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JEECUP (UP Polytechnic) Probability & Statistics — practice questions — page 3

Explore 138 free Probability & Statistics questions in JEECUP (UP Polytechnic) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Probability & Statistics questions and exercises with answers

Showing questions 61–90 of 138.

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 →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 →

Worked practice questions

Domain check

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Questions
  1. Question
    Domain of cos⁻¹ x
    Choices
    1. [−1, 1]
    2. R
    3. R − (−1, 1)
    Correct choice
    [−1, 1]
  2. Question
    Domain of sec⁻¹ x
    Choices
    1. [−1, 1]
    2. R − (−1, 1)
    3. R
    Correct choice
    R − (−1, 1)
  3. Question
    Domain of cot⁻¹ x
    Choices
    1. R − (−1, 1)
    2. [−1, 1]
    3. R
    Correct choice
    R
  4. Question
    Domain of cosec⁻¹ x
    Choices
    1. R − (−1, 1)
    2. R
    3. [−1, 1]
    Correct choice
    R − (−1, 1)
  5. Question
    Domain of tan⁻¹ x
    Choices
    1. [−1, 1]
    2. R
    3. R − (−1, 1)
    Correct choice
    R
A value outside the domain has no inverse at all, which is where most sign and range slips begin. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Put the reasoning in order: why an inverse needs a restricted domain

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Steps
  1. An inverse exists only if the function is one-one and onto
  2. Over their natural domains the trigonometric functions are neither
  3. So restrict the domain until the function becomes bijective
  4. On that restricted piece a unique inverse now exists
  5. The agreed choice of piece is called the principal value branch
syllabus builds the chapter in exactly this order: an inverse needs one-one and onto, trigonometric functions are neither over their natural domains so the domain is restricted until they are, and that choice names the principal branch. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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True or false: existence of inverses

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Questions
  1. Statement is true
    Yes
    Statement
    A function has an inverse only when it is one-one and onto.
  2. Statement is true
    No
    Statement
    sin x is one-one over all of R, so sin⁻¹ needs no restriction.
  3. Statement is true
    Yes
    Statement
    Restricting sine to [−π/2, π/2] makes it one-one with range [−1, 1].
  4. Statement is true
    No
    Statement
    sin⁻¹ x means the same thing as (sin x)⁻¹.
  5. Statement is true
    Yes
    Statement
    (sin x)⁻¹ is 1/sin x, which is cosec x.
  6. Statement is true
    No
    Statement
    cos⁻¹ is defined for every real number.
The whole chapter rests on these. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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