Sets, Relations & Functions · NDA previous year questions

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2009 33 questions

Q12009 · 30 Aug 2009
If $(1 + 3 + 5 + \dots + p) + (1 + 3 + 5 + \dots + q) = (1 + 3 + 5 + \dots + r)$ where each set of parentheses contains the sum of consecutive odd integers as shown, what is the smallest possible value of $(p + q + r)$ where $p > 6$ ?
1. A.12
2. B.21
3. C.45
4. D.54
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Answer: B
Q22009 · 30 Aug 2009
Let $A = {x ∣ x \leq 9, x \in N}$ . Let $B = {a, b, c}$ be the subset of $A$ where $(a + b + c)$ is a multiple of 3. What is the largest possible number of subsets like $B$ ?
1. A.12
2. B.21
3. C.27
4. D.30
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Answer: D
Q32009 · 30 Aug 2009
Let $A = {- 1, 2, 5, 8}$ , $B = {0, 1, 3, 6, 7}$ and $R$ be the relation 'is one less than' from $A$ to $B$ , then how many elements will $R$ contain ?
1. A.2
2. B.3
3. C.5
4. D.9
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Answer: B
Q42009 · 30 Aug 2009
A mapping $f : R \to R$ which is defined as $f (x) = cos x; x \in R$ is :
1. A.One-one only
2. B.Onto only
3. C.One-one onto
4. D.Neither one-one nor onto
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Answer: D
Q462009 · 30 Aug 2009
If $P (A)$ denotes the power set of $A$ and $A$ is the void set, then what is number of elements in $P {P {P (A)}}$ ?
1. A.0
2. B.1
3. C.4
4. D.16
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Answer: C
Q472009 · 30 Aug 2009
1. A. $e$
2. B. $e^{3}$
3. C. $e^{- 9}$
4. D. $e^{9}$
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Answer: C
Q512009 · 30 Aug 2009
Which one of the following functions $f : R \to R$ is injective ?
1. A. $f (x) = ∣ x ∣$ for all $x \in R$
2. B. $f (x) = x^{2}$ for all $x \in R$
3. C. $f (x) = 11$ for all $x \in R$
4. D. $f (x) = - x$ for all $x \in R$
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Answer: D
Q1072009 · 30 Aug 2009
If $X = {(4^{n} - 3 n - 1) ∣ n \in N}$ and $Y = {9 (n - 1) ∣ n \in N}$ , then what is $X \cup Y$ equal to ?
1. A. $X$
2. B. $Y$
3. C. $N$
4. D.A null set
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Answer: B
Q1082009 · 30 Aug 2009
Sets $A$ and $B$ have $n$ elements in common. How many elements will $(A \times B)$ and $(B \times A)$ have in common ?
1. A.0
2. B.1
3. C. $n$
4. D. $n^{2}$
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Answer: D
Q1172009 · 30 Aug 2009
A function $f$ is such that $f^{'} (x) = 6 - 4 sin 2 x$ and $f (0) = 3$ . What is $f (x)$ equal to ?
1. A. $6 x + 2 cos 2 x$
2. B. $6 x - 2 cos 2 x$
3. C. $6 x - 2 cos 2 x + 1$
4. D. $6 x + 2 cos 2 x + 1$
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Answer: D
Q1182009 · 30 Aug 2009
If $f (x) = e^{x}$ and $g (x) = ln x$ , then what is the value of $(g \circ f)^{'} (x)$ ?
1. A.0
2. B.1
3. C. $e$
4. D.None of the above
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Answer: B
Q1192009 · 30 Aug 2009
Let $g (x) = x^{3} - 4 x + 6$ . If $f^{'} (x) = g^{'} (x)$ and $f (1) = 2$ , then what is $f (x)$ equal to ?
1. A. $x^{3} - 4 x + 3$
2. B. $x^{3} - 4 x + 6$
3. C. $x^{3} - 4 x + 1$
4. D. $x^{3} - 4 x + 5$
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Answer: D
Q1202009 · 30 Aug 2009
Let $f : R \to R$ be defined by $f (x) = ∣ x ∣/ x, x \neq = 0$ , $f (0) = 2$ . What is range of $f$ ?
