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Bihar Board Class 12 (Arts) Relations, Functions & Inverse Trigonometry — practice questions — page 2

Explore 65 free Relations, Functions & Inverse Trigonometry questions in Bihar Board Class 12 (Arts) 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 65.

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 →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 →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 →For a function f: A → B, range is always: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 →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 →For R = {(a,b) : a divides b} on ℕ, R is:Read the answer and worked solution →If |A| = 3 and |B| = 4, then |A × B| equals:Read the answer and worked solution →f(x) = 2x + 3 on ℝ 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 →Principal values worked in the chapterRead the answer and worked solution →Order the steps for finding a principal valueRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →For a binomial distribution B(n, p), the MEAN and VARIANCE are:Read the answer and worked solution →

Worked practice questions

Three of these are wrong. Find the one that holds.

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Questions
  1. Question
    Three of these statements about sin⁻¹ are false.
    Choices
    1. Item
      Its principal range is [−π/2, π/2]
      Correct
      Yes
    2. Explanation
      That is the range of cos⁻¹, not sin⁻¹.
      Item
      Its principal range is [0, π]
    3. Explanation
      That is (sin x)⁻¹. The −1 here means inverse function.
      Item
      It equals 1/sin x
    4. Explanation
      Sine only outputs [−1, 1], so the inverse accepts only that.
      Item
      It is defined for every real x
  2. Question
    Three of these statements about sec⁻¹ are false.
    Choices
    1. Item
      Its principal range is [0, π] − {π/2}
      Correct
      Yes
    2. Explanation
      sec is undefined at π/2, so that point must be removed.
      Item
      Its principal range is [0, π]
    3. Explanation
      That is where sec⁻¹ is NOT defined. Its domain is R − (−1, 1).
      Item
      Its domain is [−1, 1]
    4. Explanation
      cosec⁻¹ removes 0. sec⁻¹ removes π/2.
      Item
      It removes 0 from its range
Each wrong option is a real exam trap: a swapped range, a reciprocal confusion, or an unrestricted domain. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Principal values worked in the chapter

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Questions
  1. Question
    Principal value of sin⁻¹(1/√2)
    Choices
    1. π/3
    2. π/6
    3. π/4
    Correct choice
    π/4
  2. Question
    Principal value of cot⁻¹(−1/√3)
    Choices
    1. 2π/3
    2. −π/3
    3. π/3
    Correct choice
    2π/3
  3. Question
    Why is cot⁻¹(−1/√3) not −π/3?
    Choices
    1. cot(−π/3) is undefined
    2. −π/3 is outside (0, π)
    3. −π/3 is not a real number
    Correct choice
    −π/3 is outside (0, π)
Both values are computed in full in your syllabus Examples 1 and 2: sin⁻¹(1/√2) = π/4 because sin(π/4) = 1/√2 and π/4 lies in [−π/2, π/2] cot⁻¹(−1/√3) = 2π/3 because cot(2π/3) = −1/√3 and 2π/3 lies in (0, π). Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Order the steps for finding a principal value

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Steps
  1. Let y be the inverse value you are asked for
  2. Rewrite it as the direct trigonometric equation
  3. Find an angle that satisfies that equation
  4. Check the angle lies inside the principal value branch
  5. If it does not, shift to the equivalent angle that does
This is the method your syllabus uses in Examples 1 and 2: name the value, convert to the direct function, find the angle then check it lies in the principal branch. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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