Limits, Continuity & Derivatives · NDA previous year questions

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2009 20 questions

Q202009 · 30 Aug 2009
What is the maximum value of $sin θ cos θ$ ?
1. A.1
2. B. $1/2$
3. C. $1/ 2$
4. D. $3 /2$
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Answer: B
Q212009 · 30 Aug 2009
If $sin x + cosec x = 2$ , then what is the value of $sin^{4} x + cosec^{4} x$ ?
1. A.2
2. B.4
3. C.8
4. D.16
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Answer: A
Q222009 · 30 Aug 2009
What is the value of $tan 1 5^{\circ} + cot 1 5^{\circ}$ ?
1. A. $3$
2. B. $23$
3. C.4
4. D.2
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Answer: C
Q232009 · 30 Aug 2009
If $A + B + C = π /2$ , then what is the value of $tan A tan B + tan B tan C + tan C tan A$ ?
1. A.0
2. B.1
3. C. $- 1$
4. D. $tan A tan B tan C$
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Answer: B
Q242009 · 30 Aug 2009
If angles of a triangle are in the ratio $1 : 2 : 3$ , then what is the ratio of its corresponding sides ?
1. A. $3 : 2 : 1$
2. B. $1 : 2 : 3$
3. C. $1 : 3 : 2$
4. D. $2 : 3 : 4$
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Answer: C
Q252009 · 30 Aug 2009
If $C (n, 12) = C (n, 8)$ , then what is the value of $C (22, n)$ ?
1. A.131
2. B.231
3. C.256
4. D.292
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Answer: B
Q372009 · 30 Aug 2009
The function $y = tan^{- 1} x - x$
1. A.is always decreasing
2. B.is always increasing
3. C.first increases and then decreases
4. D.first decreases and then increases
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Answer: A
Q382009 · 30 Aug 2009
If $n (A) = 115$ , $n (B) = 326$ , $n (A - B) = 47$ , then what is $n (A \cup B)$ equal to ?
1. A.373
2. B.165
3. C.370
4. D.394
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Answer: A
Q482009 · 30 Aug 2009
Consider the following function $f : R \to R$ such that $f (x) = x$ if $x \geq 0$ and $f (x) = - x^{2}$ if $x < 0$ . Then which one of the following is correct ?
1. A. $f (x)$ is continuous at every $x \in R$ .
2. B. $f (x)$ is continuous at $x = 0$ only.
3. C. $f (x)$ is discontinuous at $x = 0$ only.
4. D. $f (x)$ is discontinuous at every $x \in R$ .
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Answer: A
Q522009 · 30 Aug 2009
What is the derivative of $lo g_{x} 5$ with respect to $lo g_{5} x$ ?
1. A. $- (lo g_{5} x)^{- 2}$
2. B. $(lo g_{5} x)^{- 2}$
3. C. $- (lo g_{x} 5)^{- 2}$
4. D. $(lo g_{x} 5)^{- 2}$
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Answer: A
Q1152009 · 30 Aug 2009
The velocity of telegraphic communication is given by $v = x^{2} ln (1/ x)$ where $x$ is the displacement. For maximum velocity, $x$ equals to ?
1. A. $e^{1/2}$
2. B. $e^{- 1/2}$
3. C. $(2 e)^{- 1}$
4. D. $2 e^{- 1/2}$
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Answer: B
Q772009 · 19 Apr 2009
The profit function, in rupees, of a firm selling $x$ items ( $x \geq 0$ ) per week is given by $P (x) = - 3500 + (400 - x) x$ . How many items should the firm sell so that the firm has maximum profit?
1. A. $400$
2. B. $300$
3. C. $200$
4. D. $100$
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Answer: C
Q782009 · 19 Apr 2009
A stone thrown vertically upward satisfies the equation $s = 64 t - 16 t^{2}$ , where $s$ is in metre and $t$ is in second. What is the time required to reach the maximum height?
1. A. $1 s$
2. B. $2 s$
3. C. $3 s$
4. D. $4 s$
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Answer: B
Q792009 · 19 Apr 2009
If $f (x) = 3 x^{2} + 6 x - 9$ , then
1. A. $f (x)$ is increasing in $(- 1, 3)$
2. B. $f (x)$ is decreasing in $(3, \infty)$
3. C. $f (x)$ is increasing in $(- \infty, - 1)$
4. D. $f (x)$ is decreasing in $(- \infty, - 1)$
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Answer: A, D
Q802009 · 19 Apr 2009
If $f (x) = sin^{2} x^{2}$ , then what is $f^{'} (x)$ equal to?
1. A. $4 x sin (x^{2}) cos (x^{2})$
2. B. $2 sin (x^{2}) cos (x^{2})$
3. C. $4 sin (x^{2}) sin^{2} x$
4. D. $2 x cos^{2} (x^{2})$
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Answer: A
Q812009 · 19 Apr 2009
If $f (x) = cos x, g (x) = ln x$ and $y = (g \circ f) (x)$ , then what is the value of $\frac{d y}{d x}$ at $x = 0$ ?
1. A. $0$
2. B. $1$
3. C. $- 1$
4. D. $2$
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Answer: A
Q822009 · 19 Apr 2009
If $f (x) = {3 x - 4, 2 x + λ, 0 \leq x \leq 2 2 < x \leq 3$ is continuous at $x = 2$ , then what is the value of $λ$ ?
1. A. $1$
2. B. $- 1$
3. C. $2$
4. D. $- 2$
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Answer: D
Q832009 · 19 Apr 2009
If $x cos θ + y sin θ = 2$ is perpendicular to the line $x - y = 3$ , then what is one of the values of $θ$ ?
1. A. $π /6$
2. B. $π /4$
3. C. $π /2$
4. D. $π /3$
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Answer: B
Q1172009 · 19 Apr 2009
What is the set of all points, where the function $f (x) = \frac{x}{1 + ∣ x ∣}$ is differentiable?
1. A. $(- \infty, \infty)$
2. B. $(0, \infty)$ only
3. C. $(- \infty, 0) \cup (0, \infty)$ only
4. D. $(- \infty, 0)$ only
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Answer: A
Q1182009 · 19 Apr 2009
Let $y (x) = a x^{n}$ and $δ y$ denote small change in $y$ . What is the limit of $\frac{δ y}{δ x}$ as $δ x \to 0$ ?
1. A.0
2. B.1
3. C. $an x^{n - 1}$
4. D. $a x^{n} lo g (a x)$
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Answer: C