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Indian Navy Pilot Calculus — practice questions

Explore 30 free Calculus questions in Indian Navy Pilot Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Calculus questions and exercises with answers

Showing questions 1–30 of 30.

$\displaystyle\int \dfrac{1}{\sqrt{1 - x^2}}\,dx$ equals:Read the answer and worked solution →sin(2θ) equals:Read the answer and worked solution →In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:Read the answer and worked solution →Match the trig identity to its resultRead the answer and worked solution →Sort each inverse function into its domainRead the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Put the reasoning in order: why an inverse needs a restricted domainRead the answer and worked solution →True or false: existence of inversesRead the answer and worked solution →True or false: reading the tableRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Complete the summary tableRead the answer and worked solution →Complete the rule about restricting a domainRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Principal values worked in the chapterRead the answer and worked solution →Order the steps for finding a principal valueRead the answer and worked solution →True or false: principal valuesRead the answer and worked solution →Match each identity to the condition it needsRead the answer and worked solution →Assertion and reason: identitiesRead the answer and worked solution →Match each mathematician to the year your syllabus givesRead the answer and worked solution →Trace how trigonometry travelledRead the answer and worked solution →True or false: the historical noteRead the answer and worked solution →

Worked practice questions

$\displaystyle\int \dfrac{1}{\sqrt{1 - x^2}}\,dx$ equals:

  1. $\log|1 - x^2| + C$
  2. $\sin^{-1} x + C$
  3. $\tan^{-1} x + C$
  4. $\cos^{-1} x + C$
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Correct answer: B. $\sin^{-1} x + C$

$\int \dfrac{1}{\sqrt{a^2 - x^2}}\,dx = \sin^{-1}(x/a) + C$, which with $a = 1$ gives $\sin^{-1} x + C$. The integral of the negative integrand would give $\cos^{-1} x + C$, since $\dfrac{d}{dx}\sin^{-1} x = +\dfrac{1}{\sqrt{1-x^2}}$ and $\dfrac{d}{dx}\cos^{-1} x = -\dfrac{1}{\sqrt{1-x^2}}$.

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sin(2θ) equals:

  1. 2 sin θ cos θ
  2. sin²θ - cos²θ
  3. sin θ + cos θ
  4. 2 sin θ
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Correct answer: A. 2 sin θ cos θ

**Double-angle formula:** sin(2θ) = 2 sinθ cosθ. (Derived from sin(θ + θ).)

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In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:

  1. a/sinA = b/sinB = c/sinC
  2. a + b + c = 0
  3. sinA = sinB
  4. a²+b² = c²
Show answer and solution

Correct answer: A. a/sinA = b/sinB = c/sinC

**Sine rule:** a/sinA = b/sinB = c/sinC = 2R (where R is circumradius). Useful for solving triangles when you know any side + opposite angle + one more piece.

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SequencesBinomial TheoremSequences and SeriesGeometryProbability & StatisticsVectors & 3D GeometryPermutations and CombinationsLinear Programming