JEE doubts
700 doubts found
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.
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.