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Indian Navy SSR Logarithms — practice questions

Explore 68 free Logarithms questions in Indian Navy SSR 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 68.

Function f: A → B is onto (surjective) if:Read the answer and worked solution →Inverse of function f exists if and only if f is:Read the answer and worked solution →Range of f(x) = sin(x) from R to R:Read the answer and worked solution →The distance between the points $(1,2)$ and $(1,5)$ is:Read the answer and worked solution →Find the midpoint of A(2, −3) and B(8, 5).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 →

Worked practice questions

Function f: A → B is onto (surjective) if:

  1. Every b ∈ B is image of some a ∈ A
  2. Random
  3. Empty
  4. Always
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Correct answer: A. Every b ∈ B is image of some a ∈ A

**Surjection (onto):** range = codomain. Every element of B has at least one preimage. Bijection = injective + surjective.

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Inverse of function f exists if and only if f is:

  1. Even
  2. Continuous
  3. Bijective (one-one AND onto)
  4. Linear
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Correct answer: C. Bijective (one-one AND onto)

f⁻¹ exists iff f is bijection. We have (f⁻¹ ∘ f)(x) = x. So (f⁻¹ ∘ f)(x) = (f ∘ f⁻¹)(y). e.g., f(x) = x³ is bijective; f⁻¹(y) = y^(1/3). f(x) = x² is not.

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Range of f(x) = sin(x) from R to R:

  1. R
  2. Random
  3. [0, 1]
  4. [-1, 1] (sine bounded)
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Correct answer: D. [-1, 1] (sine bounded)

sin x ∈ [-1, 1] for all real x. f is many-one (periodic), so not bijection from R to R. Restricting domain to [-π/2, π/2] makes it bijection [-π/2, π/2] → [-1, 1], inverse = arcsin.

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