Trigonometry · NDA previous year questions

2018 11 questions

1. Q342018 · 9 Sept 2018
   
   1. A.The triangle ABC is isosceles
   2. B.The triangle ABC is equilateral
   3. C.The triangle ABC is scalene
   4. D.No conclusion can be drawn with regard to the nature of the triangle
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   Answer: A

2. Q352018 · 9 Sept 2018

   What is $\frac{2\tan \theta }{1+{\tan }^2\theta }$ equal to?

   1. A.$\cos 2\theta$
   2. B.$\tan 2\theta$
   3. C.$\sin 2\theta$
   4. D.$\mathrm{cosec}2\theta$
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   Answer: C

3. Q382018 · 9 Sept 2018

   A is an angle in the fourth quadrant. It satisfies the trigonometric equation $3(3-{\tan }^{2}A-\cot A{)}^2=1$. Which one of the following is a value of A?

   1. A.$300^{\circ }$
   2. B.$315^{\circ }$
   3. C.$330^{\circ }$
   4. D.$345^{\circ }$
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   Answer: A

4. Q392018 · 9 Sept 2018

   What is/are the solution(s) of the trigonometric equation $\mathrm{cosec}x+\cot x=\sqrt{3}$, where $0<x<2\pi$?

   1. A.$\frac{5\pi }{3}$ only
   2. B.$\frac{\pi }{3}$ only
   3. C.$\pi$ only
   4. D.$\pi ,\frac{\pi }{3},\frac{5\pi }{3}$
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   Answer: B

5. Q402018 · 9 Sept 2018

   If $\theta =\frac{\pi }{8}$, then what is the value of $(2\cos \theta +1{)}^{10}(2\cos 2\theta -1{)}^{10}(2\cos \theta -1{)}^{10}(2\cos 4\theta -1{)}^{10}$?

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

6. Q442018 · 9 Sept 2018

   A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the balloon is $48^{\circ }$. If the height of the balloon above the bridge is 122 m, then what is the length of the bridge?

   1. A.$122\sin 48^{\circ }$ m
   2. B.$122\tan 42^{\circ }$ m
   3. C.$122\cos 48^{\circ }$ m
   4. D.$122\tan 48^{\circ }$ m
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   Answer: B

7. Q452018 · 9 Sept 2018

   The top of a hill observed from the top and bottom of a building of height h is at angles of elevation $\frac{\pi }{6}$ and $\frac{\pi }{3}$ respectively. What is the height of the hill?

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

8. Q922018 · 9 Sept 2018

   In a triangle ABC, if taken in order, consider the following statements: 1. $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}=\vec{0}$ 2. $\overrightarrow{AB}+\overrightarrow{BC}-\overrightarrow{CA}=\vec{0}$ 3. $\overrightarrow{AB}-\overrightarrow{BC}+\overrightarrow{CA}=\vec{0}$ 4. $\overrightarrow{BA}-\overrightarrow{BC}+\overrightarrow{CA}=\vec{0}$ How many of the above statements are correct?

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

9. Q452018 · 22 Apr 2018

   A spherical balloon of radius $r$ subtends an angle $\alpha$ at the eye of an observer, while the angle of elevation of its centre is $\beta$. What is the height of the centre of the balloon (neglecting the height of the observer)?

   1. A.$\frac{r\sin \beta }{\sin \left(\frac{\alpha }{2}\right)}$
   2. B.$\frac{r\sin \beta }{\sin \left(\frac{\alpha }{4}\right)}$
   3. C.$\frac{r\sin \left(\frac{\beta }{2}\right)}{\sin \alpha }$
   4. D.$\frac{r\sin \alpha }{\sin \left(\frac{\beta }{2}\right)}$
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   Answer: A

10. Q462018 · 22 Apr 2018

    In a triangle ABC if $a=2,b=3$ and $\sin A=2/3$, then what is angle B equal to?

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

11. Q472018 · 22 Apr 2018

    What is the distance between the points which divide the line segment joining $(4,3)$ and $(5,7)$ internally and externally in the ratio $2:3$?

    1. A.$\frac{12\sqrt{17}}{5}$
    2. B.$\frac{13\sqrt{17}}{5}$
    3. C.$\frac{\sqrt{17}}{5}$
    4. D.$\frac{6\sqrt{17}}{5}$
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    Answer: A