Algebra in JEE Main: sequences and series, complex numbers, probability and binomial

Summary: Read the NTA syllabus line for each chapter first, because it is narrower than most books. Then learn a small set of methods per chapter, practise previous years' questions, and revise all four together every week so they stay fresh.

Start with the syllabus, not the book

Many algebra books were written for an older, wider JEE syllabus, and a student who works through them page by page spends weeks on material that is no longer asked. The JEE Main 2026 syllabus from NTA words these chapters quite narrowly:

• Sequence and series: arithmetic and geometric progressions, inserting arithmetic and geometric means, and the relation between AM and GM.
• Complex numbers and quadratic equations: the algebra of complex numbers, the Argand plane, modulus and argument, and quadratic equations with the relations between roots and coefficients.
• Binomial theorem: positive integral index, general term, middle term and simple applications.
• Statistics and probability: measures of dispersion, addition and multiplication theorems, Bayes' theorem, and the probability distribution of a random variable.

Keep a printout of the syllabus next to your problem book and skip exercises that fall outside it. The list can change from year to year, so check it for your exam year; our post on the reduced JEE Main syllabus tracks what was removed.

Sequences and series

Questions here usually test if you can set up the right unknowns. For three numbers in AP, take them as a − d, a, a + d; for three in GP, take a/r, a, ar. The sum or product then gives you one unknown straight away. Students who take the terms as a, a + d, a + 2d make the algebra twice as long.

The AM-GM relation is the other half of this chapter. It turns up in questions that ask for the minimum of an expression with positive terms. If you see "positive real numbers" and "minimum value" in the same question, AM ≥ GM is the first thing to try.

Example: for positive x, find the minimum of x + 9/x.
AM ≥ GM gives (x + 9/x)/2 ≥ √(x · 9/x) = 3, so x + 9/x ≥ 6, with equality when x = 9/x, that is x = 3. The minimum is 6.

Notes on this chapter: Sequences and series.

Complex numbers

Two skills carry most of this chapter. The first is moving comfortably between the forms x + iy and r(cos θ + i sin θ), and getting the argument in the right quadrant. The second is reading equations in z as geometry: |z − a| = r is a circle, |z − a| = |z − b| is the perpendicular bisector of the segment joining a and b. Once you see the picture, many locus questions take a few lines.

The most common error is the argument. arg(−1 − i) is −3π/4 (principal value), not π/4, even though tan θ = 1 in both cases. Always mark which quadrant the point is in before taking an inverse tangent.

Quadratic equations belong to the same unit. Questions on the nature of roots, the sum and product of roots, and conditions for roots to lie in an interval are regular, and a rough graph of the parabola settles most interval questions quickly. Notes: Complex numbers and quadratic equations.

Binomial theorem

Almost every question in this chapter starts with the general term, T_r+1 = C(n, r) a^n−r b^r. Write it first, collect the powers of x, and the question tells you what r must be.

Example: find the term independent of x in (x + 1/x²)⁶.
T_r+1 = C(6, r) x^6−r (x⁻²)^r = C(6, r) x^6−3r.
For no x, 6 − 3r = 0, so r = 2. The term is C(6, 2) = 15.

Other favourites are the middle term, the greatest coefficient and simple divisibility or remainder questions using (1 + x)ⁿ. Notes: Binomial theorem.

Probability

Probability is the chapter where students either feel confident or feel lost, with little in between. The difference is usually in how carefully the sample space is defined. Before using any formula, write down in words what one outcome looks like and whether all outcomes are equally likely.

Bayes' theorem questions follow a fixed shape: several causes, each with a prior probability, and an observed result. Draw a tree. A tree diagram turns almost every Bayes question into two multiplications and one division.

Example: bag A has 3 red and 2 black balls; bag B has 1 red and 4 black. A bag is chosen at random and a ball drawn is red. Find the probability it came from bag A.
P(red from A) = 1/2 × 3/5 = 3/10. P(red from B) = 1/2 × 1/5 = 1/10.
P(A | red) = (3/10) ÷ (3/10 + 1/10) = 3/4.

Random variables and their distributions (mean and variance of a discrete distribution) are also in the syllabus and are quick marks once the formulas are familiar. Notes: Probability (Class 11) and Probability (Class 12).

A four-week plan for all four chapters

If these chapters have been taught but feel shaky, this plan brings them to exam level in a month alongside your other work. It assumes about an hour a day for algebra.

After the month, keep a short weekly mixed set going so the methods do not fade. Timed daily practice on NCERT-level questions is also available free on our Daily NCERT test series.

Common questions