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JEE Main · Mathematics — Algebra · Maharashtra, India

Mathematics — Algebra for the JEE Main Exam — Maharashtra candidates

8% of the JEE Main test plan. Complex numbers, quadratic equations, matrices and determinants, sequences and series, binomial theorem — approximately 25% of JEE Mathematics. Calibrated for Maharashtrian candidates.

Examiners do not award marks for content alone — they award them for the ability to demonstrate competency in the precise format the test demands. Mathematics — Algebra sits at roughly 8% of the Joint Entrance Examination Main content distribution — Algebra is the most diverse Maths section in JEE, spanning discrete topics that each require their own techniques. Matrices and determinants, complex numbers, and quadratic theory each appear in JEE Advanced as multi-mark questions. Sequence-and-series problems are high-frequency in JEE Main. Pass rates for the JEE Main are published annually by the awarding body and vary by cohort and locale. For Maharashtra candidates preparing for JEE Main, the calibration of study to local context matters: Maharashtra hosts the largest single-state JEE Main, NEET, and CET cohorts in India. MHT-CET is the state-level entrance test; many candidates sit JEE Main, MHT-CET, and NEET in the same year.

Pass rates for JEE Main (Maharashtra, India) are published periodically by the awarding body.

Common failure modes

These are the patterns that cause most candidates to lose marks on this topic. Recognising them in advance is half the work.

  • !Forgetting that complex cube roots of unity ω satisfy 1 + ω + ω² = 0
  • !Misapplying Vieta's formulas (sum/product of roots) when roots are complex
  • !Expanding (a+b)^n with incorrect binomial coefficients — especially middle-term errors
  • !Row-reducing a matrix to find the inverse without tracking the elementary operations correctly
  • !Confusing arithmetic and geometric progression sum formulas under time pressure

Study tips

  • 1Memorise the three properties of cube roots of unity: ω³ = 1, 1 + ω + ω² = 0, ω̄ = ω². These reduce half the complex-number JEE problems.
  • 2Drill the |z₁ + z₂| triangle inequality and the polar/exponential form of complex numbers — JEE Advanced uses both.
  • 3For quadratic theory, practice finding conditions for: (a) both roots positive, (b) roots of opposite sign, (c) imaginary roots. These are standard JEE 'condition' questions.
  • 4Matrix determinant: memorise the 3×3 cofactor expansion and practice the shortcut for triangular matrices (product of diagonal).
  • 5For sequences, do telescoping-sum problems — they appear every year in JEE Main and look harder than they are.
  • 6JEE Main and NEET are offered in Marathi (मराठी) at all Maharashtra centres — choose the medium that matches your school instruction medium for best comprehension speed.
  • 7For NEET: Maharashtra State CET Cell runs separate state-quota counselling alongside MCC all-India counselling — register for both to maximise admission chances.
  • 8Mumbai and Pune are the highest-density centres; book test slots within 30 minutes of your home pin code to avoid Mumbai monsoon-season transit delays on test day.

Sample JEE Main Mathematics — Algebra questions

These sample items mirror the format and difficulty of real JEE Main questions. Practice with thousands more on the free Koydo question bank.

  1. 1

    If ω is a complex cube root of unity, the value of (1 + ω − ω²)³ is:

    • A−8Correct
    • B8
    • C1
    • D−1
    Why this answer?

    Illustrative JEE-style: Since 1 + ω + ω² = 0, we have 1 + ω = −ω². So (1 + ω − ω²)³ = (−ω² − ω²)³ = (−2ω²)³ = −8ω⁶ = −8(ω³)² = −8(1)² = −8.

  2. 2

    The sum of the first n terms of the series 1 + 3 + 5 + 7 + ... is:

    • An(n+1)/2
    • Bn²Correct
    • Cn(n+1)
    • D2n−1
    Why this answer?

    Illustrative JEE-style: This is an arithmetic progression with first term 1 and common difference 2. Sₙ = n/2 × [2(1) + (n−1)(2)] = n/2 × 2n = n².

  3. 3

    The number of terms in the expansion of (x + y)^10 is:

    • A10
    • B11Correct
    • C20
    • D9
    Why this answer?

    Illustrative JEE-style: The binomial expansion (x + y)^n has (n + 1) terms. For n = 10, there are 11 terms.

Frequently asked questions

How many algebra questions appear in JEE Main?
Approximately 6–8 questions out of 30 in Mathematics (roughly 25%). Complex numbers and quadratics together account for 3–4 questions; matrices and sequences contribute the remainder.
Is the binomial theorem tested beyond (a+b)^n expansions?
Yes. JEE tests binomial approximation for |x| < 1, the general term T_{r+1}, and the greatest term and middle term of an expansion. These require formula fluency under time pressure.
What is the JEE Main pass rate for Maharashtrian candidates?
Pass rates for JEE Main candidates in Maharashtra, India are published periodically by the awarding body. Practice questions, full-length simulations, and weak-area drills are the highest-impact way to improve your odds.
How long should Maharashtrian candidates study Mathematics — Algebra for the JEE Main?
For most candidates, focused mastery of Mathematics — Algebra requires 20–40 hours of deliberate practice — drilling sample questions, reviewing failure modes, and timing yourself against exam conditions. Maharashtra hosts the largest single-state JEE Main, NEET, and CET cohorts in India. MHT-CET is the state-level entrance test; many candidates sit JEE Main, MHT-CET, and NEET in the same year. Combine Mathematics — Algebra study with full-length mock exams in the final two weeks before your test date.

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Related study guides

Regulatory citation: NTA JEE Main Information Bulletin — Mathematics syllabus (Complex Numbers, Quadratic Equations, Matrices/Determinants, Sequences and Series, Binomial Theorem).