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BITSAT Permutations and Combinations — practice questions — page 2

Explore 100 free Permutations and Combinations questions in BITSAT Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Permutations and Combinations questions and exercises with answers

Showing questions 31–60 of 100.

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 →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 →

Worked practice questions

Match each inverse function to its domain

Read exercise and reference answers
Matching pairs
  1. Left
    sin⁻¹ x
    Right
    [−1, 1]
  2. Left
    cos⁻¹ x
    Right
    [−1, 1]
  3. Left
    cosec⁻¹ x
    Right
    R − (−1, 1)
  4. Left
    sec⁻¹ x
    Right
    R − (−1, 1)
  5. Left
    tan⁻¹ x
    Right
    R
  6. Left
    cot⁻¹ x
    Right
    R
Domains split three ways: [−1, 1] for sin⁻¹ and cos⁻¹, R − (−1, 1) for cosec⁻¹ and sec⁻¹, and all of R for tan⁻¹ and cot⁻¹. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Match each inverse function to its principal value branch

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Matching pairs
  1. Left
    sin⁻¹ x
    Right
    [−π/2, π/2]
  2. Left
    cos⁻¹ x
    Right
    [0, π]
  3. Left
    cosec⁻¹ x
    Right
    [−π/2, π/2] − {0}
  4. Left
    sec⁻¹ x
    Right
    [0, π] − {π/2}
  5. Left
    tan⁻¹ x
    Right
    (−π/2, π/2)
  6. Left
    cot⁻¹ x
    Right
    (0, π)
The principal branch is the one interval on which the function is made one-one so the inverse is single valued. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Flip and pair: function with its principal range

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Matching pairs
  1. A
    sin⁻¹ x
    B
    [−π/2, π/2]
  2. A
    cos⁻¹ x
    B
    [0, π]
  3. A
    cosec⁻¹ x
    B
    [−π/2, π/2] − {0}
  4. A
    sec⁻¹ x
    B
    [0, π] − {π/2}
  5. A
    tan⁻¹ x
    B
    (−π/2, π/2)
  6. A
    cot⁻¹ x
    B
    (0, π)
Learning the six ranges as pairs is the fastest route through most exam questions on this chapter. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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