Sets, Relations & Functions · NDA previous year questions

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2020 24 questions

Q112020 · 6 Sept 2020
Let $S = {1, 2, 3, \dots}$ . A relation $R$ on $S \times S$ is defined by $x R y$ if $lo g_{a} x > lo g_{a} y$ where $a = \frac{1}{2}$ . Then the relation is
1. A.reflexive only
2. B.symmetric only
3. C.transitive only
4. D.both symmetric and transitive
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Answer: C
Q162020 · 6 Sept 2020
1. A.18
2. B.19
3. C.21
4. D.23
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Answer: C
Q172020 · 6 Sept 2020
1. A. $a + b + 43$
2. B. $a + b + 63$
3. C. $a + b + 96$
4. D. $a + b + 106$
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Answer: D
Q182020 · 6 Sept 2020
1. A. $p + b + 60$
2. B. $p + b + 40$
3. C. $p + a + 60$
4. D. $p + a + 40$
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Answer: A
Q192020 · 6 Sept 2020
Directions for the following two (02) items: Read the following information and answer the two items that follow: Let $\frac{t a n 3 A}{t a n A} = K$ , where $tan A \neq = 0$ and $K \neq = \frac{1}{3}$ . What is $tan^{2} A$ equal to?
1. A. $\frac{K + 3}{3 K - 1}$
2. B. $\frac{K - 3}{3 K - 1}$
3. C. $\frac{3 K - 3}{K - 3}$
4. D. $\frac{K + 3}{3 K + 1}$
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Answer: B
Q202020 · 6 Sept 2020
Directions for the following two (02) items: Read the following information and answer the two items that follow: Let $\frac{t a n 3 A}{t a n A} = K$ , where $tan A \neq = 0$ and $K \neq = \frac{1}{3}$ . For real values of $tan A$ , $K$ cannot lie between
1. A. $\frac{1}{3}$ and 3
2. B. $\frac{1}{2}$ and 2
3. C. $\frac{1}{5}$ and 5
4. D. $\frac{1}{7}$ and 7
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Answer: A
Q212020 · 6 Sept 2020
Directions for the following two (02) items: Read the following information and answer the two items that follow: ABCD is a trapezium such that AB and CD are parallel and BC is perpendicular to them. Let $∠ A D B = θ$ , $∠ A B D = α$ , $B C = p$ and $C D = q$ . Consider the following: 1. $A D sin θ = A B sin α$ 2. $B D sin θ = A B sin (θ + α)$ . 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
Q222020 · 6 Sept 2020
Directions for the following two (02) items: Read the following information and answer the two items that follow: ABCD is a trapezium such that AB and CD are parallel and BC is perpendicular to them. Let $∠ A D B = θ$ , $∠ A B D = α$ , $B C = p$ and $C D = q$ . What is $A B$ equal to?
1. A. $\frac{( p ^{2} + q ^{2} ) s i n θ}{p c o s θ + q s i n θ}$
2. B. $\frac{( p ^{2} - q ^{2} ) c o s θ}{p c o s θ + q s i n θ}$
3. C. $\frac{( p ^{2} + q ^{2} ) s i n θ}{q c o s θ + p s i n θ}$
4. D. $\frac{( p ^{2} - q ^{2} ) c o s θ}{q c o s θ + p s i n θ}$
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Answer: A
Q232020 · 6 Sept 2020
If $tan θ = \frac{c o s 1 7 ^{\circ} - s i n 1 7 ^{\circ}}{c o s 1 7 ^{\circ} + s i n 1 7 ^{\circ}}$ , then what is the value of $θ$ ?
1. A. $0^{\circ}$
2. B. $2 8^{\circ}$
3. C. $3 8^{\circ}$
4. D. $5 2^{\circ}$
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Answer: B
Q242020 · 6 Sept 2020
$A$ and $B$ are positive acute angles such that $cos 2 B = 3 sin^{2} A$ and $3 sin 2 A = 2 sin 2 B$ . What is the value of $(A + 2 B)$ ?
1. A. $\frac{π}{6}$
2. B. $\frac{π}{4}$
3. C. $\frac{π}{3}$
4. D. $\frac{π}{2}$
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Answer: D
Q252020 · 6 Sept 2020
What is $sin 3 x + cos 3 x + 4 sin^{3} x - 3 sin x + 3 cos x - 4 cos^{3} x$ equal to?
