Trigonometry · NDA previous year questions

The angle of elevation of the tip of a flag staff from a point 10 m due South of its base is $60^{\circ }$. What is the height of the flag staff correct to the nearest meter?

1. A.15 m
2. B.16 m
3. C.17 m
4. D.18 m

What is $\frac{\sin \theta }{\mathrm{cosec}\theta }+\frac{\cos \theta }{\sec \theta }$ equal to?

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

If $\tan \theta +\sec \theta =4$, then what is the value of $\sin \theta$?

1. A.8/17
2. B.8/15
3. C.15/17
4. D.23/32

What is the value of $\cos \left\{{\cos }^{-1}\frac{4}{5}+{\cos }^{-1}\frac{12}{13}\right\}$?

1. A.63/65
2. B.33/65
3. C.22/65
4. D.11/65

What is the angle subtended by 1 m pole at a distance 1 km on the ground in sexagesimal measure?

1. A.$\frac{9}{50\pi }$ degree
2. B.$\frac{9}{5\pi }$ degree
3. C.3.4 minute
4. D.3.5 minute

If $\cot A\cdot \cot B=2$, then what is the value of $\cos (A+B)\cdot \sec (A-B)$?

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

Consider the following statements : 1. $1^{\circ }$ in radian measure is less than 0.02 radians. 2. 1 radian in degree measure is greater than $45^{\circ }$. 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

What is the value of $(1+i{)}^5+(1-i{)}^5$ where $i=\sqrt{-1}$?

1. A.$-8$
2. B.$8$
3. C.$8i$
4. D.$-8i$

What is the value of $\tan 9^{\circ }-\tan 27^{\circ }-\tan 63^{\circ }+\tan 81^{\circ }$?

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

If $x=y\cos \left(\frac{2\pi }{3}\right)=z\cos \left(\frac{4\pi }{3}\right)$, then what is $xy+yz+zx$ equal to?

1. A.$-1$
2. B.0
3. C.1
4. D.2

If $\sin A+\sin B+\sin C=3$ then what is $\cos A+\cos B+\cos C$ equal to?

1. A.$-1$
2. B.0
3. C.1
4. D.3

At a point 15 m away from the base of a 15 m high house, the angle of elevation of the top is

1. A.$90^{\circ }$
2. B.$60^{\circ }$
3. C.$45^{\circ }$
4. D.$30^{\circ }$

The simultaneous equations $3x+5y=7$ and $6x+10y=18$ have

1. A.no solution
2. B.infinitely many solutions
3. C.unique solution
4. D.any finite number of solutions

What is the principal value of ${\sec }^{-1}\left(\frac{2}{\sqrt{3}}\right)$?

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

In any triangle ABC, the sides are 6 cm, 10 cm and 14 cm. Then the triangle is obtuse angled with the obtuse angle equal to

1. A.$150^{\circ }$
2. B.$135^{\circ }$
3. C.$120^{\circ }$
4. D.$105^{\circ }$

In a triangle ABC, if $A={\tan }^{-1}2$ and $B={\tan }^{-1}3$, then $C$ is equal to

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

A tower of height 15 m stands vertically on the ground. From a point on the ground the angle of elevation of the top of the tower is found to be $30^{\circ }$. What is the distance of the point from the foot of the tower ?

1. A.$15\sqrt{3}$ m
2. B.$10\sqrt{3}$ m
3. C.$5\sqrt{3}$ m
4. D.30 m

If $\tan A-\tan B=x$ and $\cot B-\cot A=y$, then what is $\cot (A-B)$ equal to ?

1. A.$\frac{1}{y}-\frac{1}{x}$
2. B.$\frac{1}{x}-\frac{1}{y}$
3. C.$\frac{1}{x}+\frac{1}{y}$
4. D.$-\frac{1}{x}-\frac{1}{y}$

In a triangle ABC, a = 8, b = 10 and c = 12. What is angle C equal to?

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

If $\sin \theta =x+\frac{a}{x}$ for all $x\in R-\{0\}$, then which one of the following is correct?

1. A.$a\ge 4$
2. B.$a\ge \frac{1}{2}$
3. C.$a\le \frac{1}{4}$
4. D.$a\le \frac{1}{2}$

The equation ${\tan }^{4}x-2{\sec }^{2}x+a^2=0$ will have at least one real solution if

1. A.$|a|\le 4$
2. B.$|a|\le 2$
3. C.$|a|\le \sqrt{3}$
4. D.None of the above

The sides a, b, c of a triangle ABC are in arithmetic progression and 'a' is the smallest side. What is cos A equal to?

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

If ${\int }_1^2\{k^2+(4-4k)x+4x^3\}dx\le 12$, then which one of the following is correct?

1. A.$k=3$
2. B.$0\le k<3$
3. C.$k\le 4$
4. D.$k=0$

A man standing on the bank of a river observes that the angle of elevation of the top of a tree just on the opposite bank is $60^{\circ }$. The angle of elevation is $30^{\circ }$ from a point at a distance $y$ metres from the bank. What is the height of the tree?

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

One of the angles of a triangle is $1/2$ radian and the other is $99^{\circ }$. What is the third angle in radian measure?

1. A.$\frac{9\pi -10}{\pi }$
2. B.$\frac{90\pi -100}{7\pi }$
3. C.$\frac{90\pi -10}{\pi }$
4. D.None of the above