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MP Board Class 12 (MPBSE) Permutations and Combinations — practice questions — page 2

Explore 60 free Permutations and Combinations questions in MP Board Class 12 (MPBSE) 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 60.

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 →Tap every quantity that is a probabilityRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: the multiplication ruleRead the answer and worked solution →True or false: the Historical NoteRead the answer and worked solution →Sort each statement by which idea it describesRead the answer and worked solution →

Worked practice questions

Assertion and reason: identities

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Questions
  1. Reason
    It holds only where x lies in [−π/2, π/2], the principal branch.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    sin⁻¹ (sin x) = x cannot be claimed for every real x.
  2. Reason
    [−1, 1] is exactly the domain of sin⁻¹.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    sin (sin⁻¹ x) = x holds for every x in [−1, 1].
  3. Reason
    An inverse function swaps the roles of input and output.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    If y = sin⁻¹ x then x = sin y.
Each pair turns on whether the stated interval is the right one. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Match each mathematician to the year your syllabus gives

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Matching pairs
  1. Left
    Aryabhata
    Right
    476 A.D.
  2. Left
    Brahmagupta
    Right
    598 A.D.
  3. Left
    Bhaskara I
    Right
    600 A.D.
  4. Left
    Bhaskara II
    Right
    1114 A.D.
From the Historical Note closing the chapter. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Trace how trigonometry travelled

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Steps
  1. The study of trigonometry begins in India
  2. Indian results pass to Arabia
  3. From Arabia the knowledge reaches Europe
  4. The Indian approach is adopted worldwide
syllabus records that the study of trigonometry began in India, passed to Arabia, and reached Europe from there. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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