Sets, Relations & Functions · NDA previous year questions

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2011 17 questions

Q622011 · 21 Aug 2011
If $A = {a, b, c}$ , then what is the number of proper subsets of A ?
1. A.5
2. B.6
3. C.7
4. D.8
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Answer: C
Q1042011 · 21 Aug 2011
If $Φ$ is a null set, then which one of the following is correct?
1. A. $Φ = 0$
2. B. $Φ = {0}$
3. C. $Φ = {Φ}$
4. D. $Φ = {}$
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Answer: D
Q82011 · 17 Apr 2011
If $P, Q, R$ are three non-collinear points, then what is $P Q \cap P R$ equal to?
1. A.Null set
2. B. ${P}$
3. C. ${P, Q, R}$
4. D. ${Q, R}$
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Answer: B
Q172011 · 17 Apr 2011
Let $M$ be the set of men and $R$ is a relation ‘is son of’ defined on $M$ . Then $R$ is
1. A.an equivalence relation
2. B.a symmetric relation only
3. C.a transitive relation only
4. D.None of the above
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Answer: D
Q222011 · 17 Apr 2011
If $A, B, C$ are non-empty sets such that $A \cap C = Φ$ , then what is $(A \times B) \cap (C \times B)$ equal to?
1. A. $A \times C$
2. B. $A \times B$
3. C. $B \times C$
4. D. $Φ$
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Answer: D
Q232011 · 17 Apr 2011
If $A = {4 n + 2 ∣ n is a natural number}$ and $B = {3 n ∣ n is a natural number}$ , then what is $(A \cap B)$ equal to?
1. A. ${12 n^{2} + 6 n ∣ n is a natural number}$
2. B. ${24 n - 12 ∣ n is a natural number}$
3. C. ${60 n + 30 ∣ n is a natural number}$
4. D. ${12 n - 6 ∣ n is a natural number}$
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Answer: D
Q382011 · 17 Apr 2011
If $f (x)$ is an even function, then what is $\int_{0}^{π} f (cos x) d x$ equal to?
1. A.0
2. B. $\int_{0}^{π /2} f (cos x) d x$
3. C. $2 \int_{0}^{π /2} f (cos x) d x$
4. D.1
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Answer: C
Q392011 · 17 Apr 2011
What is the value of $k$ for which the system of equations $k x + 2 y = 5$ and $3 x + y = 1$ has no solution?
1. A.0
2. B.3
3. C.6
4. D.15
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Answer: C
Q592011 · 17 Apr 2011
Consider the following with regard to a relation $R$ on a set of real numbers defined by $x R y$ if and only if $3 x + 4 y = 5$ : 1. $0 R 1$ 2. $1 R \frac{1}{2}$ 3. $\frac{2}{3} R \frac{3}{4}$ Which of the 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: C
Q642011 · 17 Apr 2011
What is the set of points $(x, y)$ satisfying the equations $x^{2} + y^{2} = 4$ and $x + y = 2$ ?
1. A. ${(2, 0), (- 2, 0), (0, 2)}$
2. B. ${(0, 2), (0, - 2)}$
3. C. ${(0, 2), (2, 0)}$
4. D. ${(2, 0), (- 2, 0), (0, 2), (0, - 2)}$
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Answer: C
Q902011 · 17 Apr 2011
What is the solution set for the equation $x^{4} - 26 x^{2} + 25 = 0$ ?
1. A. ${- 5, - 1, 1, 5}$
2. B. ${- 5, - 1}$
3. C. ${1, 5}$
4. D. ${- 5, 0, 1, 5}$
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Answer: A
Q912011 · 17 Apr 2011
For the next four (4) items that follow : $A B C$ is a triangle right angled at $B$ . The hypotenuse $(A C)$ is four times the perpendicular $(B D)$ drawn to it from the opposite vertex and $A D < D C$ . What is one of the acute angles of the triangle?
1. A. $1 5^{\circ}$
2. B. $3 0^{\circ}$
3. C. $4 5^{\circ}$
4. D.None of the above
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Answer: A
Q922011 · 17 Apr 2011
For the next four (4) items that follow : $A B C$ is a triangle right angled at $B$ . The hypotenuse $(A C)$ is four times the perpendicular $(B D)$ drawn to it from the opposite vertex and $A D < D C$ . What is angle $A B D$ ?
1. A. $1 5^{\circ}$
2. B. $3 0^{\circ}$
3. C. $4 5^{\circ}$
4. D.None of the above
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Answer: A
Q932011 · 17 Apr 2011
For the next four (4) items that follow : $A B C$ is a triangle right angled at $B$ . The hypotenuse $(A C)$ is four times the perpendicular $(B D)$ drawn to it from the opposite vertex and $A D < D C$ . What is $A D : D C$ equal to?
1. A. $(7 - 23) : 1$
2. B. $(7 - 43) : 1$
3. C. $1 : 2$
4. D.None of the above
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Answer: B
Q942011 · 17 Apr 2011
For the next four (4) items that follow : $A B C$ is a triangle right angled at $B$ . The hypotenuse $(A C)$ is four times the perpendicular $(B D)$ drawn to it from the opposite vertex and $A D < D C$ . What is $tan (A - C)$ equal to ?
1. A.0
2. B.1
3. C.2
4. D.None of the above
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Answer: D
Q1082011 · 17 Apr 2011
What are the points of intersection of the curve $4 x^{2} - 9 y^{2} = 1$ with its conjugate axis?
1. A.(1/2, 0) and (-1/2, 0)
2. B.(0, 2) and (0, -2)
3. C.(0, 3) and (0, -3)
4. D.No such points exist
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Answer: D
Q1172011 · 17 Apr 2011
What is the range of $f (x) = cos 2 x - sin 2 x$ ?
1. A. $[2, 4]$
2. B. $[- 1, 1]$
3. C. $[- 2, 2]$
4. D. $(- 2, 2)$
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Answer: C