Limits, Continuity & Derivatives · NDA previous year questions

2021 33 questions

1. Q782021 · 18 Apr 2021

   If the function $f(x)=\{\begin{array}{ll}5,& x=1\\ b-ax,& x>1\end{array}$ is continuous, then what is the value of $(a+b)$?

   1. A.5
   2. B.10
   3. C.15
   4. D.20
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   Answer: A

2. Q972021 · 18 Apr 2021

   The curve $y=-x^3+3x^2+2x-27$ has the maximum slope at:

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

3. Q982021 · 18 Apr 2021

   A 24 cm long wire is bent to form a triangle with one of the angles as 60°. What is the altitude of the triangle having the greatest possible area?

   1. A.4√3 cm.
   2. B.2√3 cm.
   3. C.6 cm.
   4. D.3 cm.
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   Answer: A

4. Q992021 · 18 Apr 2021

   If $f(x)=e^{|x|}$, then which one of the following is correct?

   1. A.$f^{\prime }(0)=1$.
   2. B.$f^{\prime }(0)=-1$.
   3. C.$f^{\prime }(0)=0$.
   4. D.$f^{\prime }(0)$ does not exist.
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   Answer: D

5. Q1022021 · 18 Apr 2021

   If x + y = 20 and P = xy, then what is the maximum value of P?

   1. A.100
   2. B.96
   3. C.84
   4. D.50
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   Answer: A

6. Q1032021 · 18 Apr 2021

   What is the derivative of sin(ln x) + cos(ln x) with respect to x at x = e?

   1. A.$\frac{\cos 1-\sin 1}{e}$
   2. B.$\frac{\sin 1-\cos 1}{e}$
   3. C.$\frac{\cos 1+\sin 1}{e}$
   4. D.1
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   Answer: A

7. Q1042021 · 18 Apr 2021

   If $x=e^t\cos t$ and $y=e^t\sin t$, then what is $\frac{\mathrm{d}x}{\mathrm{d}y}$ at $t=0$ equal to?

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

8. Q1052021 · 18 Apr 2021

   What is the maximum value of sin 2x ⋅ cos 2x?

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