JEE · Maths doubts
167 doubts found
I keep getting “Standard equations” questions wrong in Conic Sections. What's the trap?
mismatching the axis of the parabola with its equation.
I keep getting “Standard limit” questions wrong in Limits & Continuity. What's the trap?
evaluating it as 0/0 and stopping.
I keep getting “Product and quotient rules” questions wrong in Differentiation. What's the trap?
differentiating a product as just u'v'.
I keep getting “Methods of integration” questions wrong in Integration. What's the trap?
reaching for by-parts when a simple substitution works.
I keep getting “Conditional probability” questions wrong in Probability. What's the trap?
assuming P(A|B) equals P(B|A).
I keep getting “Direction ratios” questions wrong in Vectors & 3D Geometry. What's the trap?
confusing direction ratios with direction cosines (which are normalised).
What is the difference between real roots and complex roots?
Real roots occur when D≥0 (the parabola meets the x-axis); complex roots occur when D<0 (it doesn't).
What is the difference between real part and imaginary part?
In a+bi, a is the real part (on the x-axis) and b is the imaginary coefficient (on the y-axis).
What is the difference between arithmetic progression and geometric progression?
An AP grows by adding a fixed number each step; a GP grows by multiplying by a fixed ratio each step.
What is the difference between permutation and combination?
A permutation counts ordered arrangements (a password); a combination counts unordered selections (a team) — nCr = nPr / r!.
What is the difference between binomial coefficient and term?
The binomial coefficient nCr is just the number multiplying a term; the term itself also includes the powers of a and b.
What is the difference between degrees and radians?
Degrees split a circle into 360 parts; radians measure the arc length per unit radius (2π in a full circle) and are used in calculus.
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 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.