JEE · Maths doubts
167 doubts found
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 “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.
What does “Definite integral” actually mean in Integration, and why does it matter for JEE?
the definite integral gives the (signed) area under a curve between two limits.
What does “Independent vs mutually exclusive” actually mean in Probability, and why does it matter for JEE?
independent events don't affect each other; mutually exclusive events cannot both happen.
What does “Cross product” actually mean in Vectors & 3D Geometry, and why does it matter for JEE?
a×b = |a||b|sinθ·n̂ gives a vector perpendicular to both a and b.
I keep getting “Sum and product of roots” questions wrong in Quadratic Equations. What's the trap?
dropping the minus sign in −b/a.
I keep getting “Modulus and conjugate” questions wrong in Complex Numbers. What's the trap?
forgetting that z times its conjugate equals |z|² (a real number).
I keep getting “Geometric progression” questions wrong in Sequences & Series. What's the trap?
adding the ratio instead of multiplying by it.
I keep getting “Combination” questions wrong in Permutations & Combinations. What's the trap?
using combinations when order actually matters.
I keep getting “General term” questions wrong in Binomial Theorem. What's the trap?
treating the general term as the rth term instead of the (r+1)th.
I keep getting “Radians vs degrees” questions wrong in Trigonometry. What's the trap?
using degrees in derivative/limit formulas.
I keep getting “Perpendicular and parallel lines” questions wrong in Straight Lines. What's the trap?
thinking perpendicular lines have equal slopes.
I keep getting “Focus and directrix” questions wrong in Conic Sections. What's the trap?
confusing the focus (a point) with the directrix (a line).
I keep getting “Continuity” questions wrong in Limits & Continuity. What's the trap?
thinking every function is continuous everywhere.