Trigonometry · NDA previous year questions

The angle of elevation of the top of a tower from a point $20\mathrm{m}$ away from its base is $45^{\circ }$. What is the height of the tower?

1. A.$10\mathrm{m}$
2. B.$20\mathrm{m}$
3. C.$30\mathrm{m}$
4. D.$40\mathrm{m}$

Let $\theta$ be a positive angle. If the number of degrees in $\theta$ is divided by the number of radians in $\theta$, then an irrational number $180/\pi$ results. If the number of degrees in $\theta$ is multiplied by the number of radians in $\theta$, then an irrational number $125\pi /9$ results. The angle $\theta$ must be equal to

1. A.$30^{\circ }$
2. B.$45^{\circ }$
3. C.$50^{\circ }$
4. D.$60^{\circ }$

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.$\pi /4$

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

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

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

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.$\pi /3$

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

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

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

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.$\pi /6$

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

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

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

In any triangle ABC, a = 18, b = 24 and c = 30. Then what is sin C equal to?

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

If ${\sin }^{-1}\left(\frac{2a}{1+a^2}\right)+{\sin }^{-1}\left(\frac{2b}{1+b^2}\right)=2{\tan }^{-1}x$, then x is equal to

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

A man walks 10 m towards a lamp post and notices that the angle of elevation of the top of the post increases from $30^{\circ }$ to $45^{\circ }$. The height of the lamp post is

1. A.10 m
2. B.$(5\sqrt{3}+5)\text{ m}$
3. C.$(5\sqrt{3}-5)\text{ m}$
4. D.$(10\sqrt{3}+10)\text{ m}$

The angles of a triangle are in AP and the least angle is $30^{\circ }$. What is the greatest angle (in radian)?

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

From the top of a lighthouse 70 m high with its base at sea level, the angle of depression of a boat is $15^{\circ }$. The distance of the boat from the foot of the lighthouse is:

1. A.$70(2-\sqrt{3})\mathrm{m}$
2. B.$70(2+\sqrt{3})\mathrm{m}$
3. C.$70(3-\sqrt{3})\mathrm{m}$
4. D.$70(3+\sqrt{3})\mathrm{m}$

The angle of elevation of a tower at a level ground is $30^{\circ }$. The angle of elevation becomes $\theta$ when moved 10 m towards the tower. If the height of tower is $5\sqrt{3}\mathrm{m}$, then what is $\theta$ equal to?

1. A.$45^{\circ }$
2. B.$60^{\circ }$
3. C.$75^{\circ }$
4. D.None of the above

In a triangle ABC if the angles A, B, C are in AP, then which one of the following is correct?

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

If ${\sin }^{-1}1+{\sin }^{-1}\frac{4}{5}={\sin }^{-1}x$, then what is x equal to?

1. A.3/5
2. B.4/5
3. C.1
4. D.0

If $\mathrm{cosec}\theta -\cot \theta =\frac{1}{\sqrt{3}}$ where $\theta \ne 0$, then what is the value of $\cos \theta$?

1. A.0
2. B.$\frac{\sqrt{3}}{2}$
3. C.$\frac{1}{2}$
4. D.$\frac{1}{\sqrt{2}}$

From the top of a building of height h meter, the angle of depression of an object on the ground is $\theta$. What is the distance (in meter) of the object from the foot of the building?

1. A.$h\cot \theta$
2. B.$h\tan \theta$
3. C.$h\cos \theta$
4. D.$h\sin \theta$

If ${\tan }^{-1}2,{\tan }^{-1}3$ are two angles of a triangle, then what is the third angle?

1. A.${\tan }^{-1}2$
2. B.${\tan }^{-1}4$
3. C.$\pi /4$
4. D.$\pi /3$