Limits, Continuity & Derivatives · NDA previous year questions

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2019 35 questions

Q12019 · 17 Nov 2019
Let $S = {2, 4, 6, 8, \dots, 20}$ . What is the maximum number of subsets does $S$ have?
1. A.10
2. B.20
3. C.512
4. D.1024
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Answer: D
Q22019 · 17 Nov 2019
Let $A \cup B = {x ∣ (x - a) (x - b) > 0$ , where $a < b}$ What are $A$ and $B$ equal to?
1. A. $A = {x ∣ x > a}$ and $B = {x ∣ x > b}$
2. B. $A = {x ∣ x < a}$ and $B = {x ∣ x > b}$
3. C. $A = {x ∣ x < a}$ and $B = {x ∣ x < b}$
4. D. $A = {x ∣ x > a}$ and $B = {x ∣ x < b}$
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Answer: B
Q32019 · 17 Nov 2019
If $A = {x : 0 \leq x \leq 2}$ and $B = {y; y is a prime number}$ , then what is $A \cap B$ equal to?
1. A. $\emptyset$
2. B. ${1}$
3. C. ${2}$
4. D. ${1, 2}$
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Answer: C
Q42019 · 17 Nov 2019
In a school, 50% students play cricket and 40% play football. If 10% of students play both the games, then what per cent of students play neither cricket nor football?
1. A.10%
2. B.15%
3. C.20%
4. D.25%
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Answer: C
Q52019 · 17 Nov 2019
If a set $A$ contains 3 elements and another set $B$ contains 6 elements, then what is the minimum number of elements that $(A \cup B)$ can have?
1. A.3
2. B.6
3. C.8
4. D.9
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Answer: B
Q242019 · 17 Nov 2019
What is the value of $k$ for which the sum of the squares of the roots of $2 x^{2} - 2 (k - 2) x - (k + 1) = 0$ is minimum?
1. A. $- 1$
2. B.1
3. C. $\frac{3}{2}$
4. D.2
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Answer: C
Q472019 · 17 Nov 2019
What is the minimum value of $\frac{a ^{2}}{c o s ^{2} x} + \frac{b ^{2}}{s i n ^{2} x}$ where $a > 0$ and $b > 0$ ?
1. A. $(a + b)^{2}$
2. B. $(a - b)^{2}$
3. C. $a^{2} + b^{2}$
4. D. $∣ a^{2} + b^{2} ∣$
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Answer: A
Q482019 · 17 Nov 2019
What is $sin (α + β) - 2 sin α cos β + sin (α - β)$ equal to?
1. A.0
2. B. $2 sin α$
3. C. $2 sin β$
4. D. $sin α + sin β$
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Answer: A
Q492019 · 17 Nov 2019
If $cosec θ = \frac{29}{21}$ where $0 < θ < 9 0^{\circ}$ , then what is the value of $4 sec θ + 4 tan θ$ ?
1. A.5
2. B.10
3. C.15
4. D.20
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Answer: B
Q502019 · 17 Nov 2019
Consider the following statements: 1. $cos θ + sec θ$ can never be equal to 1.5. 2. $tan θ + cot θ$ can never be less than 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: A
Q722019 · 17 Nov 2019
For what value of $k$ is the function $f (x) = ⎩ ⎨ ⎧ 2 x + \frac{1}{4} k (x + \frac{1}{2})^{2}, x < 0, x = 0, x > 0$ continuous?
1. A. $\frac{1}{4}$
2. B. $\frac{1}{2}$
3. C.1
4. D.2
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Answer: A
Q732019 · 17 Nov 2019
What is the value of $lim_{x \to 0} \frac{s i n x ^{\circ}}{t a n 3 x ^{\circ}}$ ?
1. A. $\frac{1}{4}$
2. B. $\frac{1}{3}$
3. C. $\frac{1}{2}$
4. D.1
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Answer: B
Q742019 · 17 Nov 2019
Consider the following statements in respect of the function $f (x) = sin (\frac{1}{x})$ for $x \neq = 0$ and $f (0) = 0$ : 1. $lim_{x \to 0} f (x)$ exists 2. $f (x)$ is continuous at $x = 0$ 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: D
Q752019 · 17 Nov 2019
What is the derivative of $2^{(s i n x)^{2}}$ with respect to $sin x$ ?
1. A. $sin x 2^{(s i n x)^{2}} ln 4$
2. B. $2 sin x 2^{(s i n x)^{2}} ln 4$
3. C. $ln (sin x) 2^{(s i n x)^{2}}$
4. D. $2 sin x cos x 2^{(s i n x)^{2}}$
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Answer: A
Q762019 · 17 Nov 2019
Directions for the following three (03) items : Read the following information and answer the three items that follow : Let $f (x) = x^{2} + 2 x - 5$ and $g (x) = 5 x + 30$ If $h (x) = 5 f (x) - xg (x)$ , then what is the derivative of $h (x)$ ?
