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Bihar Board Class 12 (Commerce) Vectors & 3D Geometry — practice questions — page 2

Explore 64 free Vectors & 3D Geometry questions in Bihar Board Class 12 (Commerce) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Vectors & 3D Geometry questions and exercises with answers

Showing questions 31–60 of 64.

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 →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead the answer and worked solution →Which theorem answers which question?Read the answer and worked solution →True or false: total probability and BayesRead the answer and worked solution →Match each historical figure to their contributionRead the answer and worked solution →The Historical NoteRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →Order the reasoning: from a partition to a posteriorRead the answer and worked solution →Tap every quantity that is a probabilityRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: the multiplication ruleRead the answer and worked solution →True or false: the Historical NoteRead 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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More Mathematics topics

Three Dimensional GeometryApplication of DerivativesMatricesLinear ProgrammingRelations and FunctionsContinuity and DifferentiabilityDifferential EquationsDeterminants