1. A.0
2. B.1
3. C. $2 sin 2 x$
4. D. $4 cos 4 x$
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Answer: A
Q262020 · 6 Sept 2020
The value of ordinate of the graph of $y = 2 + cos x$ lies in the interval
1. A. $[0, 1]$
2. B. $[0, 3]$
3. C. $[- 1, 1]$
4. D. $[1, 3]$
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Answer: D
Q272020 · 6 Sept 2020
What is the value of $8 cos 1 0^{\circ} \cdot cos 2 0^{\circ} \cdot cos 4 0^{\circ}$ ?
1. A. $tan 1 0^{\circ}$
2. B. $cot 1 0^{\circ}$
3. C. $csc 1 0^{\circ}$
4. D. $sec 1 0^{\circ}$
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Answer: B
Q282020 · 6 Sept 2020
What is the value of $cos 4 8^{\circ} - cos 1 2^{\circ}$ ?
1. A. $\frac{5 - 1}{4}$
2. B. $\frac{1 - 5}{4}$
3. C. $\frac{5 + 1}{2}$
4. D. $\frac{1 - 5}{8}$
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Answer: B
Q472020 · 6 Sept 2020
Consider the proper subsets of ${1, 2, 3, 4}$ . How many of these proper subsets are superset of the set ${3}$ ?
1. A.5
2. B.6
3. C.7
4. D.8
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Answer: C
Q482020 · 6 Sept 2020
1. A. $D < 0$
2. B. $D \leq 0$
3. C. $D > 0$
4. D. $D \geq 0$
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Answer: A
Q772020 · 6 Sept 2020
If $e^{θ ϕ} = c + 4 θ ϕ$ , where $c$ is an arbitrary constant and $ϕ$ is a function of $θ$ , then what is $ϕ d θ$ equal to?
1. A. $θ d ϕ$
2. B. $- θ d ϕ$
3. C. $4 θ d ϕ$
4. D. $- 4 θ d ϕ$
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Answer: B
Q782020 · 6 Sept 2020
If $p (x) = (4 e)^{2 x}$ , then what is $\int p (x) d x$ equal to?
1. A. $\frac{p ( x )}{1 + 2 l n 2} + c$
2. B. $\frac{p ( x )}{2 ( 1 + 2 l n 2 )} + c$
3. C. $\frac{2 p ( x )}{1 + l n 4} + c$
4. D. $\frac{p ( x )}{1 + l n 2} + c$
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Answer: B
Q792020 · 6 Sept 2020
What is the value of $\int_{0}^{π /4} (tan^{3} x + tan x) d x$ ?
1. A. $\frac{1}{4}$
2. B. $\frac{1}{2}$
3. C.1
4. D.2
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Answer: B
Q802020 · 6 Sept 2020
Let $y = 3 x^{2} + 2$ . If $x$ changes from 10 to 10.1, then what is the total change in $y$ ?
1. A.4.71
2. B.5.23
3. C.6.03
4. D.8.01
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Answer: C
Q842020 · 6 Sept 2020
What is the domain of the function $f (x) = cos^{- 1} (x - 2)$ ?
1. A. $[- 1, 1]$
2. B. $[1, 3]$
3. C. $[0, 5]$
4. D. $[- 2, 1]$
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Answer: B
Q972020 · 6 Sept 2020
Consider the following statements: 1. The function $f (x) = ln x$ increases in the interval $(0, \infty)$ . 2. The function $f (x) = tan x$ increases in the interval $(- \frac{π}{2}, \frac{π}{2})$ . 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: C
Q982020 · 6 Sept 2020
Which one of the following is correct in respect of the graph of $y = \frac{1}{x - 1}$ ?
1. A.The domain is ${x \in R ∣ x \neq = 1}$ and the range is the set of reals.
2. B.The domain is ${x \in R ∣ x \neq = 1}$ , the range is ${y \in R ∣ y \neq = 0}$ and the graph intersects $y$ -axis at $(0, - 1)$ .
3. C.The domain is the set of reals and the range is the singleton set ${0}$ .
4. D.The domain is ${x \in R ∣ x \neq = 1}$ and the range is the set of points on the $y$ -axis.
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Answer: B
Q1042020 · 6 Sept 2020
The sum of deviations of $n$ number of observations measured from 2.5 is 50. The sum of deviations of the same set of observations measured from 3.5 is $- 50$ . What is the value of $n$ ?
1. A.50
2. B.60
3. C.80
4. D.100
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Answer: D