Sets, Relations & Functions · NDA previous year questions

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2019 21 questions

Q62019 · 17 Nov 2019
If $A, B$ and $C$ are subsets of a given set, then which one of the following relations is not correct?
1. A. $A \cup (A \cap B) = A \cup B$
2. B. $A \cap (A \cup B) = A$
3. C. $(A \cap B) \cup C = (A \cup C) \cap (B \cup C)$
4. D. $(A \cup B) \cap C = (A \cap C) \cup (B \cap C)$
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Answer: A
Q72019 · 17 Nov 2019
1. A. $A = {x ∣ x > a}$ and $B = {x ∣ x > b}$
2. B. $A = {x ∣ x < a}$ and $B = {x ∣ x > b}$
3. C. $A = {x ∣ x < a}$ and $B = {x ∣ x < b}$
4. D. $A = {x ∣ x > a}$ and $B = {x ∣ x < b}$
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Answer: C
Q82019 · 17 Nov 2019
What is the value of $[\frac{i + 3}{2}]^{2019} + [\frac{i - 3}{2}]^{2019} ?$
1. A.1
2. B. $- 1$
3. C. $2 i$
4. D. $- 2 i$
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Answer: C
Q232019 · 17 Nov 2019
If both $p$ and $q$ belong to the set ${1, 2, 3, 4}$ , then how many equations of the form $p x^{2} + q x + 1 = 0$ will have real roots?
1. A.12
2. B.10
3. C.7
4. D.6
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Answer: C
Q672019 · 17 Nov 2019
Directions for the following three (03) items : Read the following information and answer the three items that follow : Consider the function $f (x) = g (x) + h (x)$ where $g (x) = sin (\frac{x}{4})$ and $h (x) = cos (\frac{4 x}{5})$ What is the period of the function $g (x)$ ?
1. A. $π$
2. B. $2 π$
3. C. $4 π$
4. D. $8 π$
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Answer: D
Q682019 · 17 Nov 2019
Directions for the following three (03) items : Read the following information and answer the three items that follow : Consider the function $f (x) = g (x) + h (x)$ where $g (x) = sin (\frac{x}{4})$ and $h (x) = cos (\frac{4 x}{5})$ What is the period of the function $g (x)$ ? What is the period of the function $h (x)$ ?
1. A. $π$
2. B. $\frac{4 π}{5}$
3. C. $\frac{5 π}{2}$
4. D. $\frac{3 π}{2}$
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Answer: C
Q692019 · 17 Nov 2019
Directions for the following three (03) items : Read the following information and answer the three items that follow : Consider the function $f (x) = g (x) + h (x)$ where $g (x) = sin (\frac{x}{4})$ and $h (x) = cos (\frac{4 x}{5})$ What is the period of the function $g (x)$ ? What is the period of the function $f (x)$ ?
1. A. $10 π$
2. B. $20 π$
3. C. $40 π$
4. D. $80 π$
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Answer: C
Q712019 · 17 Nov 2019
Directions for the following three (03) items : Read the following information and answer the three items that follow : Consider the function $f (x) = g (x) + h (x)$ where $g (x) = sin (\frac{x}{4})$ and $h (x) = cos (\frac{4 x}{5})$ What is the period of the function $g (x)$ ? Consider the following statements : 1. $f [g (x)]$ is a polynomial of degree 3. 2. $g [g (x)]$ is a polynomial of degree 2. 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: D
Q1002019 · 17 Nov 2019
If the range of a set of observations on a variable $X$ is known to be 25 and if $Y = 40 + 3 X$ , then what is the range of the set of corresponding observations on $Y$ ?
1. A.25
2. B.40
3. C.75
4. D.115
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Answer: C
Q1182019 · 17 Nov 2019
Which one of the following is the second degree polynomial function $f (x)$ where $f (0) = 5$ , $f (- 1) = 10$ and $f (1) = 6$ ?
1. A. $5 x^{2} - 2 x + 5$
2. B. $3 x^{2} - 2 x - 5$
3. C. $3 x^{2} - 2 x + 5$
4. D. $3 x^{2} - 10 x + 5$
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Answer: C
Q12019 · 21 Apr 2019
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?
1. A.R is reflexive and symmetric, but not transitive
2. B.R is symmetric and transitive, but not reflexive
3. C.R is reflexive and transitive, but not symmetric
4. D.R is neither reflexive nor transitive, but symmetric
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Answer: D
Q22019 · 21 Apr 2019
A relation R is defined on the set N of natural numbers as $x R y \Rightarrow x^{2} - 4 x y + 3 y^{2} = 0$ . Then which one of the following is correct?
1. A.R is reflexive and symmetric, but not transitive
2. B.R is reflexive and transitive, but not symmetric
3. C.R is reflexive, symmetric and transitive
4. D.R is reflexive, but neither symmetric nor transitive
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Answer: D
Q42019 · 21 Apr 2019
Consider the following statements for the two non-empty sets A and B: 1. $(A \cap B) \cup (A \cap \overset{ˉ}{B}) \cup (\overset{ˉ}{A} \cap B) = A \cup B$ 2. $(A \cup (\overset{ˉ}{A} \cap \overset{ˉ}{B})) = A \cup B$ 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: A
Q52019 · 21 Apr 2019
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?
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
Q62019 · 21 Apr 2019
If $A = {λ, {λ, μ}}$ , then the power set of A is
1. A. ${ϕ, {ϕ}, {λ}, {λ, μ}}$
2. B. ${ϕ, {λ}, {{λ, μ}}, {λ, {λ, μ}}}$
3. C. ${ϕ, {λ}, {λ, μ}, {λ, {λ, μ}}}$
4. D. ${{λ}, {λ, μ}, {λ, {λ, μ}}}$
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Answer: B
Q692019 · 21 Apr 2019
A function f defined by $f (x) = ln (x^{2} + 1 - x)$ is
1. A.an even function
2. B.an odd function
3. C.Both even and odd function
4. D.Neither even nor odd function
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Answer: B
Q702019 · 21 Apr 2019
The domain of the function f defined by $f (x) = lo g_{x} 10$ is
1. A. $x > 10$
2. B. $x > 0$ excluding $x = 10$
3. C. $x \geq 10$
4. D. $x > 0$ excluding $x = 1$
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Answer: D
Q732019 · 21 Apr 2019
The domain of the function $f (x) = (2 - x) (x - 3)$ is
1. A. $(0, \infty)$
2. B. $[0, \infty)$
3. C. $[2, 3]$
4. D. $(2, 3)$
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Answer: C
Q742019 · 21 Apr 2019
If $f (x) = \frac{x - 2}{x + 2}$ , $x \neq = - 2$ , then what is $f^{- 1} (x)$ equal to?
1. A. $\frac{4 ( x + 2 )}{x - 2}$
2. B. $\frac{x + 2}{4 ( x - 2 )}$
3. C. $\frac{x + 2}{x - 2}$
4. D. $\frac{2 ( 1 + x )}{1 - x}$
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Answer: D
Q752019 · 21 Apr 2019
If $f (x) = lo g_{10} (1 + x)$ , then what is $4 f (4) + 5 f (1) - lo g_{10} 2$ equal to ?
1. A.0
2. B.1
3. C.2
4. D.4
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Answer: D
Q762019 · 21 Apr 2019
$lim_{x \to 0} \frac{1 - c o s ^{3} 4 x}{x ^{2}}$ is equal to
1. A.0
2. B.12
3. C.24
4. D.36
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Answer: C