1. A. ${1, 2}$
2. B. ${1, - 1}$
3. C. ${- 1, 1, 2}$
4. D. ${1}$
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Answer: C
Q12009 · 19 Apr 2009
If $A$ and $B$ are subsets of a set $X$ , then what is $(A \cap (X - B)) \cup B$ equal to?
1. A. $A \cup B$
2. B. $A \cap B$
3. C. $A$
4. D. $B$
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Answer: A
Q22009 · 19 Apr 2009
The total number of subsets of a finite set $A$ has $56$ more elements than the total number of subsets of another finite set $B$ . What is the number of elements in the set $A$ ?
1. A. $5$
2. B. $6$
3. C. $7$
4. D. $8$
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Answer: B
Q32009 · 19 Apr 2009
What is the smallest natural number $n$ such that $n!$ is divisible by $990$ ?
1. A. $9$
2. B. $11$
3. C. $33$
4. D. $99$
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Answer: B
Q42009 · 19 Apr 2009
Which one of the following is correct?
1. A. $A \times (B - C) = (A - B) \times (A - C)$
2. B. $A \times (B - C) = (A \times B) - (A \times C)$
3. C. $A \cap (B \cup C) = (A \cap B) \cup C$
4. D. $A \cup (B \cap C) = (A \cup B) \cap C$
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Answer: B
Q52009 · 19 Apr 2009
In an examination out of 100 students, 75 passed in English, 60 passed in Mathematics and 45 passed in both English and Mathematics. What is the number of students passed in exactly one of the two subjects?
1. A.45
2. B.60
3. C.75
4. D.90
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Answer: A
Q62009 · 19 Apr 2009
Let $R$ be the set of those $x \in N$ which are multiples of $3$ with $x \leq 100$ , and $S$ the set of those $x \in N$ which are multiples of $5$ with $x \leq 100$ . What is the number of elements in $(R \times S) \cap (S \times R)$ ?
1. A. $36$
2. B. $33$
3. C. $20$
4. D. $6$
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Answer: A
Q342009 · 19 Apr 2009
If $X$ and $Y$ are any two non-empty sets, then what is $(X - Y)^{'}$ equal to?
1. A. $X^{'} - Y^{'}$
2. B. $X^{'} \cap Y$
3. C. $X^{'} \cup Y$
4. D. $X - Y^{'}$
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Answer: C
Q352009 · 19 Apr 2009
For finding the area of a triangle $A B C$ , which of the following entities are required?
1. A.Angles $A, B$ and side $a$
2. B.Angles $A, B$ and side $b$
3. C.Angles $A, B$ and side $c$
4. D.Either (a) or (b) or (c)
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Answer: D
Q362009 · 19 Apr 2009
Let $A = [1324]$ and $B = [a 0 0 b]$ , where $a, b$ are natural numbers, then which one of the following is correct?
1. A.There exist more than one but finite number of $B$ s such that $A B = B A$
2. B.There exists exactly one $B$ such that $A B = B A$
3. C.There exist infinitely many $B$ s such that $A B = B A$
4. D.There cannot exist any $B$ such that $A B = B A$
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Answer: C
Q442009 · 19 Apr 2009
What is the number of proper subsets of a given finite set with $n$ elements?
1. A. $2 n - 1$
2. B. $2 n - 2$
3. C. $2^{n} - 1$
4. D. $2^{n} - 2$
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Answer: C
Q462009 · 19 Apr 2009
If $A, B$ and $C$ are three finite sets, then what is $[(A \cup B) \cap C]^{'}$ equal to?
1. A. $A^{'} \cup B^{'} \cap C^{'}$
2. B. $A^{'} \cap B^{'} \cap C^{'}$
3. C. $A^{'} \cap B^{'} \cup C^{'}$
4. D. $A \cap B \cap C$
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Answer: C
Q472009 · 19 Apr 2009
What is the value of $tan (- 157 5^{\circ})$ ?
1. A. $1$
2. B. $1/2$
3. C. $0$
4. D. $- 1$
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Answer: A