Limits, Continuity & Derivatives · NDA previous year questions

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2010 30 questions

Q122010 · 22 Aug 2010
What is the maximum number of straight lines that can be drawn with any four points in a plane such that each line contains at least two of these points?
1. A.2
2. B.4
3. C.6
4. D.12
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Answer: C
Q132010 · 22 Aug 2010
If $x + i y = 6 i 420 - 3 i 3 i 3 1 - 1 i$ , then what is $x - i y$ equal to?
1. A. $3 + i$
2. B. $1 + 3 i$
3. C. $3 i$
4. D.0
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Answer: D
Q262010 · 22 Aug 2010
A square is drawn by joining mid-points of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued indefinitely. If the side of the first square is 16 cm, then what is the sum of the areas of all the squares?
1. A.256 sq. cm
2. B.512 sq. cm
3. C.1024 sq. cm
4. D.512/3 sq. cm
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Answer: B
Q672010 · 22 Aug 2010
If the function $f (x) = \frac{x ( x - 2 )}{x ^{2} - 4}$ , $x \neq = \pm 2$ , is continuous at $x = 2$ , then what is $f (2)$ equal to?
1. A.0
2. B.1/2
3. C.1
4. D.2
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Answer: B
Q682010 · 22 Aug 2010
If $x = cos (2 t)$ and $y = sin^{2} t$ , then what is $\frac{d ^{2} y}{d x ^{2}}$ equal to?
1. A.0
2. B. $sin (2 t)$
3. C. $- cos (2 t)$
4. D. $- 1/2$
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Answer: A
Q722010 · 22 Aug 2010
At how many points is the function $f (x) = [x]$ discontinuous?
1. A.1
2. B.2
3. C.3
4. D.Infinite
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Answer: D
Q762010 · 22 Aug 2010
What is the interval over which the function $f (x) = 6 x - x^{2}, x > 0$ is increasing?
1. A. $(0, 3)$
2. B. $(3, 6)$
3. C. $(6, 9)$
4. D.None of the above
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Answer: A
Q812010 · 22 Aug 2010
If $f$ and $g$ are two increasing functions such that $f \circ g$ is defined, then which one of the following is correct?
1. A. $f \circ g$ is always an increasing function
2. B. $f \circ g$ is always a decreasing function
3. C. $f \circ g$ is neither an increasing nor a decreasing function
4. D.None of the above
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Answer: A
Q822010 · 22 Aug 2010
What is the value of $\int_{1}^{2} e^{x} (\frac{1}{x} - \frac{1}{x ^{2}}) d x$ ?
1. A. $e (\frac{e}{2} - 1)$
2. B. $e (e - 1)$
3. C. $e - \frac{1}{e}$
4. D. $0$
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Answer: A
Q872010 · 22 Aug 2010
What is the derivative of $sin^{2} x$ with respect to $cos^{2} x$ ?
1. A. $tan^{2} x$
2. B. $cot^{2} x$
3. C. $- 1$
4. D. $1$
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Answer: C
Q882010 · 22 Aug 2010
Consider the following statements : 1. $f (x) = ∣ x - 3∣$ is continuous at $x = 0$ . 2. $f (x) = ∣ x - 3∣$ is differentiable at $x = 0$ . Which of the statements given 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
Q892010 · 22 Aug 2010
What is $(1111)_{2} + (1001)_{2} - (1010)_{2}$ equal to?
1. A. $(111)_{2}$
2. B. $(1100)_{2}$
3. C. $(1110)_{2}$
4. D. $(1010)_{2}$
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Answer: C
Q902010 · 22 Aug 2010
What is $\frac{s i n θ + 1}{c o s θ}$ equal to?
1. A. $\frac{s i n θ + c o s θ - 1}{s i n θ + c o s θ + 1}$
2. B. $\frac{s i n θ + c o s θ + 1}{s i n θ + c o s θ - 1}$
3. C. $\frac{s i n θ - c o s θ - 1}{s i n θ + c o s θ + 1}$
4. D. $\frac{s i n θ - c o s θ + 1}{s i n θ + c o s θ - 1}$
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Answer: D
Q1172010 · 22 Aug 2010
If $x = k (θ + sin θ)$ and $y = k (1 + cos θ)$ , then what is the derivative of $y$ with respect to $x$ at $θ = π /2$ ?
1. A. $- 1$
2. B. $0$
3. C. $1$
4. D. $2$
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Answer: A
Q1182010 · 22 Aug 2010
What is the value of $1 + i^{2} + i^{4} + i^{6} + \dots + i^{100}$ where $i = - 1$ ?
