Mathematics
What the paper tests
The IMU CET Mathematics section is an objective paper drawn from the Class XI–XII syllabus: sets and relations, complex numbers, quadratic equations, matrices and determinants, permutations and combinations, binomial theorem, sequences and series, limits and continuity, differentiation, integration, differential equations, straight lines, circles and conics, 3-D geometry, vectors, probability and trigonometry. A large share of items are single-step formula recalls; the rest chain two or three ideas together, so clean algebraic manipulation and elimination of options buy more marks than exotic shortcuts.
Core rules to have at your fingertips
- Standard limits: lim(x→0) sin x/x = 1; lim(x→0)(1−cos x)/x² = 1/2; lim(x→0)(eˣ−1)/x = 1.
- Integration by parts: ∫u dv = uv − ∫v du, with u chosen by ILATE order.
- Probability: P(A∪B) = P(A) + P(B) − P(A∩B); independent events multiply.
- Straight line: m = (y₂−y₁)/(x₂−x₁), and perpendicular lines satisfy m₁m₂ = −1.
- Binomial general term: T(r+1) = ⁿCᵣ·a^(n−r)·b^r.
- Vectors: a·b = |a||b|cos θ; a×b is perpendicular to both.
Worked example
Evaluate ∫x·e^(2x) dx. ILATE orders algebraic before exponential, so take u = x and dv = e^(2x)dx, giving du = dx and v = e^(2x)/2. ∫x·e^(2x)dx = x·e^(2x)/2 − ∫(e^(2x)/2)dx = x·e^(2x)/2 − e^(2x)/4 + C. The reasoning is that the algebraic factor is differentiated to a constant while the exponential is integrated; the leftover integral is a pure exponential and collapses in one step.
Traps that cost marks
- Omitting the constant of integration; the option without +C is planted as a decoy.
- Mixing degrees and radians when differentiating or taking limits of trigonometric functions.
- For a line perpendicular to a plane, using the plane's direction ratios instead of its normal ratios.
- Sign slips when expanding (a − b)³ or transposing terms while expanding a determinant.
- Counting ordered pairs in a probability question that asks for unordered selections.