Sets, Relations & Functions · NDA previous year questions

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2014 23 questions

Q12014 · 28 Sept 2014
A and B are two sets having 3 elements in common. If $n (A) = 5$ , $n (B) = 4$ , then what is $n (A \times B)$ equal to ?
1. A.0
2. B.9
3. C.15
4. D.20
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Answer: D
Q22014 · 28 Sept 2014
The relation S is defined on the set of integers Z as xSy if integer x divides integer y. Then
1. A.S is an equivalence relation.
2. B.S is only reflexive and symmetric.
3. C.S is only reflexive and transitive.
4. D.S is only symmetric and transitive.
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Answer: C
Q32014 · 28 Sept 2014
What is $\frac{( 1 + i ) ^{4 n + 5}}{( 1 - i ) ^{4 n + 3}}$ equal to, where n is a natural number and $i = - 1$ ?
1. A.2
2. B. $2 i$
3. C. $- 2 i$
4. D. $i$
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Answer: A
Q42014 · 28 Sept 2014
What is $(\frac{3 + i}{3 - i})^{6}$ equal to, where $i = - 1$ ?
1. A.1
2. B.1/6
3. C.6
4. D.2
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Answer: A
Q202014 · 28 Sept 2014
If $A = (4 2 x - 3 x + 2 x + 1)$ is symmetric, then what is x equal to ?
1. A.2
2. B.3
3. C.-1
4. D.5
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Answer: D
Q502014 · 28 Sept 2014
For the next three (03) items that follow : Consider the function $f (x) = \frac{x - 1}{x + 1}$ . What is $\frac{f ( x ) + 1}{f ( x ) - 1} + x$ equal to ?
1. A.0
2. B.1
3. C. $2 x$
4. D. $4 x$
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Answer: A
Q512014 · 28 Sept 2014
For the next three (03) items that follow : Consider the function $f (x) = \frac{x - 1}{x + 1}$ . What is $f (2 x)$ equal to ?
1. A. $\frac{f ( x ) + 1}{f ( x ) + 3}$
2. B. $\frac{f ( x ) + 1}{3 f ( x ) + 1}$
3. C. $\frac{3 f ( x ) + 1}{f ( x ) + 3}$
4. D. $\frac{f ( x ) + 3}{3 f ( x ) + 1}$
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Answer: C
Q522014 · 28 Sept 2014
For the next three (03) items that follow : Consider the function $f (x) = \frac{x - 1}{x + 1}$ . What is $f (f (x))$ equal to ?
1. A. $x$
2. B. $- x$
3. C. $- \frac{1}{x}$
4. D.None of the above
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Answer: C
Q532014 · 28 Sept 2014
The function $f : N \to N$ , N being the set of natural numbers, defined by $f (x) = 2 x + 3$ is
1. A.injective and surjective
2. B.injective but not surjective
3. C.not injective but surjective
4. D.neither injective nor surjective
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Answer: B
Q542014 · 28 Sept 2014
For the next three (03) items that follow : Consider the function $f (x) = {x^{2} - 5, x + 13, x \leq 3 x > 3$ What is $lim_{x \to 3} f (x)$ equal to?
1. A.2
2. B.4
3. C.5
4. D.13
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Answer: B
Q12014 · 20 Apr 2014
Passage
For the next three (03) items that follow: In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.
The number of students who had taken only Physics is:
1. A.2
2. B.3
3. C.5
4. D.6
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Answer: A
Q22014 · 20 Apr 2014
Passage
For the next three (03) items that follow: In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.
The number of students who had taken only two subjects is:
1. A.7
2. B.8
3. C.9
4. D.10
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Answer: C
Q32014 · 20 Apr 2014
Passage
For the next three (03) items that follow: In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.
Consider the following statements: 1. The number of students who had taken only one subject is equal to the number of students who had taken only two subjects. 2. The number of students who had taken at least two subjects is four times the number of students who had taken all the three subjects. 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: B
Q42014 · 20 Apr 2014
Let $X$ be the set of all citizens of India. Elements $x, y$ in $X$ are said to be related if the difference of their age is 5 years. Which one of the following is correct?
1. A.The relation is an equivalence relation on $X$ .
2. B.The relation is symmetric but neither reflexive nor transitive.
3. C.The relation is reflexive but neither symmetric nor transitive.
4. D.None of the above
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Answer: B
Q52014 · 20 Apr 2014
Consider the following relations from $A$ to $B$ where $A = {u, v, w, x, y, z}$ and $B = {p, q, r, s}$ . 1. ${(u, p), (v, p), (w, p), (x, q), (y, q), (z, q)}$ 2. ${(u, p), (v, q), (w, r), (z, s)}$ 3. ${(u, s), (v, r), (w, q), (u, p), (v, q), (z, q)}$ 4. ${(u, q), (v, p), (w, s), (x, r), (y, q), (z, s)}$ Which of the above relations are not functions?
1. A.1 and 2
2. B.1 and 4
3. C.2 and 3
4. D.3 and 4
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Answer: C
Q62014 · 20 Apr 2014
Let $S$ denote set of all integers. Define a relation $R$ on $S$ as ' $a R b$ if $ab \geq 0$ where $a, b \in S$ '. Then $R$ is:
1. A.Reflexive but neither symmetric nor transitive relation
2. B.Reflexive, symmetric but not transitive relation
3. C.An equivalence relation
4. D.Symmetric but neither reflexive nor transitive relation
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Answer: B
Q512014 · 20 Apr 2014
Let $N$ denote the set of all non-negative integers and $Z$ denote the set of all integers. The function $f : Z \to N$ given by $f (x) = ∣ x ∣$ is:
1. A.One-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: B
Q522014 · 20 Apr 2014
If $f (9) = 9$ and $f^{'} (9) = 4$ then what is $lim_{x \to 9} \frac{f ( x ) - 3}{x - 3}$ equal to?
1. A.36
2. B.9
3. C.4
4. D.None of the above
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Answer: C
Q602014 · 20 Apr 2014
For the next two (02) items that follow: Consider the function $f (x) = \frac{1 - s i n x}{( π - 2 x ) ^{2}}$ where $x \neq = \frac{π}{2}$ and $f (\frac{π}{2}) = λ$ What is $lim_{x \to \frac{π}{2}} f (x)$ equal to?
1. A.1
2. B.1/2
3. C.1/4
4. D.1/8
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Answer: D
Q692014 · 20 Apr 2014
Consider the following statements: 1. The function $f (x) = sin x$ decreases on the interval $(0, π /2)$ . 2. The function $f (x) = cos x$ increases on the interval $(0, π /2)$ . 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
Q702014 · 20 Apr 2014
What is $\int_{- \frac{π}{2}}^{\frac{π}{2}} x sin x d x$ equal to?
1. A.0
2. B.2
3. C. $- 2$
4. D. $π$
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Answer: B
Q712014 · 20 Apr 2014
What is $\int_{0}^{π /2} ln (tan x) d x$ equal to?
1. A. $ln 2$
2. B. $- ln 2$
3. C.0
4. D.None of the above
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Answer: C
Q722014 · 20 Apr 2014
What is $\int_{0}^{1} \frac{e ^{t a n^{- 1} x}}{1 + x ^{2}} d x$ equal to?
1. A. $e^{\frac{π}{4}} - 1$
2. B. $e^{\frac{π}{4}} + 1$
3. C. $e - 1$
4. D. $e$
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Answer: A