Limits, Continuity & Derivatives · NDA previous year questions

2010 30 questions

1. Q842010 · 18 Apr 2010

   The function $f(x)=x\mathrm{cosec}x$ is

   1. A.continuous for all values of x
   2. B.discontinuous everywhere
   3. C.continuous for all x except at $x=n\pi$, where n is an integer
   4. D.continuous for all x except at $x=n\pi /2$, where n is an integer
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   Answer: C

2. Q1002010 · 18 Apr 2010

   What is the value of ${\lim }_{x\to 1}\frac{(x-1{)}^2}{|x-1|}$?

   1. A.0
   2. B.1
   3. C.-1
   4. D.The limit does not exist
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   Answer: A

3. Q1032010 · 18 Apr 2010

   If $f(x)=k{x}^3-9x^2+9x+3$ is monotonically increasing in every interval, then which one of the following is correct?

   1. A.$k<3$
   2. B.$k\le 3$
   3. C.$k>3$
   4. D.$k\ge 3$
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   Answer: D

4. Q1042010 · 18 Apr 2010

   If ${\sin }^{-1}\frac{5}{x}+{\sin }^{-1}\frac{12}{x}=\frac{\pi }{2}$, then what is the value of x?

   1. A.1
   2. B.7
   3. C.13
   4. D.17
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   Answer: C

5. Q1102010 · 18 Apr 2010

   Statement I: $y=-{\tan }^{-1}(x^{-1})+1$ is an increasing function of x. Statement II: $\frac{dy}{dx}$ is positive for all values of x. Which one of the following is correct in respect of the above statements?

   1. A.Both statements I and II are independently correct and statement II is the correct explanation of statement I
   2. B.Both statements I and II are independently correct but statement II is not the correct explanation of statement I
   3. C.Statement I is correct but statement II is false
   4. D.Statement I is false but statement II is correct
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   Answer: A