Quadratic Equations · NDA previous year questions

2015 12 questions

1. Q112015 · 27 Sept 2015

   The number of real roots of the equation $x^2-3|x|+2=0$ is

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

2. Q122015 · 27 Sept 2015

   If the sum of the roots of the equation $a{x}^2+bx+c=0$ is equal to the sum of their squares, then

   1. A.$a^2+b^2=c^2$
   2. B.$a^2+b^2=a+b$
   3. C.$ab+b^2=2ac$
   4. D.$ab-b^2=2ac$
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   Answer: C

3. Q132015 · 27 Sept 2015

   If the roots of the equation $x^2-nx+m=0$ differ by 1, then

   1. A.$n^2-4m-1=0$
   2. B.$n^2+4m-1=0$
   3. C.$m^2+4n+1=0$
   4. D.$m^2-4n-1=0$
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   Answer: A

4. Q152015 · 19 Apr 2015

   If $m$ and $n$ are the roots of the equation $(x+p)(x+q)-k=0$, then the roots of the equation $$(x-m)(x-n)+k=0$$ are

   1. A.$p\text{ and }q$
   2. B.$1/p\text{ and }1/q$
   3. C.$-p\text{ and }-q$
   4. D.$p+q\text{ and }p-q$
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   Answer: C

5. Q272015 · 19 Apr 2015

   For the next two (2) items that follow : Let $\alpha$ be the root of the equation $25{\cos }^2\theta +5\cos \theta -12=0$, where $\frac{\pi }{2}<\alpha <\pi$. What is $\tan \alpha$ equal to?

   1. A.$-3/4$
   2. B.3/4
   3. C.$-4/3$
   4. D.$-4/5$
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   Answer: A

6. Q282015 · 19 Apr 2015

   For the next two (2) items that follow: Let $\alpha$ be the root of the equation $25{\cos }^2\theta +5\cos \theta -12=0$, where $\frac{\pi }{2}<\alpha <\pi$. What is $\sin 2\alpha$ equal to?

   1. A.24/25
   2. B.$-24/25$
   3. C.$-5/12$
   4. D.$-21/25$
   Show answer

   Answer: B

7. Q292015 · 19 Apr 2015

   $(1-\sin A+\cos A{)}^2$ is equal to

   1. A.$2(1-\cos A)(1+\sin A)$
   2. B.$2(1-\sin A)(1+\cos A)$
   3. C.$2(1-\cos A)(1-\sin A)$
   4. D.None of the above
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   Answer: B

8. Q302015 · 19 Apr 2015

   What is $$\frac{\cos \theta }{1-\tan \theta }+\frac{\sin \theta }{1-\cot \theta }$$ equal to?

   1. A.$\sin \theta -\cos \theta$
   2. B.$\sin \theta +\cos \theta$
   3. C.$2\sin \theta$
   4. D.$2\cos \theta$
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   Answer: B

9. Q312015 · 19 Apr 2015

   The equation ${\tan }^{-1}(1+x)+{\tan }^{-1}(1-x)=\frac{\pi }{2}$ is satisfied by

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

10. Q322015 · 19 Apr 2015

    For the next three (3) items that follow: Consider $x=4{\tan }^{-1}\left(\frac{1}{5}\right),y={\tan }^{-1}\left(\frac{1}{70}\right)\text{ and }z={\tan }^{-1}\left(\frac{1}{99}\right)$. What is $x$ equal to?

    1. A.${\tan }^{-1}\left(\frac{60}{119}\right)$
    2. B.${\tan }^{-1}\left(\frac{120}{119}\right)$
    3. C.${\tan }^{-1}\left(\frac{90}{169}\right)$
    4. D.${\tan }^{-1}\left(\frac{170}{169}\right)$
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    Answer: B

11. Q332015 · 19 Apr 2015

    For the next three (3) items that follow: Consider $x=4{\tan }^{-1}\left(\frac{1}{5}\right),y={\tan }^{-1}\left(\frac{1}{70}\right)\text{ and }z={\tan }^{-1}\left(\frac{1}{99}\right)$. What is $x-y$ equal to?

    1. A.${\tan }^{-1}\left(\frac{828}{845}\right)$
    2. B.${\tan }^{-1}\left(\frac{8287}{8450}\right)$
    3. C.${\tan }^{-1}\left(\frac{8281}{8450}\right)$
    4. D.${\tan }^{-1}\left(\frac{8287}{8471}\right)$
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    Answer: C

12. Q342015 · 19 Apr 2015

    For the next three (3) items that follow: Consider $x=4{\tan }^{-1}\left(\frac{1}{5}\right),y={\tan }^{-1}\left(\frac{1}{70}\right)\text{ and }z={\tan }^{-1}\left(\frac{1}{99}\right)$. What is $x-y+z$ equal to?

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

    Answer: D