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Mathematics — Tier 3

Calculus, vectors, complex numbers, probability, and matrices for Classes XI–XII

Sample Practice Questions

  1. The number of ways to arrange 5 objects in 3 positions (permutation) ⁵P₃ =

    • 10
    • 20
    • 60
    • 120
    Show answer

    Answer: 60

  2. Binomial probability P(X=k) = C(n,k) × p^k × (1−p)^(n−k). For n=5, p=0.5, P(X=3):

    • 1/4
    • 5/16
    • 3/8
    • 1/8
    Show answer

    Answer: 5/16

  3. The probability that both events A and B occur: P(A∩B) = P(A)×P(B) only when:

    • A and B are mutually exclusive
    • A and B are independent
    • A implies B
    • A and B are complementary
    Show answer

    Answer: A and B are independent

  4. The cross product A×B has magnitude:

    • |A||B|cosθ
    • |A||B|sinθ
    • |A|+|B|
    • 0 always
    Show answer

    Answer: |A||B|sinθ

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Practice Questions

Practise NGSE questions on Mathematics — Tier 3. Answers are revealed after each question.

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