Trigonometry · NDA previous year questions

2017 7 questions

1. Q332017 · 10 Sept 2017

   $\sqrt{1+\sin A}=-\left(\sin \frac{A}{2}+\cos \frac{A}{2}\right)$ is true if

   1. A.$\frac{3\pi }{2}<A<\frac{5\pi }{2}$ only
   2. B.$\frac{\pi }{2}<A<\frac{3\pi }{2}$ only
   3. C.$\frac{3\pi }{2}<A<\frac{7\pi }{2}$
   4. D.$0<A<\frac{3\pi }{2}$
   Show answer

   Answer: C

2. Q342017 · 10 Sept 2017

   In triangle $ABC$, if $\frac{{\sin }^{2}A+{\sin }^{2}B+{\sin }^{2}C}{{\cos }^{2}A+{\cos }^{2}B+{\cos }^{2}C}=2$ then the triangle is

   1. A.right-angled
   2. B.equilateral
   3. C.isosceles
   4. D.obtuse-angled
   Show answer

   Answer: A

3. Q382017 · 10 Sept 2017

   The angle of elevation of a stationary cloud from a point $25\text{ m}$ above a lake is $15^{\circ }$ and the angle of depression of its image in the lake is $45^{\circ }$. The height of the cloud above the lake level is

   1. A.$25\text{ m}$
   2. B.$25\sqrt{3}\text{ m}$
   3. C.$50\text{ m}$
   4. D.$50\sqrt{3}\text{ m}$
   Show answer

   Answer: B

4. Q392017 · 10 Sept 2017

   The angles of elevation of the top of a tower from the top and foot of a pole are respectively $30^{\circ }$ and $45^{\circ }$. If $h_T$ is the height of the tower and $h_P$ is the height of the pole, then which of the following are correct? 1. $\frac{2h_P{h}_T}{3+\sqrt{3}}=h_P^2$ 2. $\frac{h_T-h_P}{\sqrt{3}+1}=\frac{h_P}{2}$ 3. $\frac{2(h_P+h_T)}{h_P}=4+\sqrt{3}$ Select the correct answer using the code given below.

   1. A.1 and 3 only
   2. B.2 and 3 only
   3. C.1 and 2 only
   4. D.1, 2 and 3
   Show answer

   Answer: C

5. Q402017 · 10 Sept 2017

   In a triangle $ABC$, $a-2b+c=0$. The value of $\cot \left(\frac{A}{2}\right)\cot \left(\frac{C}{2}\right)$ is

   1. A.$\frac{9}{2}$
   2. B.3
   3. C.$\frac{3}{2}$
   4. D.1
   Show answer

   Answer: B

6. Q492017 · 23 Apr 2017

   From the top of a lighthouse, 100 m high, the angle of depression of a boat is ${\tan }^{-1}\left(\frac{5}{12}\right)$. What is the distance between the boat and the lighthouse?

   1. A.120 m
   2. B.180 m
   3. C.240 m
   4. D.360 m
   Show answer

   Answer: C

7. Q502017 · 23 Apr 2017

   If a vertex of a triangle is $(1,1)$ and the midpoints of two sides of the triangle through this vertex are $(-1,2)$ and $(3,2)$, then the centroid of the triangle is

   1. A.$\left(-\frac{1}{3},\frac{7}{3}\right)$
   2. B.$\left(-1,\frac{7}{3}\right)$
   3. C.$\left(\frac{1}{3},\frac{7}{3}\right)$
   4. D.$\left(1,\frac{7}{3}\right)$
   Show answer

   Answer: D