Trigonometry · NDA previous year questions

2009 32 questions

1. Q642009 · 19 Apr 2009

   If ${\sin }^{2}x+{\sin }^{2}y=1$, then what is the value of $\cot (x+y)$?

   1. A.$1$
   2. B.$\sqrt{3}$
   3. C.$0$
   4. D.$1/\sqrt{3}$
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   Answer: C

2. Q652009 · 19 Apr 2009

   What is the value of $\cos 10^{\circ }+\cos 110^{\circ }+\cos 130^{\circ }$?

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

3. Q662009 · 19 Apr 2009

   If $\frac{dy}{dx}=1+x+y+xy$ and $y(-1)=0$, then what is $y(x)$ equal to?

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

4. Q672009 · 19 Apr 2009

   What is the value of ${\int }_0^{\pi /2}\ln (\tan x)dx$?

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

5. Q682009 · 19 Apr 2009

   What is $\int {\tan }^{2}x{\sec }^{4}xdx$ equal to?

   1. A.$\frac{{\sec }^{5}x}{5}+\frac{{\sec }^{3}x}{3}+c$
   2. B.$\frac{{\tan }^{5}x}{5}+\frac{{\tan }^{3}x}{3}+c$
   3. C.$\frac{{\tan }^{5}x}{5}+\frac{{\sec }^{3}x}{3}+c$
   4. D.$\frac{{\sec }^{5}x}{5}+\frac{{\tan }^{3}x}{3}+c$
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   Answer: B

6. Q692009 · 19 Apr 2009

   What is ${\lim }_{x\to 0}\frac{{\sin }^{2}ax}{bx}$ ($a,b$ are constants) equal to?

   1. A.$0$
   2. B.$a/b$
   3. C.$a^2/b$
   4. D.Does not exist
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   Answer: A

7. Q702009 · 19 Apr 2009

   If $f(x)=\tan x+e^{-2x}-7x^3$, then what is the value of $f^{\prime }(0)$?

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