}$$, where p, q$$\in$${1, 2, 3, 4, 5, 6}. What is the cardinality of the set S?
NDA 2016 Paper 2
6
If $$A = \{ x \in R:{x^2} + 6x - 7 < 0\} $$ and $$B = \{ x \in R:{x^2} + 9x + 14 > 0\} $$, then which of the following is/are correct?

I. $$A \cap B = \{ x \in R: - 2 < x < 1\} $$

II. $$A/B = \{ x \in R: - 7 < x < - 2\} $$

Select the correct answer using the code given below.
NDA 2016 Paper 2
7
Let R be a relation from A = {1, 2, 3, 4} to B= {1, 3, 5} such that R = {(a, b) : a < b, where a$$\in$$A and b$$\in$$B}. What is RoR$$-$$1 equal to?
NDA 2016 Paper 2
8
What is the number of natural numbers less than or equal to 1000 which are neither divisible by 10 nor 15 nor 25?
NDA 2016 Paper 1
9
Suppose, there is a relation * between the positive numbers x and y given by x * y if and only if x $$\le$$ y2. Then, which one of the following is correct?
NDA 2016 Paper 1
10
Let R be a relation on the set N of natural numbers defined by 'nRm $$\Leftrightarrow$$ n is a factor of m'. Then, which one of the following is correct?
NDA 2016 Paper 1
11
If E is the universal set and A = B $$\cup$$ C, then the set E $$-$$ (E $$-$$ (E $$-$$ (E $$-$$ (E $$-$$A)))) is same as the set
NDA 2017 Paper 2
12
If A = {x : x is a multiple of 2}, B = {x : x is a multiple of 5} and C = {x : x is a multiple of 10}, then A $$\cap$$ (B $$\cap$$ C) is equal to
NDA 2017 Paper 2
13
If we define a relation R on the set N $$\times$$ N as (a, b) R (c, d) $$ \Leftrightarrow $$ a + d = b + c for all (a, b), (c, d) $$\in$$N $$\times$$ N, then the relation is
NDA 2017 Paper 2
14
Let S be the set of all persons living in Delhi. We say that x, y in S are related if they were born in Delhi on the same day. Which one of the following is correct?
NDA 2017 Paper 1
15
Consider the following in respect of sets A and B.

1. (A $$-$$ B) $$\cup$$ B = A

2. (A $$-$$ B) $$\cup$$ A = A

3. (A $$-$$ B) $$\cap$$ B = $$\phi$$

4. A $$ \subseteq $$ B $$\Rightarrow$$ A $$\cup$$ B = B

Which of the above are correct?
NDA 2017 Paper 1
16
If A, B and C are subsets of a universal set, then which one the following is not correct?

where, A' is the complement of A
NDA 2018 Paper 2
17
How many students like to play all the three games?
NDA 2018 Paper 2
18
How many students like to play exactly only one game?
NDA 2018 Paper 2
19
Let A = {x $$\in$$ R :- 1 $$\le$$ x $$\le$$ 1}, B = {y$$\in$$R :- 1 $$\le$$ y $$\le$$ 1} and S be the subset of A $$\times$$ B, defined by S = {(x, y) $$\in$$ A $$\times$$ B : x2 + y2 = 1}. Which one of the following is correct?
NDA 2018 Paper 2
20
Let A and B be subsets of X and C = (A $$\cap$$ B') $$\cap$$ (A' $$\cap$$ B), where A' and B' are complements of A and B respectively in X. What is C equal to?
NDA 2018 Paper 1
21
What is the number of students who are good in either Hindi or Mathematics but not English?
NDA 2018 Paper 1
22
What is the number of students who are good in Hindi and Mathematics but not in English?
NDA 2018 Paper 1
23
A survey of 850 students in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance?
NDA 2018 Paper 1
24
Let S = {2, 4, 6, 8, ........, 20}.

