Mathematics — Algebra for the JEE Main Exam — Indian candidates

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.
• 6For candidates in India, JEE Main test windows are typically denser in the spring; book test centres in metro cities (Delhi, Mumbai, Bengaluru, Chennai, Kolkata) early to secure preferred dates.

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.

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