Trigonometry · NDA previous year questions

2020 12 questions

1. Q292020 · 6 Sept 2020

   Consider the following statements: 1. If ABC is a right-angled triangle, right-angled at A and if $\sin B=\frac{1}{3}$, then $\mathrm{cosec}C=3$. 2. If $b\cos B=c\cos C$ and if the triangle ABC is not right-angled, then ABC must be isosceles. 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
   Show answer

   Answer: B

2. Q302020 · 6 Sept 2020

   Consider the following statements: 1. If in a triangle ABC, $A=2B$ and $b=c$, then it must be an obtuse-angled triangle. 2. There exists no triangle ABC with $A=40^{\circ }$, $B=65^{\circ }$ and $\frac{a}{c}=\sin 40^{\circ }\mathrm{cosec}15^{\circ }$. 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
   Show answer

   Answer: B

3. Q312020 · 6 Sept 2020

   Directions for the following three (03) items: Read the following information and answer the three items that follow: Let $a{\sin }^{2}x+b{\cos }^{2}x=c$; $b{\sin }^{2}y+a{\cos }^{2}y=d$ and $p\tan x=q\tan y$. What is ${\tan }^{2}x$ equal to?

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

   Answer: A

4. Q322020 · 6 Sept 2020

   Directions for the following three (03) items: Read the following information and answer the three items that follow: Let $a{\sin }^{2}x+b{\cos }^{2}x=c$; $b{\sin }^{2}y+a{\cos }^{2}y=d$ and $p\tan x=q\tan y$. What is ${\tan }^{2}x$ equal to? What is $\frac{d-a}{b-d}$ equal to?

   1. A.${\sin }^{2}y$
   2. B.${\cos }^{2}y$
   3. C.${\tan }^{2}y$
   4. D.${\cot }^{2}y$
   Show answer

   Answer: C

5. Q332020 · 6 Sept 2020

   Directions for the following three (03) items: Read the following information and answer the three items that follow: Let $a{\sin }^{2}x+b{\cos }^{2}x=c$; $b{\sin }^{2}y+a{\cos }^{2}y=d$ and $p\tan x=q\tan y$. What is ${\tan }^{2}x$ equal to? What is $\frac{p^2}{q^2}$ equal to?

   1. A.$\frac{(b-c)(b-d)}{(a-d)(a-c)}$
   2. B.$\frac{(a-d)(c-a)}{(b-c)(d-b)}$
   3. C.$\frac{(d-a)(c-a)}{(b-c)(d-b)}$
   4. D.$\frac{(b-c)(b-d)}{(c-a)(a-d)}$
   Show answer

   Answer: B

6. Q342020 · 6 Sept 2020

   Directions for the following three (03) items: Read the following information and answer the three items that follow: Let $t_n={\sin }^n\theta +{\cos }^n\theta$. What is $\frac{t_3-t_5}{t_5-t_7}$ equal to?

   1. A.$\frac{t_1}{t_3}$
   2. B.$\frac{t_3}{t_5}$
   3. C.$\frac{t_5}{t_7}$
   4. D.$\frac{t_1}{t_7}$
   Show answer

   Answer: A

7. Q352020 · 6 Sept 2020

   Directions for the following three (03) items: Read the following information and answer the three items that follow: Let $t_n={\sin }^n\theta +{\cos }^n\theta$. What is $t_1^2-t_2$ equal to?

   1. A.$\cos 2\theta$
   2. B.$\sin 2\theta$
   3. C.$2\cos \theta$
   4. D.$2\sin \theta$
   Show answer

   Answer: B

8. Q362020 · 6 Sept 2020

   Directions for the following three (03) items: Read the following information and answer the three items that follow: Let $t_n={\sin }^n\theta +{\cos }^n\theta$. What is the value of $t_{10}$ where $\theta =45^{\circ }$ ?

   1. A.1
   2. B.$\frac{1}{4}$
   3. C.$\frac{1}{16}$
   4. D.$\frac{1}{32}$
   Show answer

   Answer: C

9. Q372020 · 6 Sept 2020

   Directions for the following three (03) items: Read the following information and answer the three items that follow: Let $\alpha =\beta =15^{\circ }$. What is the value of $\sin \alpha +\cos \beta$ ?

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

   Answer: D

10. Q382020 · 6 Sept 2020

    Directions for the following three (03) items: Read the following information and answer the three items that follow: Let $\alpha =\beta =15^{\circ }$. What is the value of $\sin 7\alpha -\cos 7\beta$ ?

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

    Answer: D

11. Q392020 · 6 Sept 2020

    Directions for the following three (03) items: Read the following information and answer the three items that follow: Let $\alpha =\beta =15^{\circ }$. What is the value of $\sin \alpha +\cos \beta$ ? What is $\sin (\alpha +1^{\circ })+\cos (\beta +1^{\circ })$ equal to?

    1. A.$\sqrt{3}\cos 1^{\circ }+\sin 1^{\circ }$
    2. B.$\sqrt{3}\cos 1^{\circ }-\frac{1}{2}\sin 1^{\circ }$
    3. C.$\frac{1}{\sqrt{2}}(\sqrt{3}\cos 1^{\circ }-\sin 1^{\circ })$
    4. D.$\frac{1}{2}(\sqrt{3}\cos 1^{\circ }+\sin 1^{\circ })$
    Show answer

    Answer: Dropped in the final answer key (full marks to everyone)

12. Q402020 · 6 Sept 2020

    If $\sin x+\sin y=\cos y-\cos x$, where $0<y<x<\frac{\pi }{2}$, then what is $\tan \left(\frac{x-y}{2}\right)$ equal to?

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

    Answer: C