What are the maximum number of subsets of S?
NDA 2019 Paper 2
25
Let A $$\cup$$ B = {x | (x $$-$$ a) (x $$-$$ b) > 0, where a < b}. What are A nd B equal to?
NDA 2019 Paper 2
26
If A = {x : 0 $$\le$$ x $$\le$$ 2} and B = {y : y is a prime number}, then what is A $$\cap$$ B equal to?
NDA 2019 Paper 2
27
In a school, 50% students play cricket and 40% play football. If 10% of students play both these games, then what per cent of students play neither cricket not football?
NDA 2019 Paper 2
28
If a set A contains 3 elements and another set B contains 6 elements, then what is the minimum number of elements that (A $$\cup$$ B) can have?
NDA 2019 Paper 2
29
If A, B and C are subsets of a given set, then which one of the following relations is not correct?
NDA 2019 Paper 2
30
Suppose X = {1, 2, 3, 4} and R is a relation on X. If R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}, then which one of the following is correct?
NDA 2019 Paper 1
31
A relation R is defined on the set N of natural numbers as xRy $$\Rightarrow$$ x2 $$-$$ 4xy + 3y2 = 0. Then, which one of the following is correct?
NDA 2019 Paper 1
32
If $$A = \{ x \in Z:{x^3} - 1 = 0\} $$ and $$B = \{ x \in Z:{x^2} + x + 1 = 0\} $$, where, Z is set of complex numbers, then what is A $$\cap$$ B equal to?
NDA 2019 Paper 1
33
Consider the following statements for the two non-empty sets A and B.

1. $$(A \cap B) \cup (A \cap \overline B ) \cup (\overline A \cap B) = A \cup B$$

2. $$(A \cup (\overline A \cap \overline B )) = A \cup B$$

Which of the above statements is/are correct?
NDA 2019 Paper 1
34
Let X be a non-empty set and let A, B, C be subsets of X. Consider the following statements.

1. $$A \subset C \Rightarrow (A \cap B) \subset (C \cap B),\,(A \cup B) \subset (C \cup B)$$

2. $$(A \cap B) \subset (C \cap B)$$ for all sets $$B \Rightarrow A \subset C$$

3. $$(A \cup B) \subset (C \cup B)$$ for all sets $$B \Rightarrow A \subset C$$

Which of the above statements are correct?
NDA 2019 Paper 1
35
If A = {$$\lambda$$, {$$\lambda$$, $$\mu$$}}, then the power set of A is
NDA 2019 Paper 1
36
What can be the minimum number of students in the school?
NDA 2019 Paper 1
37
What can be the maximum number of students in the school?
NDA 2019 Paper 1
38

Let $A = \{x \in \mathbb{R} : -1 <x <1\}$. Which of the following is/are bijective functions from A to itself?

1. $f(x) = x|x|$

2. $g(x) = \cos(\pi x)$

Select the correct answer using the code given below:

NDA Mathematics 21 April 2024
39

Let $R$ be a relation on the open interval $(-1, 1)$ and is given by $R = \{(x, y) : |x + y| < 2\}$. Then which one of the following is correct?

NDA Mathematics 21 April 2024
40

For any three non-empty sets $A, B, C$, what is $$(A \cup B - \{(A - B) \cup (B - A) \cup (A \cap B)\})$$ equal to?

NDA Mathematics 21 April 2024
41

Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{6, 7\}$. What is the number of onto functions from $A$ to $B$?

NDA Mathematics 21 April 2024
42
A set S contains (2n + 1) elements. There are 4096 subsets of S which contain at most n elements. What is n equal to?
NDA Mathematics 3 September 2023
43

The Cartesian product A × A has 16 elements among which are (0, 2) and (1, 3). Which of the following statements is/are correct?

1. It is possible to determine set A.

2. A × A contains the element (3, 2).

Select the correct answer using the code given below:

NDA Mathematics 3 September 2023
44

Let A = {1, 2, 3, ..., 20}. Define a relation R from A to A by R = {(x, y) : 4x - 3y = 1}, where x, y ∈ A. Which of the following statements is/are correct?

1. The domain of R is {1, 4, 7, 10, 13, 16).

2. The range of R is {1, 5, 9, 13, 17).

3. The range of R is equal to codomain of R.

Select the correct answer using the code given below:

NDA Mathematics 3 September 2023
45

Consider the following statements: 

1. The relation f defined by $f(x)= \begin{cases}x^3, & 0 \leq x \leq 2 \\ 4 x, & 2 \leq x \leq 8\end{cases}$ is a function.

2. The relation g defined by $g(x)= \begin{cases}x^2, & 0 \leq x \leq 4 \\ 3 x, & 4 \leq x \leq 8\end{cases}$ is a function.

Which of the statements given above is/are correct?

NDA Mathematics 3 September 2023
46

Consider the following statements 

1. A = (A ∪ B) ∪ (A - B),

2. A ∪ (B - A) = (A ∪ B)

3. B = (A ∪ B) - (A - B)

Which of the statements given above are correct?