1. A. $0$
2. B. $1$
3. C. $- 1$
4. D.None of the above
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Answer: B
Q52010 · 18 Apr 2010
Directions : For the next 3 (three) questions to follow : Consider the following lists : Each item under List I is associated with one or more items under List II. $List I (Function) A. sin x B. cos x C. tan x$ $List II (Property) 1. Periodic function 2. Non-periodic function 3. Continuous at every point on (- \infty, \infty) 4. Discontinuous function 5. Differentiable at every point on (- \infty, \infty) 6. Not differentiable at every point on (- \infty, \infty) 7. has period π 8. has period 2 π 9. increases on (0, π /2) 10. decreases on (0, π /2) 11. increases on (π /2, π) 12. decreases on (π /2, π)$ A is associated with
1. A.1, 3, 5, 8, 9, 12
2. B.2, 4, 6, 8, 10, 11
3. C.1, 3, 5, 7, 10, 11
4. D.None of the above
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Answer: A
Q62010 · 18 Apr 2010
1. A.2, 3, 5, 8, 9, 12
2. B.1, 3, 5, 8, 10, 12
3. C.1, 3, 5, 8, 9, 12
4. D.None of the above
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Answer: B
Q72010 · 18 Apr 2010
Directions : For the next 3 (three) questions to follow : Consider the following lists : Each item under List I is associated with one or more items under List II. $List I (Function) A. sin x B. cos x C. tan x$ $List II (Property) 1. Periodic function 2. Non-periodic function 3. Continuous at every point on (- \infty, \infty) 4. Discontinuous function 5. Differentiable at every point on (- \infty, \infty) 6. Not differentiable at every point on (- \infty, \infty) 7. has period π 8. has period 2 π 9. increases on (0, π /2) 10. decreases on (0, π /2) 11. increases on (π /2, π) 12. decreases on (π /2, π)$ C is associated with
1. A.1, 4, 6, 7, 9, 11
2. B.2, 4, 6, 8, 9
3. C.1, 4, 6, 7, 9
4. D.None of the above
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Answer: A
Q82010 · 18 Apr 2010
If p and q are positive integers, then which one of the following equations has $p - q$ as one of its roots?
1. A. $x^{2} - 2 p x - (p^{2} - q) = 0$
2. B. $x^{2} - 2 p x + (p^{2} - q) = 0$
3. C. $x^{2} + 2 p x - (p^{2} - q) = 0$
4. D. $x^{2} + 2 p x + (p^{2} - q) = 0$
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Answer: B
Q92010 · 18 Apr 2010
Given two squares of sides x and y such that $y = x + x^{2}$ . What is the rate of change of area of the second square with respect to the area of the first square?
1. A. $1 + 3 x + 2 x^{2}$
2. B. $1 + 2 x + 3 x^{2}$
3. C. $1 - 2 x + 3 x^{2}$
4. D. $1 - 2 x - 3 x^{2}$
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Answer: A
Q432010 · 18 Apr 2010
What is the maximum point on the curve $x = e^{x} y$ ?
1. A. $(1, e)$
2. B. $(1, e^{- 1})$
3. C. $(e, 1)$
4. D. $(e^{- 1}, 1)$
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Answer: B
Q502010 · 18 Apr 2010
What is the derivative of $x a^{2} - x^{2} + a^{2} sin^{- 1} (\frac{x}{a})$ ?
1. A. $a^{2} - x^{2}$
2. B. $2 a^{2} - x^{2}$
3. C. $x^{2} - a^{2}$
4. D. $2 x^{2} - a^{2}$
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Answer: B
Q512010 · 18 Apr 2010
If $(- 5, 4)$ divides the line segment between the coordinate axes in the ratio $1 : 2$ , then what is its equation?
1. A. $8 x + 5 y + 20 = 0$
2. B. $5 x + 8 y - 7 = 0$
3. C. $8 x - 5 y + 60 = 0$
4. D. $5 x - 8 y + 57 = 0$
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Answer: C
Q522010 · 18 Apr 2010
What is the value of $cos 1 5^{\circ} cos 4 5^{\circ} sin 1 5^{\circ} sin 4 5^{\circ} \times cos 4 5^{\circ} sin 4 5^{\circ} cos 1 5^{\circ} sin 1 5^{\circ}$ ?
1. A. $\frac{1}{4}$
2. B. $\frac{3}{2}$
3. C. $- \frac{1}{4}$
4. D. $- \frac{3}{4}$
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Answer: C
Q532010 · 18 Apr 2010
Out of 32 persons, 30 invest in National Savings Certificates and 17 invest in shares. What is the number of persons who invest in both?
1. A.13
2. B.15
3. C.17
4. D.19
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Answer: B