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COMEDK Sequences and Series — practice questions — page 3

Explore 115 free Sequences and Series questions in COMEDK Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sequences and Series questions and exercises with answers

Showing questions 61–90 of 115.

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 →Complete the definition of conditional probabilityRead the answer and worked solution →True or false: conditional probabilityRead the answer and worked solution →Independent or mutually exclusive?Read the answer and worked solution →Match each rule to its nameRead the answer and worked solution →IndependenceRead the answer and worked solution →Order the steps for a Bayes' theorem questionRead the answer and worked solution →Complete the conditions for a partitionRead the answer and worked solution →True or false: independence versus exclusivityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Tap every statement that follows from independenceRead the answer and worked solution →The multiplication ruleRead 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 →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead the answer and worked solution →Which theorem answers which question?Read the answer and worked solution →True or false: total probability and BayesRead the answer and worked solution →Match each historical figure to their contributionRead the answer and worked solution →The Historical NoteRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →Order the reasoning: from a partition to a posteriorRead the answer and worked solution →

Worked practice questions

Three of these are wrong. Find the one that holds.

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Questions
  1. Question
    Three of these statements about sin⁻¹ are false.
    Choices
    1. Item
      Its principal range is [−π/2, π/2]
      Correct
      Yes
    2. Explanation
      That is the range of cos⁻¹, not sin⁻¹.
      Item
      Its principal range is [0, π]
    3. Explanation
      That is (sin x)⁻¹. The −1 here means inverse function.
      Item
      It equals 1/sin x
    4. Explanation
      Sine only outputs [−1, 1], so the inverse accepts only that.
      Item
      It is defined for every real x
  2. Question
    Three of these statements about sec⁻¹ are false.
    Choices
    1. Item
      Its principal range is [0, π] − {π/2}
      Correct
      Yes
    2. Explanation
      sec is undefined at π/2, so that point must be removed.
      Item
      Its principal range is [0, π]
    3. Explanation
      That is where sec⁻¹ is NOT defined. Its domain is R − (−1, 1).
      Item
      Its domain is [−1, 1]
    4. Explanation
      cosec⁻¹ removes 0. sec⁻¹ removes π/2.
      Item
      It removes 0 from its range
Each wrong option is a real exam trap: a swapped range, a reciprocal confusion, or an unrestricted domain. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Principal values worked in the chapter

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Questions
  1. Question
    Principal value of sin⁻¹(1/√2)
    Choices
    1. π/3
    2. π/6
    3. π/4
    Correct choice
    π/4
  2. Question
    Principal value of cot⁻¹(−1/√3)
    Choices
    1. 2π/3
    2. −π/3
    3. π/3
    Correct choice
    2π/3
  3. Question
    Why is cot⁻¹(−1/√3) not −π/3?
    Choices
    1. cot(−π/3) is undefined
    2. −π/3 is outside (0, π)
    3. −π/3 is not a real number
    Correct choice
    −π/3 is outside (0, π)
Both values are computed in full in your syllabus Examples 1 and 2: sin⁻¹(1/√2) = π/4 because sin(π/4) = 1/√2 and π/4 lies in [−π/2, π/2] cot⁻¹(−1/√3) = 2π/3 because cot(2π/3) = −1/√3 and 2π/3 lies in (0, π). Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Order the steps for finding a principal value

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Steps
  1. Let y be the inverse value you are asked for
  2. Rewrite it as the direct trigonometric equation
  3. Find an angle that satisfies that equation
  4. Check the angle lies inside the principal value branch
  5. If it does not, shift to the equivalent angle that does
This is the method your syllabus uses in Examples 1 and 2: name the value, convert to the direct function, find the angle then check it lies in the principal branch. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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