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Indian Navy AA (Artificer Apprentice) Logarithms — practice questions

Explore 47 free Logarithms 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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Logarithms questions and exercises with answers

Showing questions 1–30 of 47.

$\sin^2\theta + \cos^2\theta$ equals:Read the answer and worked solution →Equivalence classes of 'congruent mod 3' on Z:Read the answer and worked solution →The midpoint of the segment joining $(2,3)$ and $(4,7)$ is: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. $1$
Show answer and solution

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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Equivalence classes of 'congruent mod 3' on Z:

  1. 1 class
  2. Random
  3. Infinite
  4. 3 classes: [0], [1], [2]
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Correct answer: D. 3 classes: [0], [1], [2]

3 classes: {..., -6, -3, 0, 3, 6, ...} = [0] [1] = ..., -5, -2, 1, 4, 7, ... [2] = ..., -4, -1, 2, 5, 8, ... Union = Z. Disjoint. 3 cosets of subgroup 3Z.

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The midpoint of the segment joining $(2,3)$ and $(4,7)$ is:

  1. (6, 10)
  2. (1, 2)
  3. (2, 4)
  4. (3, 5)
Show answer and solution

Correct answer: D. (3, 5)

((2+4)/2, (3+7)/2) = (3,5).

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