Sets, Relations & Functions · NDA previous year questions

2009 33 questions

1. Q482009 · 19 Apr 2009

   For which acute angle $\theta$ is ${\mathrm{cosec}}^2\theta =3\sqrt{3}\cot \theta -5$?

   1. A.$5\pi /12$
   2. B.$\pi /3$
   3. C.$\pi /6$
   4. D.$\pi /4$
   Show answer

   Answer: C

2. Q492009 · 19 Apr 2009

   If ${\tan }^2\theta =2{\tan }^2\phi +1$, then which one of the following is correct?

   1. A.$\cos (2\theta )=\cos (2\phi )-1$
   2. B.$\cos (2\theta )=\cos (2\phi )+1$
   3. C.$\cos (2\theta )=[\cos (2\phi )-1]/2$
   4. D.$\cos (2\theta )=[\cos (2\phi )+1]/2$
   Show answer

   Answer: C

3. Q722009 · 19 Apr 2009

   The function $f(x)=x^2-2x$ increases for all

   1. A.$x>-1$
   2. B.$x<-1\text{ only}$
   3. C.$x>1\text{ only}$
   4. D.$x<1$
   Show answer

   Answer: C

4. Q732009 · 19 Apr 2009

   What is ${\int }_0^{1}x(1-x{)}^{n}dx$ equal to?

   1. A.$\frac{1}{n(n+1)}$
   2. B.$\frac{1}{(n+1)(n+2)}$
   3. C.$1$
   4. D.$0$
   Show answer

   Answer: B

5. Q742009 · 19 Apr 2009

   Let $a$ and $b$ be two distinct roots of a polynomial equation $f(x)=0$. Then there exists at least one root lying between $a$ and $b$ of the polynomial equation

   1. A.$f(x)=0$
   2. B.$f^{\prime }(x)=0$
   3. C.$f^{\prime \prime }(x)=0$
   4. D.None of the above
   Show answer

   Answer: B

6. Q752009 · 19 Apr 2009

   If $3^x+3^y=3^{x+y}$, then what is $\frac{dy}{dx}$ equal to?

   1. A.$\frac{3^{x+y}-3^x}{3^y}$
   2. B.$\frac{3^{x-y}(3^y-1)}{1-3^x}$
   3. C.$\frac{3^x+3^y}{3^x-3^y}$
   4. D.$\frac{3^x+3^y}{1+3^{x+y}}$
   Show answer

   Answer: B

7. Q762009 · 19 Apr 2009

   What is $\int \sec x^{\circ }dx$ equal to?

   1. A.$\ln (\sec x^{\circ }+\tan x^{\circ })+c$
   2. B.$\frac{\pi \ln \tan \left(\frac{\pi }{4}+\frac{x}{2}\right)}{180}+c$
   3. C.$\frac{180}{\pi }\ln \tan \left(\frac{\pi }{4}+\frac{x}{2}\right)+c$
   4. D.$\frac{180}{\pi }\ln \tan \left(\frac{\pi }{4}+\frac{\pi x}{360}\right)+c$
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   Answer: D

8. Q1162009 · 19 Apr 2009

   Let $f:R\to R$ be a function defined as $f(x)=x|x|$ for each $x\in R$, $R$ being the set of real numbers. Which one of the following is correct?

   1. A.$f$ is one-one but not onto
   2. B.$f$ is onto but not one-one
   3. C.$f$ is both one-one and onto
   4. D.$f$ is neither one-one nor onto
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   Answer: C