Limits, Continuity & Derivatives · NDA previous year questions

2018 35 questions

1. Q712018 · 22 Apr 2018

   If $y=e^{x^2}\sin 2x$, then what is $\frac{dy}{dx}$ at $x=\pi$ equal to?

   1. A.$(1+\pi )e^{{\pi }^2}$
   2. B.$2\pi e^{{\pi }^2}$
   3. C.$2e^{{\pi }^2}$
   4. D.$e^{{\pi }^2}$
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   Answer: C

2. Q722018 · 22 Apr 2018

   Consider the following information for the next three (03) items that follow: Three sides of a trapezium are each equal to 6 cm. Let $\alpha \in \left(0,\frac{\pi }{2}\right)$ be the angle between a pair of adjacent sides. If the area of the trapezium is the maximum possible, then what is $\alpha$ equal to?

   1. A.$\frac{\pi }{6}$
   2. B.$\frac{\pi }{4}$
   3. C.$\frac{\pi }{3}$
   4. D.$\frac{2\pi }{5}$
   Show answer

   Answer: C

3. Q732018 · 22 Apr 2018

   Consider the following information for the next three (03) items that follow: Three sides of a trapezium are each equal to 6 cm. Let $\alpha \in \left(0,\frac{\pi }{2}\right)$ be the angle between a pair of adjacent sides. If the area of the trapezium is maximum, what is the length of the fourth side?

   1. A.8 cm
   2. B.9 cm
   3. C.10 cm
   4. D.12 cm
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   Answer: D

4. Q742018 · 22 Apr 2018

   Consider the following information for the next three (03) items that follow: Three sides of a trapezium are each equal to 6 cm. Let $\alpha \in \left(0,\frac{\pi }{2}\right)$ be the angle between a pair of adjacent sides. What is the maximum area of the trapezium?

   1. A.$36\sqrt{3}\mathrm{c}{\mathrm{m}}^2$
   2. B.$30\sqrt{3}\mathrm{c}{\mathrm{m}}^2$
   3. C.$27\sqrt{3}\mathrm{c}{\mathrm{m}}^2$
   4. D.$24\sqrt{3}\mathrm{c}{\mathrm{m}}^2$
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   Answer: C

5. Q752018 · 22 Apr 2018

   What is $\int \frac{dx}{2^x-1}$ equal to?

   1. A.$\ln (2^x-1)+c$
   2. B.$\frac{\ln (1-2^{-x})}{\ln 2}+c$
   3. C.$\frac{\ln (2^{-x}-1)}{2\ln 2}+c$
   4. D.$\frac{\ln (1+2^{-x})}{\ln 2}+c$
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   Answer: B

6. Q762018 · 22 Apr 2018

   What is ${\int }_0^{\pi }{e}^x\sin xdx$ equal to?

   1. A.$\frac{e^{\pi }+1}{2}$
   2. B.$\frac{e^{\pi }-1}{2}$
   3. C.$e^{\pi }+1$
   4. D.$\frac{e^{\pi }+1}{4}$
   Show answer

   Answer: A

7. Q772018 · 22 Apr 2018

   What is ${\int }_1^{e}x\ln xdx$ equal to?

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

8. Q1182018 · 22 Apr 2018

   If $f(x)=|x|+|x-1|$, then which one of the following is correct?

   1. A.$f(x)$ is continuous at $x=0$ and $x=1$
   2. B.$f(x)$ is continuous at $x=0$ but not at $x=1$
   3. C.$f(x)$ is continuous at $x=1$ but not at $x=0$
   4. D.$f(x)$ is neither continuous at $x=0$ nor at $x=1$
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   Answer: A

9. Q1192018 · 22 Apr 2018

   What is the derivative of the function $f(x)=e^{\tan x}+\ln (\sec x)-e^{\ln x}$ at $x=\frac{\pi }{4}$?

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

10. Q1202018 · 22 Apr 2018

    A train covers the first 5 km of its journey at a speed of 30 km/hr and the next 15 km at a speed of 45 km/hr. What is the average speed of the train?

    1. A.35 km/hr
    2. B.37.5 km/hr
    3. C.39.5 km/hr
    4. D.40 km/hr
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    Answer: D