Start learning →

MP DTE Permutations and Combinations — practice questions — page 3

Explore 121 free Permutations and Combinations questions in MP DTE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Permutations and Combinations with Quill →

Permutations and Combinations questions and exercises with answers

Showing questions 61–90 of 121.

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 →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 →

Worked practice questions

True or false: reading the table

Read exercise and reference answers
Questions
  1. Statement is true
    Yes
    Statement
    The principal range of cos⁻¹ is [0, π].
  2. Statement is true
    No
    Statement
    The principal range of tan⁻¹ is a closed interval.
  3. Statement is true
    Yes
    Statement
    cot⁻¹ has domain R and principal range (0, π).
  4. Statement is true
    Yes
    Statement
    sec⁻¹ has π/2 removed from its principal range.
  5. Statement is true
    No
    Statement
    cosec⁻¹ has π/2 removed from its principal range.
  6. Statement is true
    Yes
    Statement
    cosec⁻¹ and sec⁻¹ share the domain R − (−1, 1).
Each statement is a row of the summary table, stated straight or bent. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

Open this exercise →

Spot the one that does not belong

Read exercise and reference answers
Questions
  1. Items
    1. sin⁻¹ x
    2. cos⁻¹ x
    3. tan⁻¹ x
    Odd item
    tan⁻¹ x
  2. Items
    1. sec⁻¹ x
    2. tan⁻¹ x
    3. cot⁻¹ x
    Odd item
    sec⁻¹ x
  3. Items
    1. [−π/2, π/2]
    2. [0, π]
    3. (−π/2, π/2)
    Odd item
    [0, π]
  4. Items
    1. cosec⁻¹ x
    2. sec⁻¹ x
    3. cos⁻¹ x
    Odd item
    cos⁻¹ x
  5. Items
    1. (0, π)
    2. [−1, 1]
    3. R − (−1, 1)
    Odd item
    (0, π)
Each group is built on a single row or column of the summary table. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

Open this exercise →

Two are true, one is not

Read exercise and reference answers
Questions
  1. False statement
    tan⁻¹ has domain [−1, 1]
    Statements
    1. tan⁻¹ has domain [−1, 1]
    2. sin⁻¹ has domain [−1, 1]
    3. cos⁻¹ has principal range [0, π]
  2. False statement
    sec⁻¹ removes 0 from its range
    Statements
    1. cot⁻¹ has principal range (0, π)
    2. sec⁻¹ removes 0 from its range
    3. cosec⁻¹ has domain R − (−1, 1)
  3. False statement
    Every trigonometric function is one-one on its natural domain
    Statements
    1. The principal value of an inverse lies in its principal branch
    2. sin (sin⁻¹ x) = x for x in [−1, 1]
    3. Every trigonometric function is one-one on its natural domain
The false statement in each round is a range or domain swapped for a neighbouring one. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

Open this exercise →

How to practise

  1. Choose a Permutations and Combinations question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Mathematics topics

SequencesProbability & StatisticsBinomial TheoremSequences and SeriesGeometryLinear ProgrammingLimits and ContinuityCorrelation and Regression