JEE doubts
700 doubts found
What is the difference between roots and factors?
Roots are the x-values that make the expression zero; factors are the (x − root) pieces whose product is the polynomial.
What is the difference between modulus and argument?
The modulus is a complex number's distance from the origin; the argument is the angle it makes with the positive real axis.
What is the difference between finite series and infinite series?
A finite series always has a sum; an infinite series has one only if it converges (e.g. a GP with |r|<1).
What is the difference between with repetition and without repetition?
With repetition, items can be reused (like digits in a PIN); without repetition, each item is used at most once (like ranking people).
When do I use T_(r+1) = nCr·a^(n−r)·b^r in Binomial Theorem, and what does it mean?
the general (r+1)th term of (a+b)^n.
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).
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.