KCET Mathematics - Elimination, Identities, and Domains
KCET Mathematics carries 60 one-mark questions and shares 80 minutes with Physics and Chemistry, making it the most time-pressured section; solving a question in under 30 seconds usually means answering by elimination rather than full derivation. The syllabus is first and second PUC: sets and functions, trigonometry, matrices and determinants, complex numbers, coordinate geometry, calculus, vectors and three-dimensional geometry, probability and statistics.
Core rules to keep loaded
- L'Hôpital's rule applies only to 0/0 or ∞/∞ forms; standard limits such as sin x/x → 1 are faster.
- For definite integrals, an odd integrand over [−a, a] integrates to zero.
- Independent events multiply; mutually exclusive events add.
- Vectors: a·b = 0 means perpendicular, a×b = 0 means parallel, and a triangle's area is ½|a×b|.
- Conic eccentricity: e² = 1 − b²/a² for an ellipse, e² = 1 + b²/a² for a hyperbola.
Worked example
Evaluate ∫₀^{π/2} sin²x dx. Use sin²x = (1 − cos 2x)/2. The integral becomes ½∫₀^{π/2} dx − ½∫₀^{π/2} cos 2x dx = ½·(π/2) − ¼[sin 2x]₀^{π/2} = π/4 − 0 = π/4. Spotting the identity beats integrating by parts.
Traps that cost marks
Squaring both sides can admit extraneous roots, so verify against the domain. sin⁻¹x returns only the principal value, not the general solution. Omitting the constant of integration loses a mark on indefinite integrals. nPr and nCr are constantly swapped - order matters only in the former. In three dimensions, direction ratios and direction cosines are different quantities. In probability, P(A∪B) = P(A) + P(B) − P(A∩B); dropping the intersection term is the commonest error.