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Indian Navy Pilot Relations and Functions — practice questions — page 2

Explore 37 free Relations and Functions questions in Indian Navy Pilot Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Relations and Functions questions and exercises with answers

Showing questions 31–37 of 37.

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 →Roster form or set-builder form?Read the answer and worked solution →True or false: sets and relationsRead the answer and worked solution →

Worked practice questions

Match each identity to the condition it needs

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Matching pairs
  1. Left
    sin (sin⁻¹ x) = x
    Right
    holds for x in [−1, 1]
  2. Left
    sin⁻¹ (sin x) = x
    Right
    holds for x in [−π/2, π/2]
  3. Left
    y = sin⁻¹ x
    Right
    means x = sin y
  4. Left
    (sin x)⁻¹
    Right
    means 1/sin x, i.e. cosec x
Your syllabus states both identities together with the interval each one holds on quoting one without its condition is the usual slip. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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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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