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Mathematics — Stream SX/SB

Calculus, probability, vectors, matrices, and combinatorics for Class 12 / college

Key Concepts
  • Differential and integral calculus
  • Coordinate geometry and conic sections
  • Vectors and three-dimensional geometry
  • Probability and statistics
Important Formulae
Power rule (integration) ∫xⁿ dx = xⁿ⁺¹/(n+1) + C, n ≠ −1
Dot product a·b = |a||b| cosθ
Conditional probability P(A|B) = P(A∩B)/P(B)
Quick Tips
  • Always add the constant of integration to indefinite integrals.
  • For probability, define the sample space clearly before counting.
Sample Practice Questions

  1. The probability of a sure (certain) event is:

    • 0
    • 1/2
    • 1
    • Greater than 1
    Show answer

    Answer: 1

  2. The dot product of two perpendicular vectors is:

    • 0
    • 1
    • Their magnitudes multiplied
    • Undefined
    Show answer

    Answer: 0

  3. The indefinite integral ∫ x dx is:

    • x² + C
    • x²/2 + C
    • 1 + C
    • 2x + C
    Show answer

    Answer: x²/2 + C

  4. The derivative of eˣ with respect to x is:

    • eˣ
    • x·eˣ⁻¹
    • 1
    • ln x
    Show answer

    Answer: eˣ

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Practice Questions

Practise KVPY questions on Mathematics — Stream SX/SB. Answers are revealed after each question.

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Mathematics