Sets, Relations & Functions · NDA previous year questions

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2013 31 questions

Q52013 · 11 Aug 2013
If $A$ is a finite set having $n$ elements, then the number of relations which can be defined in $A$ is
1. A. $2^{n}$
2. B. $n^{2}$
3. C. $2^{n^{2}}$
4. D. $n^{n}$
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Answer: C
Q72013 · 11 Aug 2013
Which one of the following is an example of non-empty set?
1. A.Set of all even prime numbers
2. B. ${x : x^{2} - 2 = 0$ and $x$ is rational $}$
3. C. ${x : x$ is a natural number, $x < 8$ and simultaneously $x > 12}$
4. D. ${x : x$ is a point common to any two parallel lines $}$
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Answer: A
Q82013 · 11 Aug 2013
What is one of the square roots of $3 + 4 i$ , where $i = - 1$ ?
1. A. $2 + i$
2. B. $2 - i$
3. C. $- 2 + i$
4. D. $- 3 - i$
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Answer: A
Q102013 · 11 Aug 2013
The relation $R$ in the set $Z$ of integers given by $R = {(a, b) : a - b is divisible by 5}$ is
1. A.reflexive
2. B.reflexive but not symmetric
3. C.symmetric and transitive
4. D.an equivalence relation
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Answer: D
Q112013 · 11 Aug 2013
What is $\sum_{r = 0}^{n} C (n, r)$ equal to?
1. A. $2^{n} - 1$
2. B. $n$
3. C. $n!$
4. D. $2^{n}$
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Answer: D
Q122013 · 11 Aug 2013
What is $0.9 + 0.09 + 0.009 + \dots$ equal to?
1. A.1
2. B.1.01
3. C.1.001
4. D.1.1
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Answer: A
Q212013 · 11 Aug 2013
If $A$ is a subset of $B$ , then which one of the following is correct?
1. A. $A^{c} \subseteq B^{c}$
2. B. $B^{c} \subseteq A^{c}$
3. C. $A^{c} = B^{c}$
4. D. $A \subseteq A \cap B$
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Answer: B, D
Q232013 · 11 Aug 2013
Let $f$ be a function from the set of natural numbers to the set of even natural numbers given by $f (x) = 2 x$ . Then $f$ is
1. A.one to one but not onto
2. B.onto but not one-one
3. C.both one-one and onto
4. D.neither one-one nor onto
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Answer: C
Q242013 · 11 Aug 2013
1. A. $(2 - 3 - 1 2)$
2. B. $\frac{1}{2} (2 - 3 - 1 2)$
3. C. $\frac{1}{4} (2 - 3 - 1 2)$
4. D.None of the above
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Answer: D
Q252013 · 11 Aug 2013
If $(2431) \times (5 - 3 - 2 1) = (117 - 1 λ)$ then what is $λ$ equal to?
1. A.7
2. B. $- 7$
3. C.9
4. D. $- 9$
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Answer: B
Q262013 · 11 Aug 2013
What is the angle (in circular measure) between the hour hand and the minute hand of a clock when the time is half past 4?
1. A. $\frac{π}{3}$
2. B. $\frac{π}{4}$
3. C. $\frac{π}{6}$
4. D.None of the above
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Answer: B
Q272013 · 11 Aug 2013
The angles of elevation of the top of a tower from two places situated at distances 21 m and $x$ m from the base of the tower are $4 5^{\circ}$ and $6 0^{\circ}$ respectively. What is the value of $x$ ?
1. A. $73$
2. B. $7 - 3$
3. C. $7 + 3$
4. D.14
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Answer: A
Q282013 · 11 Aug 2013
What is $\frac{c o t 5 4 ^{\circ}}{t a n 3 6 ^{\circ}} + \frac{t a n 2 0 ^{\circ}}{c o t 7 0 ^{\circ}}$ equal to?
1. A.0
2. B.1
3. C.2
4. D.3
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Answer: C
Q292013 · 11 Aug 2013
A person standing on the bank of a river observes that the angle subtended by a tree on the opposite of bank is $6 0^{\circ}$ . When he retires 40 m from the bank, he finds the angle to be $3 0^{\circ}$ . What is the breadth of the river?
1. A.60 m
2. B.40 m
3. C.30 m
4. D.20 m
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Answer: D
Q302013 · 11 Aug 2013
If the angles of a triangle are $3 0^{\circ}$ and $4 5^{\circ}$ and the included side is $(3 + 1)$ , then what is the area of the triangle?
1. A. $\frac{3 + 1}{2}$
2. B. $2 (3 + 1)$
3. C. $\frac{3 + 1}{3}$
4. D. $\frac{3 - 1}{2}$
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Answer: A
Q312013 · 11 Aug 2013
What is $sin^{2} 2 0^{\circ} + sin^{2} 7 0^{\circ}$ equal to?
1. A.1
2. B.0
3. C. $- 1$
4. D. $\frac{1}{2}$
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Answer: A
Q422013 · 11 Aug 2013
If $A = {1, 3, 5, 7}$ , then what is the cardinality of the power set $P (A)$ ?
1. A.8
2. B.15
3. C.16
4. D.17
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Answer: C
Q12013 · 14 Apr 2013
*Directions :* For the next six (06) questions that follow : In a state with a population of $75 \times 1 0^{6}$ , 45% of them know Hindi, 22% know English, 18% know Sanskrit, 12% know Hindi and English, 8% know English and Sanskrit, 10% know Hindi and Sanskrit and 5% know all the three languages. What is the number of people who do not know any of the above three languages ?
1. A. $3 \times 1 0^{6}$
2. B. $4 \times 1 0^{6}$
3. C. $3 \times 1 0^{7}$
4. D. $4 \times 1 0^{7}$
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Answer: C
Q22013 · 14 Apr 2013
What is the number of people who know Hindi only ?
1. A. $21 \times 1 0^{6}$
2. B. $25 \times 1 0^{6}$
3. C. $28 \times 1 0^{6}$
4. D. $3 \times 1 0^{7}$
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Answer: A
Q32013 · 14 Apr 2013
What is the number of people who know Sanskrit only ?
1. A. $5 \times 1 0^{6}$
2. B. $45 \times 1 0^{5}$
3. C. $4 \times 1 0^{6}$
4. D.None of the above
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Answer: D
Q42013 · 14 Apr 2013
What is the number of people who know English only ?
1. A. $5 \times 1 0^{6}$
2. B. $45 \times 1 0^{5}$
3. C. $4 \times 1 0^{6}$
4. D.None of the above
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Answer: D
Q52013 · 14 Apr 2013
What is the number of people who know only one language ?
1. A. $3 \times 1 0^{6}$
2. B. $4 \times 1 0^{6}$
3. C. $3 \times 1 0^{7}$
4. D. $4 \times 1 0^{7}$
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Answer: C
Q62013 · 14 Apr 2013
What is the number of people who know only two languages ?
1. A. $11.25 \times 1 0^{5}$
2. B. $11.25 \times 1 0^{6}$
3. C. $12 \times 1 0^{5}$
4. D. $12.5 \times 1 0^{5}$
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Answer: B
Q72013 · 14 Apr 2013
What is the degree of the equation $\frac{1}{x - 3} = \frac{1}{x + 2} - \frac{1}{2}$ ?
1. A.0
2. B.1
3. C.2
4. D.3
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Answer: C
Q82013 · 14 Apr 2013
Which one of the following is a null set ?
1. A. ${0}$
2. B. ${{{}}}$
3. C. ${{}}$
4. D. ${x ∣ x^{2} + 1 = 0, x \in R}$
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Answer: D