Sets, Relations & Functions · NDA previous year questions

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2022 25 questions

Q42022 · 4 Sept 2022
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?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: D
Q92022 · 4 Sept 2022
Consider the following statements : 1. The set of all irrational numbers between $2$ and $5$ 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?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: A
Q132022 · 4 Sept 2022
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?
1. A.4
2. B.5
3. C.6
4. D.7
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Answer: C
Q142022 · 4 Sept 2022
1. A.1 and 2 only
2. B.2 and 3 only
3. C.1 and 3 only
4. D.1, 2 and 3
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Answer: D
Q152022 · 4 Sept 2022
Consider the following : 1. A ∩ B = A ∩ C ⇒ B = C 2. A ∪ B = A ∪ C ⇒ B = C Which of the above is/are correct ?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
Show answer
Answer: D
Q312022 · 4 Sept 2022
Let $f (x)$ be a function satisfying $f (x + y) = f (x) f (y)$ for all $x, y \in N$ such that $f (1) = 2$ : If $\sum_{x = 2}^{n} f (x) = 2044$ , then what is the value of $n$ ?
1. A.8
2. B.9
3. C.10
4. D.11
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Answer: C
Q322022 · 4 Sept 2022
1. A.341
2. B.682
3. C.1023
4. D.1364
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Answer: B
Q332022 · 4 Sept 2022
Let $f (x)$ be a function satisfying $f (x + y) = f (x) f (y)$ for all $x, y \in N$ such that $f (1) = 2$ : If $\sum_{x = 2}^{n} f (x) = 2044$ , then what is the value of $n$ ? What is $\sum_{x = 1}^{n} 2^{x} f (x)$ equal to ?
1. A.1365
2. B.2730
3. C.4024
4. D.5460
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Answer: D
Q342022 · 4 Sept 2022
Passage
A university awarded medals in basketball, football, and volleyball. Only x students (x < 6) got medal in all the three sports and the medals went to a total of 15x students. It awarded 5x medals in basketball, (4x + 15) medals in football and (x + 25) medals in volleyball.
How many received medals in exactly two of the three sports ?
1. A.30 − 4x
2. B.35 − 7x
3. C.40 − 7x
4. D.45 − 5x
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Answer: C
Q352022 · 4 Sept 2022
Passage
A university awarded medals in basketball, football, and volleyball. Only x students (x < 6) got medal in all the three sports and the medals went to a total of 15x students. It awarded 5x medals in basketball, (4x + 15) medals in football and (x + 25) medals in volleyball.
How many received medals in at least two of three sports ?
1. A.30 − 6x
2. B.35 − 6x
3. C.40 − 5x
4. D.40 − 6x
Show answer
Answer: D
Q362022 · 4 Sept 2022
Passage
A university awarded medals in basketball, football, and volleyball. Only x students (x < 6) got medal in all the three sports and the medals went to a total of 15x students. It awarded 5x medals in basketball, (4x + 15) medals in football and (x + 25) medals in volleyball.
How many received medals in exactly one of three sports ?
1. A.21x − 40
2. B.21x − 35
3. C.20x − 35
4. D.20x − 25
Show answer
Answer: A
Q712022 · 4 Sept 2022
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 ?
1. A.−1
2. B.0
3. C.1
4. D.2
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Answer: A
Q722022 · 4 Sept 2022
If f(x) = 4x + 1 and g(x) = kx + 2 such that fog(x) = gof(x), then what is the value of k ?
1. A.7
2. B.5
3. C.4
4. D.3
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Answer: A
Q882022 · 4 Sept 2022
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
Show answer
Answer: C
Q892022 · 4 Sept 2022
If $y = ln^{2} (\frac{x ^{2} - x + 1}{x ^{2} + x + 1})$ , then what is $\frac{dy}{dx}$ at $x = 0$ equal to ?
1. A.-2
2. B.0
3. C.1
4. D.2
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Answer: B
Q902022 · 4 Sept 2022
If $\frac{d}{dx} (\frac{1 + x ^{4} + x ^{8}}{1 - x ^{2} + x ^{4}}) = a x + b x^{3}$ , then which one of the following is correct ?
1. A. $a = b$
2. B. $a = 2 b$
3. C. $a + b = 0$
4. D. $2 a = b$
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Answer: D
Q232022 · 10 Apr 2022
If A = {{1, 2, 3}}, then how many elements are there in the power set of A?
1. A.1
2. B.2
3. C.4
4. D.8
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Answer: B
Q412022 · 10 Apr 2022
Consider all the subsets of the set A = {1, 2, 3, 4}. How many of them are supersets of the set {4}?
1. A.6
2. B.7
3. C.8
4. D.9
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Answer: C
Q422022 · 10 Apr 2022
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?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
Show answer
Answer: A
Q432022 · 10 Apr 2022
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 ?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: C
Q442022 · 10 Apr 2022
Consider the following statements in respect of the relation R in the set IN of natural numbers defined by xRy if $x^{2} - 5 x y + 4 y^{2} = 0$ : 1. R is reflexive 2. R is symmetric 3. R is transitive Which of the above statements is /are correct ?
1. A.1 only
2. B.2 only
3. C.1 and 2 only
4. D.1, 2 and 3
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Answer: A
Q452022 · 10 Apr 2022
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?
1. A.1 and 2 only
2. B.2 and 3 only
3. C.1 and 3 only
4. D.1, 2 and 3
Show answer
Answer: D
Q592022 · 10 Apr 2022
What is the domain of the function $f (x) = 1 - (x - 1)^{2}$ ?
1. A.(0, 1)
2. B.[-1, 1]
3. C.(0, 2)
4. D.[0, 2]
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Answer: D
Q1072022 · 10 Apr 2022
Consider the following for the next three (03) items that follow : The algebraic sum of the deviations of a set of values $x_{1}, x_{2}, x_{3}, \dots, x_{n}$ measured from 100 is -20 and the algebraic sum of the deviations of the same set of values measured from 92 is 140. What is the algebraic sum of the deviations of the same set of values measured from 99?
1. A.0
2. B.10
3. C.20
4. D.40
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Answer: A
Q1082022 · 10 Apr 2022
Consider the following for the next three (03) items that follow : The algebraic sum of the deviations of a set of values $x_{1}, x_{2}, x_{3}, \dots, x_{n}$ measured from 100 is -20 and the algebraic sum of the deviations of the same set of values measured from 92 is 140. If the algebraic sum of the deviations of the same set of values measured from y is 180, then what is the value of y ?
1. A.80
2. B.85
3. C.90
4. D.95
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Answer: C