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NDA Application of Integrals — practice questions

Explore 14 free Application of Integrals questions in NDA Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Application of Integrals questions and exercises with answers

Showing questions 1–14 of 14.

1 radian is approximately equal to:Read the answer and worked solution →The value of sin 30° is:Read the answer and worked solution →cos²θ + sin²θ is equal to:Read the answer and worked solution →tan(π/4) is equal to:Read the answer and worked solution →sin(A + B) is equal to:Read the answer and worked solution →cos(2θ) can be written as:Read the answer and worked solution →The principal value of the range of f(x) = sin x is:Read the answer and worked solution →The angle in radians for 120° is:Read the answer and worked solution →If sin θ = 3/5 and θ is acute, then cos θ equals:Read the answer and worked solution →The general solution of sin x = 0 is:Read the answer and worked solution →The general solution of cos x = 0 is:Read the answer and worked solution →By the law of sines in a triangle, a / sin A is equal to:Read the answer and worked solution →sin 75° equals:Read the answer and worked solution →tan(45° + θ) · tan(45° − θ) is equal to:Read the answer and worked solution →

Worked practice questions

1 radian is approximately equal to:

  1. 90°
  2. 60°
  3. 57.3°
  4. 45°
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Correct answer: C. 57.3°

1. π rad = 180°. 2. 1 rad = 180°/π ≈ 180/3.14159 ≈ 57.296°. 3. Hence 1 radian ≈ 57.3°. _Source: syllabus Maths Ch 3 "Trigonometric Functions", §3.2 Angles_

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The value of sin 30° is:

  1. 0
  2. √2 / 2
  3. 1/2
  4. 1
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Correct answer: C. 1/2

1. From the standard 30-60-90 right triangle, sin 30° = opposite/hypotenuse = 1/2. 2. cos 30° = √3/2; tan 30° = 1/√3. 3. Useful to memorize the basic angle values: 0°, 30°, 45°, 60°, 90°. _Source: syllabus Maths Ch 3 §3.3 Trigonometric Functions of Specific Angles_

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cos²θ + sin²θ is equal to:

  1. 0
  2. tan²θ
  3. 2
  4. 1
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Correct answer: D. 1

1. The fundamental Pythagorean identity: cos²θ + sin²θ = 1 for all θ. 2. Two consequences: 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ. 3. Holds for any real angle, in radians or degrees. _Source: syllabus Maths Ch 3 §3.3 Pythagorean Identity_

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