Sets, Relations & Functions · NDA previous year questions

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2012 16 questions

Q72012 · 19 Aug 2012
The relation 'has the same father as' over the set of children is:
1. A.only reflexive
2. B.only symmetric
3. C.only transitive
4. D.an equivalence relation
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Answer: D
Q122012 · 19 Aug 2012
Let $P = {1, 2, 3}$ and a relation on set P is given by the set $R = {(1, 2), (1, 3), (2, 1), (1, 1), (2, 2), (3, 3), (2, 3)}$ . Then R is:
1. A.Reflexive, transitive but not symmetric
2. B.Symmetric, transitive but not reflexive
3. C.Symmetric, reflexive but not transitive
4. D.None of the above
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Answer: A
Q132012 · 19 Aug 2012
The value of the sum $\sum_{n = 1}^{13} (i^{n} + i^{n + 1})$ where $i = - 1$ is:
1. A. $i$
2. B. $- i$
3. C.0
4. D. $i - 1$
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Answer: D
Q162012 · 19 Aug 2012
If a non-empty set A contains n elements, then its power set contains how many elements?
1. A. $n^{2}$
2. B. $2^{n}$
3. C. $2 n$
4. D. $n + 1$
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Answer: B
Q172012 · 19 Aug 2012
Let $A = {x \in W, the set of whole numbers and x < 3}$ , $B = {x \in N, the set of natural numbers and 2 \leq x < 4}$ and $C = {3, 4}$ , then how many elements will $(A \cup B) \times C$ contain?
1. A.6
2. B.8
3. C.10
4. D.12
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Answer: B
Q682012 · 19 Aug 2012
Let $f : R \to R$ be a function whose inverse is $\frac{x + 5}{3}$ . What is f(x) equal to?
1. A.f(x) = 3x + 5
2. B.f(x) = 3x - 5
3. C.f(x) = 5x - 3
4. D.f(x) does not exist
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Answer: B
Q692012 · 19 Aug 2012
Consider the following statements : 1. If $y = ln (sec x + tan x)$ , then $\frac{d y}{d x} = sec x$ . 2. If $y = ln (cosec x - cot x)$ , then $\frac{d y}{d x} = cosec x$ . 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: C
Q732012 · 19 Aug 2012
Let $A = {x \in R ∣ x \geq 0}$ . A function $f : A \to A$ is defined by $f (x) = x^{2}$ . Which one of the following is correct?
1. A.The function does not have inverse
2. B.f is its own inverse
3. C.The function has an inverse but f is not its own inverse
4. D.None of the above
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Answer: C
Q742012 · 19 Aug 2012
If $y = ln (e^{m x} + e^{- m x})$ , then what is $\frac{d y}{d x}$ at $x = 0$ equal to?
1. A. $- 1$
2. B.0
3. C.1
4. D.2
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Answer: B
Q22012 · 15 Apr 2012
Let $U = {x \in N : 1 \leq x \leq 10}$ be the universal set, N being the set of natural numbers. If $A = {1, 2, 3, 4}$ and $B = {2, 3, 6, 10}$ then what is the complement of $(A - B)$ ?
1. A. ${6, 10}$
2. B. ${1, 4}$
3. C. ${2, 3, 5, 6, 7, 8, 9, 10}$
4. D. ${5, 6, 7, 8, 9, 10}$
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Answer: C
Q32012 · 15 Apr 2012
The solution of the simultaneous linear equations $2 x + y = 6$ and $3 y = 8 + 4 x$ will also be satisfied by which one of the following linear equations?
1. A. $x + y = 5$
2. B. $2 x + y = 9$
3. C. $2 x - 3 y = 10$
4. D. $2 x + 3 y = 6$
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Answer: A
Q42012 · 15 Apr 2012
Let $A = {x : x is a square of a natural number and x is less than 100}$ and B is a set of even natural numbers. What is the cardinality of $A \cap B$ ?
1. A.4
2. B.5
3. C.9
4. D.None of the above
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Answer: A
Q642012 · 15 Apr 2012
If A and B are two non-empty sets having n elements in common, then what is the number of common elements in the sets $A \times B$ and $B \times A$ ?
1. A.n
2. B. $n^{2}$
3. C.2n
4. D.zero
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Answer: B
Q652012 · 15 Apr 2012
If A and B are any two sets, then what is $A \cap (A \cup B)$ equal to?
1. A.Complement of A
2. B.Complement of B
3. C.B
4. D.A
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Answer: D
Q1112012 · 15 Apr 2012
The set $A = {x : x + 4 = 4}$ can also be represented by :
1. A.0
2. B. $ϕ$
3. C. ${ϕ}$
4. D. ${0}$
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Answer: D
Q1122012 · 15 Apr 2012
If a line makes the angles $α, β, γ$ with the axes, then what is the value of $1 + cos 2 α + cos 2 β + cos 2 γ$ equal to?
1. A.-1
2. B.0
3. C.1
4. D.2
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Answer: B