NDA Mathematics 3 September 2023
47
What is the binary number equivalent to decimal number 1011 ?
NDA Mathematics 16 April 2023
48
A mapping f : A → B defined as $f(x)=\frac{2 x+3}{3 x+5}, x \in A$ If f is to be onto, then what are A and B equal to ?
NDA Mathematics 16 April 2023
49

Consider the following statements :

1. If f is the subset of Z × Z defined by f = {(xy, x − y); x, y ∈ Z}, then f is a function from Z to Z.

2. If f is the subset of N × N defined by f = {(xy, x + y); x, y ∈ N}, then f is a function from N to N.

Which of the statements given above is/are correct?

NDA Mathematics 4 September 2022
50

Consider the following statements :

1. The set of all irrational numbers between $\sqrt{2}$ and $\sqrt{5}$ is an infinite set.

2. The set of all odd integers less than 100 is a finite set.

Which of the statements given above is/are correct?

NDA Mathematics 4 September 2022
51

Let A = {7, 8, 9, 10, 11, 12, 13; 14, 15, 16} and let f ∶ A → N be defined by f(x) = the highest prime factor of x.

How many elements are there in the range of f?

NDA Mathematics 4 September 2022
52

Let R be a relation from N to N defined by R = {(x, y): x, y ∈ N and x2 = y3}. Which of the following are not correct?

1. (x, x) ∈ R for all x ∈ N

2. (x, y) ∈ R ⇒ (y, x) ∈ R

3. (x, y) ∈ R and (y, z) ∈ R ⇒ (x, z) ∈ R

Select the correct answer using the code given below :

NDA Mathematics 4 September 2022
53

Consider the following :

1. A ∩ B = A ∩ C ⇒ B = C

2. A ∪ B = A ∪ C ⇒ B = C

Which of the above is/are correct ?

NDA Mathematics 4 September 2022
54

How many received medals in exactly two of the three sports ?

NDA Mathematics 4 September 2022
55

How many received medals in at least two of three sports ?

NDA Mathematics 4 September 2022
56

How many received medals in exactly one of three sports ?

NDA Mathematics 4 September 2022
57
Let z = [y] and y = [x] − x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z ?
NDA Mathematics 4 September 2022
58
If A = {{1, 2, 3}}, then how many elements are there in the power set of A?
NDA Mathematics 10 April 2022
59
Consider all the subsets of the set A = {1, 2, 3, 4}. How many of them are supersets of the set {4}?
NDA Mathematics 10 April 2022
60

Consider the following statements in respect of two non-empty sets A and B :

1. x ∉ (A ∪ B) ⇒ x ∉ A or x ∉ B

2. x ∉ (A ∩ B) ⇒ x ∉ A and x ∉ B

Which of the above statements is/are correct?

NDA Mathematics 10 April 2022
61

Consider the following statements in respect of two non-empty sets A and B :

1. A ∪ B = A ∩ B if A = B

2. A Δ B = ϕ  if A = B

Which of the above statements is/are correct ?

NDA Mathematics 10 April 2022
62

Consider the following statements in respect of the relation R in the set IN of natural numbers defined by xRy if x2 - 5xy + 4y2 = 0 :

1. R is reflexive

2. R is symmetric

3. R is transitive

Which of the above statements is /are correct ?

NDA Mathematics 10 April 2022
63

Consider the following statements in respect of any relation R on a set A :

1. If R is reflexive, then R-1 is also reflexive

2. If R is symmetric, then R-1 is also symmetric

3. If R is transitive, then R-1 is also transitive

Which of the above statements are correct?

NDA Mathematics 10 April 2022
64
If f(x + 1) = x2 - 3x + 2, then what is f(x) equal to?
NDA Mathematics 18 April 2021
65

Consider the following statements:

1. A = {1, 3, 5} and B = {2, 4, 7} are equivalent sets.

2. A = {1, 5, 9} and B = {1, 5, 5, 9, 9} are equal sets.

Which of the above statements is/are correct?

NDA Mathematics 18 April 2021
66

Consider the following statements:

1. The null set is a subset of every set.

2. Every set is a subset of itself.

3. If a set has 10 elements, then its power set will have 1024 elements.

Which of the above statements are correct?

NDA Mathematics 18 April 2021
67
Let R be a relation defined as xRy if and only if 2x + 3y = 20, where x, y ∈ N. How many elements of the form (x, y) are there in R?
NDA Mathematics 18 April 2021
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