Sets, Relations & Functions · NDA previous year questions

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2017 26 questions

Q22017 · 10 Sept 2017
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
1. A. $A$
2. B. $B$
3. C. $C$
4. D. ${x : x is a multiple of 100}$
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Answer: C
Q32017 · 10 Sept 2017
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
1. A.symmetric only
2. B.symmetric and transitive only
3. C.equivalence relation
4. D.reflexive only
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Answer: C
Q42017 · 10 Sept 2017
The smallest positive integer $n$ for which $(\frac{1 + i}{1 - i})^{n} = 1$ , is
1. A.1
2. B.4
3. C.8
4. D.16
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Answer: B
Q452017 · 10 Sept 2017
The equation of the line passing through the point $(2, 3)$ and the point of intersection of lines $2 x - 3 y + 7 = 0$ and $7 x + 4 y + 2 = 0$ is
1. A. $21 x + 46 y - 180 = 0$
2. B. $21 x - 46 y + 96 = 0$
3. C. $46 x + 21 y - 155 = 0$
4. D. $46 x - 21 y - 29 = 0$
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Answer: B
Q562017 · 10 Sept 2017
The inverse of the function $y = 5^{l n x}$ is
1. A. $x = y^{\frac{1}{l n 5}}, y > 0$
2. B. $x = y^{l n 5}, y > 0$
3. C. $x = y^{\frac{1}{l n 5}}, y < 0$
4. D. $x = 5 ln y, y > 0$
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Answer: A
Q572017 · 10 Sept 2017
The function $f (x) = ∣ x ∣ - x^{3}$ is
1. A.odd
2. B.even
3. C.both even and odd
4. D.neither even nor odd
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Answer: D
Q582017 · 10 Sept 2017
If $x$ is any real number, then $\frac{x ^{2}}{1 + x ^{4}}$ belongs to which one of the following intervals?
1. A. $(0, 1)$
2. B. $(0, \frac{1}{2}]$
3. C. $(0, \frac{1}{2})$
4. D. $[0, 1]$
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Answer: D
Q602017 · 10 Sept 2017
1. A.Option A
2. B.Option B
3. C.Option C
4. D.Option D
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Answer: C
Q12017 · 23 Apr 2017
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?
1. A.The relation is an equivalent relation
2. B.The relation is not reflexive but it is symmetric and transitive
3. C.The relation is not symmetric but it is reflexive and transitive
4. D.The relation is not transitive but it is reflexive and symmetric
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Answer: A
Q22017 · 23 Apr 2017
Consider the following in respect of sets $A$ and $B$ : 1. $(A - B) \cup B = A$ 2. $(A - B) \cup A = A$ 3. $(A - B) \cap B = ϕ$ 4. $A \subseteq B \Rightarrow A \cup B = B$ Which of the above are correct?
1. A.1, 2 and 3
2. B.2, 3 and 4
3. C.1, 3 and 4
4. D.1, 2 and 4
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Answer: B
Q32017 · 23 Apr 2017
The value of $i^{2 n} + i^{2 n + 1} + i^{2 n + 2} + i^{2 n + 3}$ , where $i = - 1$ , is
1. A.0
2. B.1
3. C. $i$
4. D. $- i$
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Answer: A
Q42017 · 23 Apr 2017
The value of $(\frac{- 1 + i 3}{2})^{n} + (\frac{- 1 - i 3}{2})^{n}$ where $n$ is not a multiple of 3 and $i = - 1$ , is
1. A.1
2. B. $- 1$
3. C. $i$
4. D. $- i$
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Answer: B
Q52017 · 23 Apr 2017
If $1, ω, ω^{2}$ are the cube roots of unity, then $(1 + ω) (1 + ω^{2}) (1 + ω^{3}) (1 + ω + ω^{2})$ is equal to
1. A. $- 2$
2. B. $- 1$
3. C.0
4. D.2
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Answer: C
Q192017 · 23 Apr 2017
If $S = {x : x^{2} + 1 = 0, x is real}$ , then $S$ is
1. A. ${- 1}$
2. B. ${0}$
3. C. ${1}$
4. D.an empty set
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Answer: D
Q202017 · 23 Apr 2017
Let $A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}$ . Then the number of subsets of $A$ containing two or three elements is
1. A.45
2. B.120
3. C.165
4. D.330
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Answer: C
Q212017 · 23 Apr 2017
Three-digit numbers are formed from the digits 1, 2 and 3 in such a way that the digits are not repeated. What is the sum of such three-digit numbers?
1. A.1233
2. B.1322
3. C.1323
4. D.1332
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Answer: D
Q222017 · 23 Apr 2017
The number of different words (eight-letter words) ending and beginning with a consonant which can be made out of the letters of the word ‘EQUATION’ is
1. A.5200
2. B.4320
3. C.3000
4. D.2160
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Answer: B
Q232017 · 23 Apr 2017
The value of $[C (7, 0) + C (7, 1)] + [C (7, 1) + C (7, 2)]$ $+ \dots + [C (7, 6) + C (7, 7)]$ is
1. A.254
2. B.255
3. C.256
4. D.257
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Answer: A
Q682017 · 23 Apr 2017
Which one of the following functions is neither even nor odd?
1. A. $x^{2} - 1$
2. B. $x + \frac{3}{x}$
3. C. $∣ x ∣$
4. D. $x^{2} (x - 3)$
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Answer: D
Q692017 · 23 Apr 2017
Let $f (a) = \frac{a - 1}{a + 1}$ . Consider the following: 1. $f (2 a) = f (a) + 1$ 2. $f (\frac{1}{a}) = - f (a)$ 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
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Answer: B
Q702017 · 23 Apr 2017
Let $f (x) : {x, 0, x is rational x is irrational$ and $g (x) : {0, x, x is rational x is irrational$ If $f : R \to R$ and $g : R \to R$ , then $(f - g)$ is
1. A.one-one and into
2. B.neither one-one nor onto
3. C.many-one and onto
4. D.one-one and onto
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Answer: D
Q712017 · 23 Apr 2017
1. A.0
2. B. $\frac{1}{2}$
3. C.1
4. D.2
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Answer: B
Q722017 · 23 Apr 2017
If $F (x) = 9 - x^{2}$ , then what is $lim_{x \to 1} \frac{F ( x ) - F ( 1 )}{x - 1}$ equal to?
1. A. $- \frac{1}{4 2}$
2. B. $\frac{1}{8}$
3. C. $- \frac{1}{2 2}$
4. D. $\frac{1}{2 2}$
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Answer: C
Q1022017 · 23 Apr 2017
Consider the following statements: Statement 1: Range is not a good measure of dispersion. Statement 2: Range is highly affected by the existence of extreme values. Which one of the following is correct in respect of the above statements?
1. A.Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
2. B.Both Statement 1 and Statement 2 are correct but Statement 2 is not the correct explanation of Statement 1
3. C.Statement 1 is correct but Statement 2 is not correct
4. D.Statement 2 is correct but Statement 1 is not correct
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Answer: A
Q1182017 · 23 Apr 2017
The function $f : X \to Y$ defined by $f (x) = cos x$ , where $x \in X$ , is one-one and onto if $X$ and $Y$ are respectively equal to
1. A. $[0, π]$ and $[- 1, 1]$
2. B. $[- \frac{π}{2}, \frac{π}{2}]$ and $[- 1, 1]$
3. C. $[0, π]$ and $(- 1, 1)$
4. D. $[0, π]$ and $[0, 1]$
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Answer: A