Introduction to Algebra
Algebra is a crucial branch of mathematics that deals with symbols and the rules for manipulating these symbols. In JEE Mathematics, algebra forms the foundation for many advanced topics and problem-solving techniques.
This section covers all the important algebraic concepts required for JEE preparation, including quadratic equations, complex numbers, progressions, permutations and combinations, binomial theorem, and more.
Chapters
Quadratic Equations
Learn about quadratic equations, their solutions, nature of roots, and applications in problem-solving.
Key Formula: $ax^2 + bx + c = 0$ has roots $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Complex Numbers
Master complex numbers, their algebraic operations, geometric representation, and applications.
Key Concept: $z = a + bi$ where $i^2 = -1$
Progressions
Study arithmetic, geometric, and harmonic progressions and their applications.
AP Sum: $S_n = \frac{n}{2}[2a + (n-1)d] = \frac{n}{2}(a + l)$
Binomial Theorem
Understand binomial expansion, binomial coefficients, and their properties and applications.
$(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$
Permutations & Combinations
Learn counting principles, permutations, combinations, and their applications in probability.
$^nC_r = \frac{n!}{r!(n-r)!}$ and $^nP_r = \frac{n!}{(n-r)!}$
Matrices & Determinants
Study matrices, determinants, and their applications in solving systems of linear equations.
For a 2×2 matrix: $\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$
Practice Questions
Test your understanding of algebraic concepts with these practice questions.
Downloads
Download these resources for offline study and quick reference.