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Agniveer Air Force Vectors & 3D Geometry — practice questions — page 2

Explore 34 free Vectors & 3D Geometry questions in Agniveer Air Force 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 31–34 of 34.

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 →Sort each statement by which idea it describesRead the answer and worked solution →

Worked practice questions

Spot the odd one out

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Questions
  1. Items
    1. P(E)P(F|E)
    2. P(E) + P(F)
    3. P(F)P(E|F)
    Odd item
    P(E) + P(F)
  2. Items
    1. Prior
    2. Cofactor
    3. Posterior
    4. Partition
    Odd item
    Cofactor
  3. Items
    1. Pairwise disjoint
    2. Union equals S
    3. All equally likely
    4. Nonzero probability
    Odd item
    All equally likely
Each group is one bullet of the summary. Source: syllabus Maths Part II, Ch 13 Probability.

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Assertion and reason: the multiplication rule

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Questions
  1. Reason
    You may condition on either event, provided its probability is nonzero.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    P(E ∩ F) can be written two different ways.
  2. Reason
    Independence makes P(F|E) equal to P(F).
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    For independent events the multiplication rule simplifies.
  3. Reason
    Bayes' theorem has a sum in its denominator.
    Verdict
    Both are true; the reason does not explain the assertion.
    Assertion
    Conditional probability lies between 0 and 1.
Both halves true does not mean one explains the other. Source: syllabus Maths Part II, Ch 13 Probability.

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True or false: the Historical Note

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Questions
  1. Statement is true
    Yes
    Statement
    Pascal and Fermat corresponded about a gambler's problem.
  2. Statement is true
    Yes
    Statement
    Huygens published an early book on probability.
  3. Statement is true
    Yes
    Statement
    Kolmogorov gave probability its axiomatic foundation.
  4. Statement is true
    No
    Statement
    Galileo showed a sum of 9 is likelier than 10 with three dice.
  5. Statement is true
    Yes
    Statement
    Ars Conjectandi was published posthumously.
Straight from the closing note. Source: syllabus Maths Part II, Ch 13 Probability.

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