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CBSE Practice: Mathematics Class 12

CBSE Class 12 Mathematics — Practice Problems

10 MCQ questions covering calculus, matrices, probability, vectors, and relations and functions from the NCERT syllabus. Select an option to check your answer and view the explanation.

Algebra and Calculus

Probability and Statistics

Vectors and Relations

Intuition

Mathematics provides the tools for quantitative reasoning: From algebra to geometry to calculus, mathematics gives you systematic methods for solving problems involving numbers, shapes, and change. Each concept builds on previous ones.

Why it matters: Mathematical skills are essential for science, engineering, commerce, and everyday decision-making.

The key insight: In mathematics, showing your working evidently earns partial credit and helps you identify where errors occurred.

Common Mistakes

Confusing the determinant formula for 2×22 \times 2 and 3×33 \times 3 matrices: For a 2×22 \times 2 matrix, det⁡=ad−bc\det = ad - bc. For a 3×33 \times 3 matrix, you must use cofactor expansion, there is no simple diagonal formula. Applying the 2×22 \times 2 formula to a 3×33 \times 3 matrix gives completely wrong answers.

Forgetting the constant of integration in indefinite integrals: Every indefinite integral requires +C+ C. This is not optional, without it, the answer is incomplete. For definite integrals, the constant cancels out, but for indefinite integrals (like the CBSE example), omitting +C+ C costs marks.

Confusing independent events with mutually exclusive events: Independent events satisfy P(A∩B)=P(A)P(B)P(A \cap B) = P(A)P(B), while mutually exclusive events satisfy P(A∩B)=0P(A \cap B) = 0. Mutually exclusive events with non-zero probability are never independent, if one occurs, the other cannot. Using the wrong formula gives incorrect probability calculations.

Cross-References

  • Site Home: Main landing page for CBSE notes.
  • Chemistry: Chemistry notes covering organic and physical chemistry.
  • Physics: Physics notes covering mechanics and thermodynamics.
  • Practice: Practice problems for revision.

Detailed Content

Core Concepts

Worked Examples

Common Mistakes

  • Rushing through foundational material
  • Not practising problems after reading
  • Failing to connect concepts across topics

Further Reading

See also