∫

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 derivative of eˣ with respect to x is:

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

    Answer: eˣ

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

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

    Answer: 1

  3. The mean of 2, 4 and 6 is:

    • 3
    • 4
    • 6
    • 12
    Show answer

    Answer: 4

  4. The indefinite integral ∫ x dx is:

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

    Answer: x²/2 + C

Practise more questions →

Practice Questions

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

Start Practice →

Frequently Asked Questions

What are the key concepts in Mathematics — Stream SX/SB for KVPY?

Differential and integral calculus; Coordinate geometry and conic sections; Vectors and three-dimensional geometry; Probability and statistics.

Which formulae are important for Mathematics — Stream SX/SB in KVPY?

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).

How can I practise KVPY Mathematics — Stream SX/SB questions for free?

Practise free KVPY Mathematics — Stream SX/SB questions with instant answers and explanations on Safe Learning for Kids — no sign-up required.

Mathematics