Trigonometry · NDA previous year questions

2025 30 questions

1. Q472025 · 13 Apr 2025
   Passage

   Consider the following for the two (02) items that follow: In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3: 1.

   Consider the following statements: I. The triangle is right-angled. II. One of the sides of the triangle is 3 times the other. III. The angles A, C and B of the triangle are in AP. Which of the statements given above is/are correct?

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

   Answer: C

2. Q612025 · 13 Apr 2025

   If a line in 3 dimensions makes angles α, β and γ with the positive directions of the coordinate axes, then what is cos(α+β)cos(α−β) equal to?

   1. A.${\cos }^2\gamma$
   2. B.$-{\cos }^2\gamma$
   3. C.${\sin }^2\gamma$
   4. D.$-{\sin }^2\gamma$
   Show answer

   Answer: B

3. Q812025 · 13 Apr 2025

   Consider the following for the two (02) items that follow: Let the function $y=(1-\cos x{)}^{-1}$ where $x\ne 2n\pi$ and n is an integer What is the range of the function?

   1. A.$[0,\infty )$
   2. B.$[0.5,\infty )$
   3. C.$[1,\infty )$
   4. D.$(-\infty ,0.5]$
   Show answer

   Answer: B

4. Q912025 · 13 Apr 2025

   Consider the following for the two (02) items that follow: Let $y={\sin }^{-1}\left(x-\frac{4x^3}{27}\right)$. What is y equal to?

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

   Answer: D

5. Q922025 · 13 Apr 2025

   Consider the following for the two (02) items that follow: Let $y={\sin }^{-1}\left(x-\frac{4x^3}{27}\right)$. What is $\frac{dy}{dx}$ euqal to ?

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

   Answer: C