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Indian Navy SSR Application of Integrals — practice questions

Explore 43 free Application of Integrals questions in Indian Navy SSR 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 1–30 of 43.

If $\sin\theta + \cos\theta = 1$, then $\sin\theta \cdot \cos\theta$ equals:Read the answer and worked solution →$\cos 3\theta$ equals:Read the answer and worked solution →The angle 90° in radians is:Read the answer and worked solution →Complete the arc length relationRead the answer and worked solution →Match each identity to its nameRead the answer and worked solution →The Pythagorean identitiesRead the answer and worked solution →Odd function or even function?Read the answer and worked solution →Complete the degree and radian conversionRead the answer and worked solution →True or false: identities and parityRead the answer and worked solution →Match each sum or difference formula to its resultRead the answer and worked solution →Signs in the expansionRead the answer and worked solution →Which formula does this belong to?Read the answer and worked solution →True or false: periodicityRead the answer and worked solution →Complete the complementary angle rulesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Order the steps: convert degrees to radiansRead the answer and worked solution →Flip and pair: identity with its valueRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Tap every correct identityRead the answer and worked solution →Radians and degreesRead the answer and worked solution →True or false: reading the identitiesRead the answer and worked solution →Complete the relationship between the two calculiRead the answer and worked solution →True or false: the constant of integrationRead the answer and worked solution →Differentiation or integration?Read the answer and worked solution →Tap every property of indefinite integrals the chapter givesRead the answer and worked solution →Properties in useRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →

Worked practice questions

If $\sin\theta + \cos\theta = 1$, then $\sin\theta \cdot \cos\theta$ equals:

  1. $\dfrac{1}{2}$
  2. $1$
  3. $0$
  4. $-1$
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Correct answer: C. $0$

Square both sides of $\sin\theta + \cos\theta = 1$: $(\sin\theta + \cos\theta)^2 = 1^2$ $\sin^2\theta + 2\sin\theta\cos\theta + \cos^2\theta = 1$ Using $\sin^2 + \cos^2 = 1$: $1 + 2\sin\theta\cos\theta = 1$ $\sin\theta \cos\theta = 0$. Verify: the original equation holds only when $\theta = 0°$ (so $\sin = 0$, $\cos = 1$) or $\theta = 90°$ (so $\sin = 1$, $\cos = 0$). In both cases the product is 0. ✓

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$\cos 3\theta$ equals:

  1. $3\sin\theta - 4\sin^3\theta$
  2. $3\cos\theta - 4\cos^3\theta$
  3. $4\sin^3\theta - 3\sin\theta$
  4. $4\cos^3\theta - 3\cos\theta$
Show answer and solution

Correct answer: D. $4\cos^3\theta - 3\cos\theta$

Triple-angle for cosine: $\cos 3\theta = 4\cos^3\theta - 3\cos\theta$. Derivation: $\cos 3\theta = \cos(2\theta + \theta) = \cos 2\theta \cos\theta - \sin 2\theta \sin\theta = (2\cos^2\theta - 1)\cos\theta - 2\sin\theta\cos\theta \cdot \sin\theta = 2\cos^3\theta - \cos\theta - 2\sin^2\theta\cos\theta = 2\cos^3\theta - \cos\theta - 2(1-\cos^2\theta)\cos\theta = 4\cos^3\theta - 3\cos\theta$. Companion: $\sin 3\theta = 3\sin\theta - 4\sin^3\theta$ (option C — common trap). Mnemonic: in both, the coefficients are 3 and 4, and the cubed term has the same trig function as the angle outside.

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The angle 90° in radians is:

  1. $\pi$ (full half-circle)
  2. $2\pi$ (full circle)
  3. $\pi/2$ (quarter circle)
  4. $\pi/4$ (one eighth)
Show answer and solution

Correct answer: C. $\pi/2$ (quarter circle)

180° = π radians. So 90° = π/2 radians. Quarter of a full circle (2π).

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