Trigonometry · NDA previous year questions

2014 12 questions

1. Q312014 · 28 Sept 2014

   In a triangle ABC, $\sin A-\cos B=\cos C$, then what is B equal to ?

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

2. Q322014 · 28 Sept 2014

   If $\frac{\sin (x+y)}{\sin (x-y)}=\frac{a+b}{a-b}$, then what is $\frac{\tan x}{\tan y}$ equal to?

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

3. Q332014 · 28 Sept 2014

   If $\sin A\sin (60^{\circ }-A)\sin (60^{\circ }+A)=k\sin 3A$, then what is k equal to?

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

4. Q342014 · 28 Sept 2014

   The line $y=\sqrt{3}$ meets the graph $y=\tan x$, where $x\in \left(0,\frac{\pi }{2}\right)$, in k points. What is k equal to?

   1. A.One
   2. B.Two
   3. C.Three
   4. D.Infinity
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   Answer: A

5. Q352014 · 28 Sept 2014

   Which one of the following is one of the solutions of the equation $\tan 2\theta \cdot \tan \theta =1$?

   1. A.$\pi /12$
   2. B.$\pi /6$
   3. C.$\pi /4$
   4. D.$\pi /3$
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   Answer: B

6. Q362014 · 28 Sept 2014

   For the next three (03) items that follow : Given that $16{\sin }^{5}x=p\sin 5x+q\sin 3x+r\sin x$. What is the value of p?

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

7. Q372014 · 28 Sept 2014

   For the next three (03) items that follow : Given that $16{\sin }^{5}x=p\sin 5x+q\sin 3x+r\sin x$. What is the value of q?

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

8. Q382014 · 28 Sept 2014

   For the next three (03) items that follow : Given that $16{\sin }^{5}x=p\sin 5x+q\sin 3x+r\sin x$. What is the value of r?

   1. A.5
   2. B.8
   3. C.10
   4. D.-10
   Show answer

   Answer: C

9. Q392014 · 28 Sept 2014

   What is ${\sin }^{-1}\frac{3}{5}+{\sin }^{-1}\frac{4}{5}$ equal to ?

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

   Answer: A

10. Q412014 · 28 Sept 2014

    In a triangle ABC, $c=2$, $A=45^{\circ }$, $a=2\sqrt{2}$, then what is C equal to ?

    1. A.$30^{\circ }$
    2. B.$15^{\circ }$
    3. C.$45^{\circ }$
    4. D.None of the above
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    Answer: A

11. Q442014 · 20 Apr 2014

    Consider the following statements: 1. There exists no triangle ABC for which $\sin A+\sin B=\sin C$. 2. If the angles of a triangle are in the ratio $1:2:3$, then its sides will be in the ratio $1:\sqrt{3}:2$. Which of the above statements is/are correct?

    1. A.1 only
    2. B.2 only
    3. C.Both 1 and 2
    4. D.Neither 1 nor 2
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    Answer: C

12. Q452014 · 20 Apr 2014

    Consider the following points: 1. $(0,5)$ 2. $(2,-1)$ 3. $(3,-4)$ Which of the above lie on the line $3x+y=5$ and at a distance $\sqrt{10}$ from $(1,2)$?

    1. A.1 only
    2. B.2 only
    3. C.1 and 2 only
    4. D.1, 2 and 3
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    Answer: C