Limits, Continuity & Derivatives · NDA previous year questions

2009 20 questions

1. Q772009 · 19 Apr 2009

   The profit function, in rupees, of a firm selling $x$ items ($x\ge 0$) 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

2. Q782009 · 19 Apr 2009

   A stone thrown vertically upward satisfies the equation $s=64t-16t^2$, where $s$ is in metre and $t$ is in second. What is the time required to reach the maximum height?

   1. A.$1\text{ s}$
   2. B.$2\text{ s}$
   3. C.$3\text{ s}$
   4. D.$4\text{ s}$
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   Answer: B

3. Q792009 · 19 Apr 2009

   If $f(x)=3x^2+6x-9$, 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

4. Q802009 · 19 Apr 2009

   If $f(x)={\sin }^2{x}^2$, then what is $f^{\prime }(x)$ equal to?

   1. A.$4x\sin (x^2)\cos (x^2)$
   2. B.$2\sin (x^2)\cos (x^2)$
   3. C.$4\sin (x^2){\sin }^{2}x$
   4. D.$2x{\cos }^2(x^2)$
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   Answer: A

5. 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 $\frac{dy}{dx}$ at $x=0$?

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

6. Q822009 · 19 Apr 2009

   If $f(x)=\{\begin{array}{ll}3x-4,& 0\le x\le 2\\ 2x+\lambda ,& 2<x\le 3\end{array}$ is continuous at $x=2$, then what is the value of $\lambda$?

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

7. Q832009 · 19 Apr 2009

   If $x\cos \theta +y\sin \theta =2$ is perpendicular to the line $x-y=3$, then what is one of the values of $\theta$?

   1. A.$\pi /6$
   2. B.$\pi /4$
   3. C.$\pi /2$
   4. D.$\pi /3$
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   Answer: B

8. 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

9. Q1182009 · 19 Apr 2009

   Let $y(x)=a{x}^n$ and $\delta y$ denote small change in $y$. What is the limit of $\frac{\delta y}{\delta x}$ as $\delta x\to 0$?

   1. A.0
   2. B.1
   3. C.$an{x}^{n-1}$
   4. D.$a{x}^n\log (ax)$
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   Answer: C