JEE · Maths doubts
167 doubts found
What is the difference between sine rule and cosine rule?
The sine rule (a/sinA = b/sinB) suits two angles and a side; the cosine rule (c²=a²+b²−2ab·cosC) suits two sides and the included angle.
What is the difference between slope-intercept form and point-slope form?
Slope-intercept (y=mx+c) is best when you know the slope and y-intercept; point-slope is best when you know the slope and any one point.
What is the difference between parabola and hyperbola?
A parabola has eccentricity exactly 1 and one focus; a hyperbola has e>1 and two branches with two foci.
What is the difference between continuous function and discontinuous function?
A continuous function has no breaks (limit = value everywhere); a discontinuous one has jumps, holes, or asymptotes.
What is the difference between product rule and quotient rule?
The product rule differentiates u·v as u'v+uv'; the quotient rule differentiates u/v as (u'v−uv')/v².
What is the difference between differentiation and integration?
Differentiation finds a rate/slope from a function; integration reverses it to recover the function or find accumulated area.
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).
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).
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.