1. A. $- 40$
2. B. $- 20$
3. C. $- 10$
4. D.0
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Answer: B
Q772019 · 17 Nov 2019
Directions for the following two (02) items : Read the following information and answer the two items that follow : Consider the equation $x^{y} = e^{x - y}$ What is $\frac{d y}{d x}$ at $x = 1$ equal to?
1. A.0
2. B.1
3. C.2
4. D.4
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Answer: A
Q782019 · 17 Nov 2019
Directions for the following two (02) items : Read the following information and answer the two items that follow : Consider the equation $x^{y} = e^{x - y}$ What is $\frac{d y}{d x}$ at $x = 1$ equal to? What is $\frac{d ^{2} y}{d x ^{2}}$ at $x = 1$ equal to?
1. A.0
2. B.1
3. C.2
4. D.4
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Answer: B
Q812019 · 17 Nov 2019
Directions for the following three (03) items : Read the following information and answer the three items that follow : A curve $y = m e^{m x}$ where $m > 0$ intersects $y$ -axis at a point $P$ . What is the equation of tangent to the curve at $P$ ?
1. A. $y = m x + m$
2. B. $y = - m x + 2 m$
3. C. $y = m^{2} x + 2 m$
4. D. $y = m^{2} x + m$
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Answer: D
Q822019 · 17 Nov 2019
If $f (x) = \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 6 x + 7$ increases in the interval $T$ and decreases in the interval $S$ , then which one of the following is correct?
1. A. $T = (- \infty, 2) \cup (3, \infty)$ and $S = (2, 3)$
2. B. $T = ϕ$ and $S = (- \infty, \infty)$
3. C. $T = (- \infty, \infty)$ and $S = ϕ$
4. D. $T = (2, 3)$ and $S = (- \infty, 2) \cup (3, \infty)$
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Answer: A
Q832019 · 17 Nov 2019
Directions
Directions for the following two (02) items : Read the following information and answer the two items that follow : Consider the function $f (x) = 3 x^{4} - 20 x^{3} - 12 x^{2} + 288 x + 1$
In which one of the following intervals is the function increasing?
1. A. $(- 2, 3)$
2. B. $(3, 4)$
3. C. $(- 3, - 2)$
4. D. $(- 4, - 3)$
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Answer: A
Q842019 · 17 Nov 2019
Directions
Directions for the following two (02) items : Read the following information and answer the two items that follow : Consider the function $f (x) = 3 x^{4} - 20 x^{3} - 12 x^{2} + 288 x + 1$
In which one of the following intervals is the function decreasing?
1. A. $(- 2, 3)$
2. B. $(3, 4)$
3. C. $(4, 6)$
4. D. $(6, 9)$
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Answer: B
Q852019 · 17 Nov 2019
What is $\int \frac{d x}{2 x ^{2} - 2 x + 1}$ equal to?
1. A. $\frac{t a n ^{- 1} ( 2 x - 1 )}{2} + c$
2. B. $2 tan^{- 1} (2 x - 1) + c$
3. C. $\frac{t a n ^{- 1} ( 2 x + 1 )}{2} + c$
4. D. $tan^{- 1} (2 x - 1) + c$
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Answer: D
Q862019 · 17 Nov 2019
What is $\int \frac{d x}{x ( 1 + l n x ) ^{n}}$ equal to $(n \neq = 1)$ ?
1. A. $\frac{1}{( n - 1 ) ( 1 + l n x ) ^{n - 1}} + c$
2. B. $\frac{1 - n}{( 1 + l n x ) ^{1 - n}} + c$
3. C. $\frac{n + 1}{( 1 + l n x ) ^{n + 1}} + c$
4. D. $- \frac{1}{( n - 1 ) ( 1 + l n x ) ^{n - 1}} + c$
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Answer: D
Q72019 · 21 Apr 2019
Passage
Consider the following for the next 02 (two) items that follow: In a school, all the students play at least one of three indoor games – chess, carrom and table tennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.
What can be the minimum number of students in the school?
1. A.123
2. B.111
3. C.95
4. D.63
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Answer: B
Q82019 · 21 Apr 2019
Passage
Consider the following for the next 02 (two) items that follow: In a school, all the students play at least one of three indoor games – chess, carrom and table tennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.
What can be the maximum number of students in the school?
1. A.111
2. B.123
3. C.125
4. D.135
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Answer: B