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GMAT Relations, Functions & Inverse Trigonometry — practice questions — page 3

Explore 68 free Relations, Functions & Inverse Trigonometry questions in GMAT Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Relations, Functions & Inverse Trigonometry questions and exercises with answers

Showing questions 61–68 of 68.

In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:Read the answer and worked solution →Assertion and reason: identitiesRead the answer and worked solution →Trace how trigonometry travelledRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →True or false: principal valuesRead the answer and worked solution →True or false: the historical noteRead the answer and worked solution →Complete the rule about restricting a domainRead the answer and worked solution →

Worked practice questions

In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:

  1. $1/2$
  2. $60/1024$
  3. $210/1024$
  4. $120/1024$
Show answer and solution

Correct answer: C. $210/1024$

P(X=6) = C(10,6) × (0.5)⁶ × (0.5)⁴ = 210 × (1/2)¹⁰ = 210/1024 ≈ 0.205. C(10,6) = 210.

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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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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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