JEE Advanced Maths · JEE Advanced · Probability
The JEE Advanced Maths mistakes examiners flag every series
Every JEE Advanced JEE Advanced Maths mark scheme highlights the same handful of misconceptions in its past papers, and the same handful resurface in the next series, then the one after that. The patterns are durable. They aren’t carelessness; they’re predictable shortcuts the brain takes when maths is read like English.
Below, grouped by topic, is the full set as of the current JEE Advanced specification. Each one names the misconception, explains why it happens, and shows the fix. Start any topic and the lesson works through its misconceptions one altitude at a time, or take the free diagnostic to find out which ones are yours.
Which ones are costing you marks?
The diagnostic tests for all of them with JEE Advanced-style items. You get a grade-band prediction and a list of which patterns to fix first. Free, no signup, anonymous.
Probability (4)Take the Probability diagnostic →
Reading a test's accuracy P(positive|disease) as the chance of disease P(disease|positive) — confusing P(A|B) with P(B|A), ignoring the base rate.
Answering an 'at least one' question by adding the per-case probabilities, instead of 1 − P(none).
Computing P(A or B) as P(A) + P(B) and forgetting to subtract P(A and B), the overlap.
Multiplying P(A) and P(B) to get P(A and B) when the problem never said the events are independent.
Matrices & Determinants (3)Take the Matrices & Determinants diagnostic →
Reading a zero determinant as “no solution”, confusing singularity with unsolvability and never seeing the infinite-solution family a singular system can have.
Treating the determinant as if it were linear — det(A + B) = det A + det B and det(2A) = 2·det A — when scaling an n×n matrix multiplies its determinant by 2ⁿ.
Assuming matrices multiply like numbers — AB = BA, (AB)⁻¹ = A⁻¹B⁻¹ — so a constraint such as PQ = QP is treated as automatic rather than a real restriction.
Complex Numbers (4)Take the Complex Numbers diagnostic →
Treating |z|² as z², so a complex square is assumed to behave like a real square (always non-negative) when z² can in fact be negative, complex, or anything else in the plane.
Deciding an expression is real by inspection rather than imposing w = w̄ and solving it, so genuinely real conditions on z get missed or invented.
Expecting an equation in z to fix finitely many points the way a polynomial does, and centring the circle from |z - a| = k|z - b| between the two defining points, when the condition carves out a whole locus whose centre (for k ≠ 1) lies outside the segment joining them.
Reading arg z as arctan(y/x) regardless of quadrant, and assuming a sign change in z does not disturb the periodic structure of its powers or roots.