JEE Main Algebra: Complex Numbers, Matrices, Probability & More
Algebra accounts for 7-8 JEE Main Maths questions — more than any single chapter group except Calculus. With the right formulas and practice, Algebra is highly predictable and scoreable.
Complex Numbers (2-3 questions)
Key topics: Modulus, argument, polar form. Operations in Cartesian and polar form. De Moivre's Theorem. Cube roots of unity (1 + ω + ω² = 0). JEE Main loves: |z₁ - z₂|, rotation by multiplying e^(iθ), finding locus of complex numbers.
Matrices and Determinants (2 questions)
Matrix operations, determinant expansion, adjoint and inverse. Cramers rule for solving linear equations. JEE Main frequently asks: find matrix satisfying equation A² - 5A + 6I = 0. Cayley-Hamilton theorem is useful here.
Permutation and Combination (1-2 questions)
Fundamental counting, arrangements with repetition/restriction, combinations. Circular permutations, derangements. Common question types: arrangements with identical objects, distribution problems.
Probability (2 questions)
Classical and axiomatic probability, conditional probability, Bayes theorem, independence. Binomial distribution (mean = np, variance = npq). JEE Main: 1-2 Bayes theorem questions per paper using tree diagrams.
Binomial Theorem (1-2 questions)
General term T(r+1), finding specific terms, binomial coefficients, middle term. Common question: coefficient of x^k in (a + bx)^n, or prove/find sum of binomial coefficients.
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