JEE doubts
700 doubts found
How are matrices used to solve a system of several linear equations at once?
Write the system in the form AX = B, where A holds the coefficients, X the unknowns and B the constants.
How do I find the dimensions that give the maximum area (or minimum material) — a real optimisation problem?
Turn the requirement into a single-variable function using the constraint.
How do I find the area enclosed between two curves, like a parabola and a line?
First find where they meet by setting the two functions equal — these intersection points are your limits a and b.
How do differential equations model things like population growth or radioactive decay?
Both are cases where the rate of change is proportional to the current amount: dy/dt = ky.
Why can some functions be inverted while others can't?
An inverse must send each output back to exactly one input, so the original function has to be bijective — one-one (no two inputs share an output) and onto (every target value is reached).
In a survey, 30 like tea, 25 like coffee, 10 like both — how many like at least one, and how do I avoid double counting?
Use the inclusion–exclusion principle: n(tea ∪ coffee) = n(tea) + n(coffee) − n(both).
I keep getting “Discriminant” questions wrong in Quadratic Equations. What's the trap?
thinking D<0 means 'no solution'.
I keep getting “The imaginary unit” questions wrong in Complex Numbers. What's the trap?
writing √(−1)·√(−1) = √1 = 1.
I keep getting “Arithmetic progression” questions wrong in Sequences & Series. What's the trap?
using the wrong count (n vs n−1) for the nth term.
I keep getting “Permutation” questions wrong in Permutations & Combinations. What's the trap?
using permutations when order doesn't matter.
I keep getting “Binomial expansion” questions wrong in Binomial Theorem. What's the trap?
forgetting that the powers of a and b add up to n in every term.
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).