JEE · Maths doubts
233 doubts found
What is the difference between parallel lines and perpendicular lines?
Parallel lines never meet and share the same slope; perpendicular lines cross at 90° with slopes multiplying to −1.
What is the difference between ellipse and hyperbola?
An ellipse is a closed curve with e<1 (sum of focal distances constant); a hyperbola is an open two-branch curve with e>1 (difference of focal distances constant).
What is the difference between limit and value of a function?
The limit is what f(x) approaches near a point; the value is what f actually equals there — they can differ at a discontinuity.
What is the difference between derivative and differential?
The derivative dy/dx is a rate (slope); the differential dy = f'(x)dx is the small change it predicts for a small dx.
What is the difference between definite integral and indefinite integral?
A definite integral has limits and gives a number (area); an indefinite integral has no limits and gives a family of functions (+C).
What is the difference between independent events and mutually exclusive events?
Independent events don't influence each other's probability; mutually exclusive events can't co-occur (so they're dependent).
What is the difference between dot product and cross product?
The dot product gives a scalar (zero when perpendicular); the cross product gives a vector perpendicular to both (zero when parallel).
What does “Determinant and singularity” actually mean in Matrices & Determinants, and why does it matter for JEE?
the determinant is a single number from a square matrix; if it's zero the matrix is singular and has no inverse.
What does “Second-derivative test” actually mean in Application of Derivatives, and why does it matter for JEE?
at a critical point, f''>0 means a local minimum (cup up) and f''<0 means a local maximum (cap down).
I keep getting “Integral as accumulation” questions wrong in Applications of Integrals. What's the trap?
thinking integration only computes geometric area.
What does “Separation of variables” actually mean in Differential Equations, and why does it matter for JEE?
if you can write dy/dx = g(x)·h(y), gather all y-terms on one side and x-terms on the other, then integrate.
I keep getting “Principal value branch” questions wrong in Relations, Functions & Inverse Trigonometry. What's the trap?
giving all possible angles instead of the principal value.
I keep getting “Measures of spread” questions wrong in Sets & Statistics. What's the trap?
thinking two data sets with the same mean must be alike.
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.