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Indian Navy AA (Artificer Apprentice) Sequences and Series Gp — practice questions

Explore 29 free Sequences and Series Gp questions in Indian Navy AA (Artificer Apprentice) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sequences and Series Gp questions and exercises with answers

Showing questions 1–29 of 29.

$\sin^2\theta + \cos^2\theta$ equals:Read the answer and worked solution →One radian is approximately equal to:Read the answer and worked solution →A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?Read 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

$\sin^2\theta + \cos^2\theta$ equals:

  1. $2$
  2. $0$
  3. $\tan\theta$
  4. $1$
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Correct answer: D. $1$

The **Pythagorean identity** $\sin^2\theta + \cos^2\theta = 1$ holds for every real $\theta$. It comes from Pythagoras applied to the unit circle: any point on it has coordinates $(\cos\theta, \sin\theta)$ with distance 1 from origin so the sum of squared coordinates is 1. Companion identities: - Dividing by $\cos^2\theta$: $1 + \tan^2\theta = \sec^2\theta$. - Dividing by $\sin^2\theta$: $\cot^2\theta + 1 = \csc^2\theta$.

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One radian is approximately equal to:

  1. $90^\circ$
  2. $60^\circ$
  3. $45^\circ$
  4. $57.3^\circ$
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Correct answer: D. $57.3^\circ$

1 radian = 180/π ≈ 57.3°.

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A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?

  1. $1/52$
  2. $2/52$
  3. $1/13$
  4. $1/26$
Show answer and solution

Correct answer: C. $1/13$

P(king | red) = P(red king) / P(red) = (2/52) / (26/52) = 2/26 = 1/13. Conditional probability reduces the sample space.

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Vectors & 3D GeometryBinomial TheoremSequencesSequences and SeriesProbability & StatisticsGeometryPermutations and CombinationsLinear Programming