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JEE Main Relations, Functions & Inverse Trigonometry — practice questions — page 2

Explore 84 free Relations, Functions & Inverse Trigonometry questions in JEE Main 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 31–60 of 84.

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 →If P(A) = 0.5, P(B) = 0.6, and P(A ∩ B) = 0.2, then P(A ∪ B) is:Read the answer and worked solution →$\tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) = $Read the answer and worked solution →Match each identity to the condition it needsRead the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?Read the answer and worked solution →$\sin^{-1}\left(\sin\tfrac{2\pi}{3}\right)$ equalsRead the answer and worked solution →$\cot^{-1}\left(-\tfrac{1}{\sqrt{3}}\right) = $Read the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two dice are rolled. The probability of getting AT LEAST ONE SIX is:Read the answer and worked solution →Match each mathematician to the year your syllabus givesRead the answer and worked solution →The number of ways to choose 3 books out of 5 (order does NOT matter) is:Read the answer and worked solution →Sort each inverse function into its domainRead the answer and worked solution →Complete the summary tableRead the answer and worked solution →Bayes' theorem is essentially used to:Read the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →For a discrete random variable X with values 0, 1, 2 and probabilities 0.3, 0.5, 0.2 respectively, the mean E(X) is:Read the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead 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 →Two are true, one is notRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →

Worked practice questions

True or false: principal values

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Questions
  1. Statement is true
    Yes
    Statement
    A principal value must lie inside the principal value branch.
  2. Statement is true
    Yes
    Statement
    sin⁻¹(1/√2) = π/4.
  3. Statement is true
    Yes
    Statement
    cot⁻¹(−1/√3) = 2π/3.
  4. Statement is true
    No
    Statement
    If no branch is stated, you may pick any branch you like.
  5. Statement is true
    Yes
    Statement
    When no branch is mentioned, the principal branch is meant.
Tests the one habit that decides these questions, which is checking the branch. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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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
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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