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Indian Navy Pilot Logarithms — practice questions

Explore 50 free Logarithms questions in Indian Navy Pilot 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 50.

Function f: A → B is onto (surjective) if:Read the answer and worked solution →Function f(x) = (x-1)/(x+2) on R - {-2}. f is bijection from R - {-2} to R - {?}:Read the answer and worked solution →For function f(x) = ax + b (a ≠ 0), inverse is: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 →Two dice are rolled. The probability of getting AT LEAST ONE SIX is: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 →

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
Show answer and solution

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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Function f(x) = (x-1)/(x+2) on R - {-2}. f is bijection from R - {-2} to R - {?}:

  1. R
  2. R - {1}
  3. {1}
  4. Random
Show answer and solution

Correct answer: B. R - {1}

As x → ∞, f(x) → 1 (but never equals 1). So 1 not in range. Range = R - {1}. f is bijection from R - {-2} to R - {1}. f⁻¹(y) = (2y+1)/(1-y).

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For function f(x) = ax + b (a ≠ 0), inverse is:

  1. a × x + b
  2. f⁻¹(y) = (y - b)/a
  3. Random
  4. ax - b
Show answer and solution

Correct answer: B. f⁻¹(y) = (y - b)/a

We have y = ax + b → x. So y = (y - b)/a. So f⁻¹(y) = (y - b)/a. Affine function inverse. **Same form:** linear with slope 1/a, intercept -b/a.

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