JEE · Maths doubts
233 doubts found
What is the difference between order of a differential equation and degree of a differential equation?
The order is the highest derivative that appears; the degree is the power of that highest-order derivative after the equation is made polynomial in its derivatives.
What is the difference between sin⁻¹ range and cos⁻¹ range?
sin⁻¹ returns angles in [−π/2, π/2]; cos⁻¹ returns angles in [0, π] — different principal branches chosen to keep each single-valued.
What is the difference between union (A∪B) and intersection (A∩B)?
The union is everything in A OR B (or both); the intersection is only what's in A AND B — the shared overlap.
When do I use sum = −b/a, product = c/a in Quadratic Equations, and what does it mean?
Vieta's relations between roots and coefficients.
When do I use z·z̄ = |z|² in Complex Numbers, and what does it mean?
a complex number times its conjugate is real.
When do I use aₙ = a·r^(n−1) in Sequences & Series, and what does it mean?
nth term of a geometric progression.
When do I use nCr = n!/[r!(n−r)!] in Permutations & Combinations, and what does it mean?
number of unordered selections of r from n.
What are the most common mistakes students make in Binomial Theorem?
Confusing the index of the general term, forgetting that the exponents of the two terms always sum to n, and assuming there is always a single middle term.
When do I use sin(A±B) = sinA cosB ± cosA sinB in Trigonometry, and what does it mean?
the sine addition formula.
When do I use d = |ax₀+by₀+c|/√(a²+b²) in Straight Lines, and what does it mean?
distance from a point to a line.
When do I use y² = 4ax in Conic Sections, and what does it mean?
standard parabola opening rightward.
How is Limits & Continuity tested in JEE, and what should I focus on?
Prioritise the core ideas: Limit, Continuity, Standard limit.
When do I use dy/dx = dy/du · du/dx in Differentiation, and what does it mean?
the chain rule for composite functions.
When do I use ∫(1/x) dx = ln|x| + C in Integration, and what does it mean?
the integral of 1/x.
When do I use P(A|B) = P(A∩B)/P(B) in Probability, and what does it mean?
conditional probability.
When do I use |a×b| = |a||b|sinθ in Vectors & 3D Geometry, and what does it mean?
magnitude of the cross product (vector).
What is the difference between AB and BA?
Matrix multiplication is generally non-commutative: AB and BA can differ (or one may not even be defined), so the order of multiplication matters.
What is the difference between local maximum and local minimum?
At a local maximum the function stops rising and turns down (f''<0); at a local minimum it stops falling and turns up (f''>0).
When do I use Area = ∫ₐᵇ (upper − lower) dx in Applications of Integrals, and what does it mean?
area enclosed between two curves.
What is the difference between general solution and particular solution?
A general solution carries arbitrary constants (a whole family of curves); a particular solution fixes those constants using given initial/boundary conditions.
How is Relations, Functions & Inverse Trigonometry tested in JEE, and what should I focus on?
Prioritise the core ideas: Bijective functions, Principal value branch.
When do I use n(A∪B) = n(A) + n(B) − n(A∩B) in Sets & Statistics, and what does it mean?
inclusion–exclusion for two sets.
How is Quadratic Equations tested in JEE, and what should I focus on?
Prioritise the core ideas: Discriminant, Sum and product of roots, Nature of roots.
How is Complex Numbers tested in JEE, and what should I focus on?
Prioritise the core ideas: The imaginary unit, Modulus and conjugate, Argand plane.