JEE doubts
700 doubts found
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.
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.
Why does the order matter in matrix multiplication — isn't AB the same as BA?
No — matrix multiplication is generally non-commutative.
How does the derivative tell me where a function is rising or falling (useful for graphs and trends)?
The sign of the first derivative gives the direction.
A curve dips below the x-axis on my interval — why does the plain integral give too small an area?
A definite integral gives SIGNED area, so any region below the x-axis is counted as negative and cancels part of the positive region above.
How do I find the order and degree of a differential equation, and why do they matter?
The order is simply the highest derivative that appears (a d²y/dx² makes it second order).
How do composite functions f(g(x)) work, and why does the order of composition matter?
A composite applies one function to the result of another: f(g(x)) means first do g, then feed its output into f.
Two classes have the same average marks — how can statistics show they're actually very different?
Compare their spread using standard deviation.
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.