ABHYAS · CLASS 11 STUDENTS (CBSE AND STATE BOARDS), JEE FOUNDATION

Class 11 Maths कक्षा 11 गणित

Unlimited Class 11 maths practice aligned to the NCERT syllabus: sets, relations and functions, trigonometric functions, complex numbers, linear inequalities, permutations and combinations, binomial theorem, sequences and series, straight lines, circles, limits and derivatives, statistics and probability, with hints and worked steps.

Sets

Counting with sets and Venn diagramsn(A ∪ B) = n(A) + n(B) − n(A ∩ B). For three sets add the singles, subtract the pairs and add back the triple overlap.

Relations and functions

Function values, composition and counting relationsSubstitute to find f(a). For f(g(x)), work from the inside out. If n(A) = m and n(B) = n, A × B has mn pairs, so there are 2^(mn) relations from A to B.

Trigonometric functions

Trigonometric values of any angle and allied anglesReduce the angle to an acute reference angle, then fix the sign by quadrant (All, Sin, Tan, Cos positive in quadrants I to IV). At 90° or 270° ± θ the function changes to its co-function.

Complex numbers

Complex number arithmetic and modulusAdd or subtract real and imaginary parts separately. To multiply, expand and use i² = −1. The modulus of a + bi is √(a² + b²).

Linear inequalities

Solve linear inequalities in one variableSolve like an equation, but when you multiply or divide both sides by a negative number, reverse the inequality sign.

Permutations and combinations

Permutations and combinationsOrder matters → permutations, ⁿPᵣ = n!/(n − r)!. Order does not matter → combinations, ⁿCᵣ = n!/(r!(n − r)!). Repeated letters: divide by the factorial of each repeat count.

Binomial theorem

Binomial theorem: coefficients and special termsThe general term of (a + b)ⁿ is Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ. Match the power of x to find r, then compute the coefficient.

Sequences and series

AP and GP: nth term and sumAP: aₙ = a + (n − 1)d, Sₙ = n/2 [2a + (n − 1)d]. GP: aₙ = arⁿ⁻¹, Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1.

Straight lines

Straight lines: slope, intercepts and distanceSlope = (y₂ − y₁)/(x₂ − x₁). For ax + by + c = 0, slope = −a/b and the distance of (x₁, y₁) from the line is |ax₁ + by₁ + c|/√(a² + b²).

Conic sections

Circle: centre and radius from the general equationx² + y² + 2gx + 2fy + c = 0 has centre (−g, −f) and radius √(g² + f² − c). If x² and y² have a coefficient other than 1, divide through first.

Limits and derivatives

Statistics

Mean deviation, variance and standard deviationMean deviation about the mean = Σ|xᵢ − x̄|/n. Variance σ² = Σ(xᵢ − x̄)²/n = Σx²/n − x̄². Standard deviation σ = √variance.

Probability

Probability of events: cards, dice and unionsP(E) = favourable outcomes ÷ total outcomes. P(not E) = 1 − P(E). P(A ∪ B) = P(A) + P(B) − P(A ∩ B).