Sets, Relations & Functions · NDA previous year questions

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2010 22 questions

Q12010 · 22 Aug 2010
The relation $R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}$ on a set $A = {1, 2, 3}$ is
1. A.reflexive, transitive but not symmetric
2. B.reflexive, symmetric but not transitive
3. C.symmetric, transitive but not reflexive
4. D.reflexive but neither symmetric nor transitive
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Answer: A
Q162010 · 22 Aug 2010
If $A$ and $B$ are two disjoint sets, then which one of the following is correct?
1. A. $A - B = A - (A \cap B)$
2. B. $B - A^{'} = B \cap A$
3. C. $A \cap B = (A - B) \cap B$
4. D.All of the above
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Answer: D
Q222010 · 22 Aug 2010
Let $N$ denote the set of natural numbers and $A = {n^{2} : n \in N}$ and $B = {n^{3} : n \in N}$ . Which one of the following is correct?
1. A. $A \cup B = N$
2. B.The complement of $(A \cup B)$ is an infinite set
3. C. $A \cap B$ must be a finite set
4. D. $A \cap B$ must be a proper subset of ${m^{6} : m \in N}$
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Answer: B
Q602010 · 22 Aug 2010
Consider the function $f : R \to {0, 1}$ such that $f (x) = {10 if x is rational if x is irrational$ Which one of the following is correct?
1. A.The function is one-one into
2. B.The function is many-one into
3. C.The function is one-one onto
4. D.The function is many-one onto
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Answer: D
Q612010 · 22 Aug 2010
If $f (x) = 2 x + 7$ and $g (x) = x^{2} + 7, x \in R$ , then what are the values of $x$ for which $f \circ g (x) = 25$ ?
1. A. $- 1, 1$
2. B. $- 2, 2$
3. C. $- 2, 2$
4. D.None of the above
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Answer: C
Q692010 · 22 Aug 2010
What is the value of $p$ for which the function $f (x) = p sin x + \frac{s i n 3 x}{3}$ has an extremum at $x = \frac{π}{3}$ ?
1. A.0
2. B.1
3. C. $- 1$
4. D.2
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Answer: D
Q1072010 · 22 Aug 2010
Let $U = {1, 2, 3, \dots, 20}$ . Let $A, B, C$ be the subsets of $U$ . Let $A$ be the set of all numbers which are perfect squares, $B$ be the set of all numbers which are multiples of $5$ and $C$ be the set of all numbers which are divisible by $2$ and $3$ . Consider the following statements : 1. $A, B, C$ are mutually exclusive. 2. $A, B, C$ are mutually exhaustive. 3. The number of elements in the complement set of $A \cup B$ is $12$ . Which of the statements given above are correct?
1. A.1 and 2 only
2. B.1 and 3 only
3. C.2 and 3 only
4. D.1, 2 and 3
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Answer: B
Q1202010 · 22 Aug 2010
If the cardinality of a set $A$ is $4$ and that of a set $B$ is $3$ , then what is the cardinality of the set $A △ B$ ?
1. A. $1$
2. B. $5$
3. C. $7$
4. D.Cannot be determined as the sets $A$ and $B$ are not given
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Answer: D
Q22010 · 18 Apr 2010
Let X be the set of all graduates in India. Elements x and y in X are said to be related if they are graduates of the same university. Which one of the following statements is correct?
1. A.Relation is symmetric and transitive only.
2. B.Relation is reflexive and transitive only.
3. C.Relation is reflexive and symmetric only.
4. D.Relation is reflexive, symmetric and transitive.
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Answer: D
Q32010 · 18 Apr 2010
If $x^{2} + y^{2} = 1$ , then what is $\frac{1 + x + i y}{1 + x - i y}$ equal to?
1. A. $x - i y$
2. B. $x + i y$
3. C. $2 x$
4. D. $- 2 i y$
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Answer: B
Q152010 · 18 Apr 2010
Consider the following statements: 1. Every function has a primitive. 2. A primitive of a function is unique. 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
Q162010 · 18 Apr 2010
If $A = {a, b, c, d}$ , then what is the number of proper subsets of A?
1. A.16
2. B.15
3. C.14
4. D.12
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Answer: B
Q172010 · 18 Apr 2010
What is the number of three-digit odd numbers formed by using the digits 1, 2, 3, 4, 5, 6 if repetition of digits is allowed?
1. A.60
2. B.108
3. C.120
4. D.216
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Answer: B
Q352010 · 18 Apr 2010
The order of a set A is 3 and that of a set B is 2. What is the number of relations from A to B?
1. A.4
2. B.6
3. C.32
4. D.64
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Answer: D
Q362010 · 18 Apr 2010
What is the value of $\frac{l o g _{α β} ( H )}{l o g _{α β γ} ( H )}$ ?
1. A. $lo g_{α β} (α)$
2. B. $lo g_{α β γ} (α β)$
3. C. $lo g_{α β} (α β γ)$
4. D. $lo g_{α β} (β)$
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Answer: C
Q382010 · 18 Apr 2010
For a set A, consider the following statements: 1. $A \cup P (A) = P (A)$ 2. ${A} \cap P (A) = A$ 3. $P (A) - {A} = P (A)$ where P denotes power set. Which of the statements given above is/are correct?
1. A.1 only
2. B.2 only
3. C.3 only
4. D.1, 2 and 3
Show answer
Answer: Dropped in the final answer key (full marks to everyone)
Q392010 · 18 Apr 2010
If the AM and HM of two numbers are 27 and 12 respectively, then what is their GM equal to?
1. A.12
2. B.18
3. C.24
4. D.27
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Answer: B
Q402010 · 18 Apr 2010
If $tan A = \frac{1}{2}$ and $tan B = \frac{1}{3}$ , then what is the value of $(A + B)$ ?
1. A.0
2. B. $\frac{π}{4}$
3. C. $\frac{π}{2}$
4. D. $π$
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Answer: B
Q442010 · 18 Apr 2010
The function $f (x) = e^{x}, x \in R$ is
1. A.Onto but not one-one
2. B.One-one onto
3. C.One-one but not onto
4. D.Neither one-one nor onto
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Answer: C
Q452010 · 18 Apr 2010
If $y = sin^{- 1} (\frac{4 x}{1 + 4 x ^{2}})$ , then what is $\frac{d y}{d x}$ equal to?
1. A. $\frac{1}{1 + 4 x ^{2}}$
2. B. $- \frac{1}{1 + 4 x ^{2}}$
3. C. $\frac{4}{1 + 4 x ^{2}}$
4. D. $\frac{4 x}{1 + 4 x ^{2}}$
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Answer: C
Q592010 · 18 Apr 2010
The function $f (x) = \frac{x}{x ^{2} + 1}$ from $R$ to $R$ is
1. A.One-one as well as onto
2. B.Onto but not one-one
3. C.Neither one-one nor onto
4. D.One-one but not onto
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Answer: C
Q752010 · 18 Apr 2010
If $A = P ({1, 2})$ where P denotes the power set, then which one of the following is correct?
1. A. ${1, 2} \subset A$
2. B. $1 \in A$
3. C. $ϕ \in / A$
4. D. ${1, 2} \in A$
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Answer: D