JEE doubts
700 doubts found
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.
When do I use S∞ = a/(1−r) in Sequences & Series, and what does it mean?
sum of an infinite geometric series.
How is Permutations & Combinations tested in JEE, and what should I focus on?
Prioritise the core ideas: Permutation, Combination, Fundamental principle of counting.
How do I revise Binomial Theorem quickly before the exam?
One-page summary of Binomial expansion, General term, Middle term, then timed previous-year questions.
How is Trigonometry tested in JEE, and what should I focus on?
Prioritise the core ideas: Pythagorean identity, Radians vs degrees, Range of sine and cosine.
How is Straight Lines tested in JEE, and what should I focus on?
Prioritise the core ideas: Slope, Perpendicular and parallel lines, Equation forms.
How is Conic Sections tested in JEE, and what should I focus on?
Prioritise the core ideas: Eccentricity, Focus and directrix, Standard equations.
What are the most common mistakes students make in Limits & Continuity?
Confusing limit with function value, assuming a limit needs the function defined at that point, and treating 0/0 as undefined without further analysis.
How is Differentiation tested in JEE, and what should I focus on?
Prioritise the core ideas: Derivative, Chain rule, Product and quotient rules.
How is Integration tested in JEE, and what should I focus on?
Prioritise the core ideas: Antiderivative, Definite integral, Methods of integration.
How is Probability tested in JEE, and what should I focus on?
Prioritise the core ideas: Basic probability, Independent vs mutually exclusive, Conditional probability.
How is Vectors & 3D Geometry tested in JEE, and what should I focus on?
Prioritise the core ideas: Dot product, Cross product, Direction ratios.
When do I use X = A⁻¹B in Matrices & Determinants, and what does it mean?
solution of the linear system AX = B.
When do I use dy/dt = (dy/dx)(dx/dt) in Application of Derivatives, and what does it mean?
chain rule for related rates.