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Indian Navy 10+2 B.Tech Cadet Sequences — practice questions — page 2

Explore 79 free Sequences questions in Indian Navy 10+2 B.Tech Cadet Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sequences questions and exercises with answers

Showing questions 31–60 of 79.

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 →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 →

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
  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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Binomial TheoremGeometryProbability & StatisticsSequences and SeriesVectors & 3D GeometryPermutations and CombinationsLinear ProgrammingLimits and Continuity