Limits, Continuity & Derivatives · NDA previous year questions

2012 21 questions

1. Q652012 · 19 Aug 2012

   Which one of the following is correct in respect of the function $f(x)=\frac{x^2}{|x|}$ for $x\ne 0$ and $f(0)=0$?

   1. A.f(x) is discontinuous every where
   2. B.f(x) is continuous every where
   3. C.f(x) is continuous at x = 0 only
   4. D.f(x) is discontinuous at x = 0 only
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   Answer: B

2. Q662012 · 19 Aug 2012

   What is ${\lim }_{x\to 2}\frac{x-2}{x^2-4}$ equal to?

   1. A.0
   2. B.1/4
   3. C.1/2
   4. D.1
   Show answer

   Answer: B

3. Q672012 · 19 Aug 2012

   The radius of a circle is uniformly increasing at the rate of 3 cm/s. What is the rate of increase in area, when the radius is 10 cm?

   1. A.$6\pi \mathrm{c}{\mathrm{m}}^2/s$
   2. B.$10\pi \mathrm{c}{\mathrm{m}}^2/s$
   3. C.$30\pi \mathrm{c}{\mathrm{m}}^2/s$
   4. D.$60\pi \mathrm{c}{\mathrm{m}}^2/s$
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   Answer: D

4. Q702012 · 19 Aug 2012

   If $f(x)=2^{\sin x}$, then what is the derivative of f(x)?

   1. A.$2^{\sin x}\ln 2$
   2. B.$(\sin x)2^{\sin x-1}$
   3. C.$(\cos x)2^{\sin x-1}$
   4. D.None of the above
   Show answer

   Answer: D

5. Q712012 · 19 Aug 2012

   The function $f(x)=x^3-3x^2+6$ is an increasing function for:

   1. A.$0<x<2$
   2. B.$x<2$
   3. C.$x>2\text{ or }x<0$
   4. D.all x
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   Answer: C

6. Q752012 · 19 Aug 2012

   What is the minimum value of $|x|$?

   1. A.$-1$
   2. B.0
   3. C.1
   4. D.2
   Show answer

   Answer: B

7. Q412012 · 15 Apr 2012

   What is the maximum value of $\sin 3\theta \cos 2\theta +\cos 3\theta \sin 2\theta$?

   1. A.1
   2. B.2
   3. C.4
   4. D.10
   Show answer

   Answer: A

8. Q422012 · 15 Apr 2012

   What is $\sin A\cos A\tan A+\cos A\sin A\cot A$ equal to?

   1. A.$\sin A$
   2. B.$\cos A$
   3. C.$\tan A$
   4. D.1
   Show answer

   Answer: D

9. Q432012 · 15 Apr 2012

   What is the value of ${\sec }^2{\tan }^{-1}\left(\frac{5}{11}\right)$?

   1. A.121/96
   2. B.217/921
   3. C.146/121
   4. D.267/121
   Show answer

   Answer: C

10. Q442012 · 15 Apr 2012

    Which one of the following is positive in the third quadrant?

    1. A.$\sin \theta$
    2. B.$\cos \theta$
    3. C.$\tan \theta$
    4. D.$\sec \theta$
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    Answer: C

11. Q452012 · 15 Apr 2012

    What is the value of $\sin (1920^{\circ })$?

    1. A.1/2
    2. B.$\frac{1}{\sqrt{2}}$
    3. C.$\frac{\sqrt{3}}{2}$
    4. D.1/3
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    Answer: C

12. Q682012 · 15 Apr 2012

    Which one of the following functions is differentiable for all real values of x?

    1. A.$\frac{x}{|x|}$
    2. B.$x|x|$
    3. C.$\frac{1}{|x|}$
    4. D.$\frac{1}{x}$
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    Answer: B

13. Q722012 · 15 Apr 2012

    What is the slope of the tangent to the curve $x=t^2+3t-8$, $y=2t^2-2t-5$ at $t=2$?

    1. A.7/6
    2. B.6/7
    3. C.1
    4. D.5/6
    Show answer

    Answer: B

14. Q732012 · 15 Apr 2012

    Which one of the following statements is correct?

    1. A.$e^x$ is an increasing function
    2. B.$e^x$ is a decreasing function
    3. C.$e^x$ is neither increasing nor decreasing function
    4. D.$e^x$ is a constant function
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    Answer: A

15. Q742012 · 15 Apr 2012

    If $y=\cos t$ and $x=\sin t$, then what is $\frac{dy}{dx}$ equal to?

    1. A.$xy$
    2. B.$x/y$
    3. C.$-y/x$
    4. D.$-x/y$
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    Answer: D

16. Q822012 · 15 Apr 2012

    Which one of the following statements is correct ?

    1. A.The derivative of a function f(x) at a point will exist if there is one tangent to the curve y = f(x) at that point and the tangent is parallel to y-axis
    2. B.The derivative of a function f(x) at a point will exist if there is one tangent to the curve y = f(x) at that point and the tangent must be parallel to x-axis
    3. C.The derivative of a function f(x) at a point will exist if there is one and only one tangent to the curve y = f(x) at that point and the tangent is not parallel to y-axis
    4. D.None of the above
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    Answer: C

17. Q852012 · 15 Apr 2012

    What is ${\lim }_{x\to 0}{x}^2\sin \left(\frac{1}{x}\right)$ equal to ?

    1. A.0
    2. B.1
    3. C.1/2
    4. D.Limit does not exist
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    Answer: A

18. Q862012 · 15 Apr 2012

    What is ${\lim }_{x\to -2}\left(\frac{x+2}{x^3+8}\right)$ equal to ?

    1. A.1/4
    2. B.-1/4
    3. C.1/12
    4. D.-1/12
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    Answer: C

19. Q902012 · 15 Apr 2012

    What is the rate of change of $\sqrt{x^2+16}$ with respect to $x^2$ at $x=3$ ?

    1. A.1/5
    2. B.1/10
    3. C.1/20
    4. D.None of the above
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    Answer: B

20. Q932012 · 15 Apr 2012

    Consider the following in respect of the function $f(x)=|x-3|$ : 1. f(x) is continuous at x = 3 2. f(x) is differentiable 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: C

21. Q1082012 · 15 Apr 2012

    What is the maximum value of ${\sin }^{2}x$?

    1. A.-1
    2. B.0
    3. C.1
    4. D.Infinity
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    Answer: C