Mathematics: Exact Computation and Pattern Recognition
Mathematics in MHT-CET covers the Maharashtra State Board Class 11–12 syllabus: trigonometry, straight lines, circles, conic sections, vectors, three-dimensional geometry, matrices, complex numbers, differentiation, integration, differential equations, probability and statistics. The paper rewards pattern recognition and exact computation, not lengthy proofs.
Core rules and concepts
- Differentiation: product rule (uv)' = u'v + uv'; use the chain rule for composite functions.
- Integration: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C for n ≠ −1; always add the constant for indefinite integrals.
- Vectors: a·b = |a||b|cosθ; a×b gives a perpendicular vector.
- Probability: P(A∪B) = P(A) + P(B) − P(A∩B); independence means P(A∩B) = P(A)P(B).
- Conics: for y² = 4ax, the focus is (a, 0) and the directrix is x = −a.
Worked example
Differentiate y = x² ln x. Using the product rule: y' = (2x)(ln x) + (x²)(1/x) = 2x ln x + x.
Traps that cost marks
- Dropping the +C in indefinite integration.
- Confusing permutation and combination: order matters only in permutations.
- Using degrees when the formula requires radians, especially in limits and derivatives.
- Forgetting domain restrictions, e.g. ln x requires x > 0.
- Sign errors when expanding determinants or resolving vectors.