JEE · Maths doubts
233 doubts found
What is the difference between P(A|B) and P(B|A)?
These conditional probabilities ask different questions and are generally unequal — Bayes' theorem relates them.
What is the difference between scalar quantity and vector quantity?
A scalar has only magnitude (speed, mass); a vector has magnitude and direction (velocity, force).
I keep getting “Determinant and singularity” questions wrong in Matrices & Determinants. What's the trap?
assuming every square matrix has an inverse.
I keep getting “Second-derivative test” questions wrong in Application of Derivatives. What's the trap?
confusing which sign of f'' gives a maximum.
What is the difference between signed area and total area?
A plain definite integral gives signed area (below-axis parts subtract); total (geometric) area needs you to split at the roots and add the absolute values.
I keep getting “Separation of variables” questions wrong in Differential Equations. What's the trap?
integrating before separating the variables.
What is the difference between one-one (injective) and onto (surjective)?
One-one means different inputs give different outputs (no output repeats); onto means every element of the codomain is actually hit. A function needs both (bijective) to be invertible.
What is the difference between mean and median?
The mean is the arithmetic average (sensitive to outliers); the median is the middle value (robust to outliers) — the median better represents skewed data.
When do I use x = [−b ± √(b²−4ac)] / 2a in Quadratic Equations, and what does it mean?
the quadratic formula for the roots.
When do I use |z| = √(a²+b²) in Complex Numbers, and what does it mean?
modulus (distance from origin) of z = a+bi.
When do I use aₙ = a + (n−1)d in Sequences & Series, and what does it mean?
nth term of an arithmetic progression.
When do I use nPr = n!/(n−r)! in Permutations & Combinations, and what does it mean?
number of ordered arrangements of r from n.
How is Binomial Theorem tested in JEE, and what should I focus on?
Prioritise the core ideas: Binomial expansion, General term, Middle term.
When do I use sin²θ + cos²θ = 1 in Trigonometry, and what does it mean?
the fundamental Pythagorean identity.
When do I use m = (y₂−y₁)/(x₂−x₁) in Straight Lines, and what does it mean?
slope from two points.
When do I use (x−h)²+(y−k)² = r² in Conic Sections, and what does it mean?
equation of a circle with centre (h,k), radius r.
When do I use lim(x→0) sin x / x = 1 in Limits & Continuity, and what does it mean?
a fundamental trigonometric limit.
When do I use d/dx(xⁿ) = n·x^(n−1) in Differentiation, and what does it mean?
the power rule.
When do I use ∫xⁿ dx = x^(n+1)/(n+1) + C in Integration, and what does it mean?
the power rule for integration.
When do I use P(A∪B) = P(A)+P(B)−P(A∩B) in Probability, and what does it mean?
the addition rule.
When do I use a·b = |a||b|cosθ in Vectors & 3D Geometry, and what does it mean?
dot product (scalar).
What is the difference between singular matrix and non-singular matrix?
A singular matrix has determinant 0 and no inverse (its system has no unique solution); a non-singular matrix has non-zero determinant and a unique inverse.
What is the difference between increasing function and decreasing function?
A function is increasing where f'(x) > 0 (rising) and decreasing where f'(x) < 0 (falling); f'(x) = 0 marks turning points.
What is the difference between area under a curve and area between two curves?
Area under one curve integrates f(x); area between two curves integrates the difference (upper − lower) of the two functions.