JEE · Maths doubts
233 doubts found
I keep getting “Pythagorean identity” questions wrong in Trigonometry. What's the trap?
misremembering it as sinθ + cosθ = 1.
I keep getting “Slope” questions wrong in Straight Lines. What's the trap?
inverting the formula to (x₂−x₁)/(y₂−y₁).
I keep getting “Eccentricity” questions wrong in Conic Sections. What's the trap?
mixing up which conic each eccentricity range gives.
I keep getting “Limit” questions wrong in Limits & Continuity. What's the trap?
assuming the limit always equals the function's value at that point.
I keep getting “Derivative” questions wrong in Differentiation. What's the trap?
confusing the derivative (a rate) with the function's value.
I keep getting “Antiderivative” questions wrong in Integration. What's the trap?
forgetting to add +C to an indefinite integral.
I keep getting “Basic probability” questions wrong in Probability. What's the trap?
giving a probability greater than 1.
I keep getting “Dot product” questions wrong in Vectors & 3D Geometry. What's the trap?
expecting the dot product to be a vector.
What does it mean when the determinant of the coefficient matrix comes out to be zero?
A zero determinant means the matrix is singular and has no inverse, so the neat X = A⁻¹B route fails.
A ladder slides down a wall — how fast is the top falling when I know how fast the base moves? (related rates)
The ladder length L is fixed, so x² + y² = L², where x is the base distance and y the height.
Why is the definite integral described as 'accumulation' — what does that mean physically?
A definite integral adds up a rate over an interval to give the total change.
Why does a hot cup of coffee cool quickly at first and then more slowly (Newton's law of cooling)?
Newton's law of cooling says the rate of cooling is proportional to the temperature difference from the surroundings: dT/dt = −k(T − Tₛ).
Why is sin⁻¹(1/2) just π/6 and not the infinitely many angles that also have sine 1/2?
Sine is many-one — countless angles share the same sine — so a plain 'inverse' wouldn't be a function (one input, many outputs).
One employee earns far more than the rest — should I describe salaries by the mean or the median?
Use the median.
What does “Sum and product of roots” actually mean in Quadratic Equations, and why does it matter for JEE?
for ax²+bx+c=0, the roots add to −b/a and multiply to c/a (Vieta's relations).
What does “Modulus and conjugate” actually mean in Complex Numbers, and why does it matter for JEE?
the modulus |z|=√(a²+b²) is the distance from the origin; the conjugate of a+bi is a−bi.
What does “Geometric progression” actually mean in Sequences & Series, and why does it matter for JEE?
a sequence with a constant ratio r; the nth term is a·r^(n−1).
What does “Combination” actually mean in Permutations & Combinations, and why does it matter for JEE?
a selection where order does not matter: nCr = n!/[r!(n−r)!].
What does “General term” actually mean in Binomial Theorem, and why does it matter for JEE?
the (r+1)th term is T_(r+1) = nCr·a^(n−r)·b^r.
What does “Radians vs degrees” actually mean in Trigonometry, and why does it matter for JEE?
angles can be measured in degrees or radians (π rad = 180°); calculus formulas assume radians.
What does “Perpendicular and parallel lines” actually mean in Straight Lines, and why does it matter for JEE?
parallel lines have equal slopes; perpendicular lines have slopes whose product is −1.
What does “Focus and directrix” actually mean in Conic Sections, and why does it matter for JEE?
a conic is the set of points whose distances to a focus and a directrix are in the fixed ratio e.
What does “Continuity” actually mean in Limits & Continuity, and why does it matter for JEE?
a function is continuous at a point if its limit there equals its actual value (no breaks or jumps).
What does “Chain rule” actually mean in Differentiation, and why does it matter for JEE?
to differentiate a composite function, differentiate the outer function and multiply by the derivative of the inner.