Binomial Theorem

Maths · Class 11

Simulation · Maths · Class 11

Find any term of (a + b)ⁿ

"Find any term of (a + b)ⁿ" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "The general term" in Binomial Theorem. The bars are the binomial coefficients of (a + b)ⁿ. Slide r to pick a term: b comes from r of the n brackets and a from the rest, so the term is nCr aⁿ⁻ʳ bʳ. Tᵣ₊₁ = nCr aⁿ⁻ʳ bʳ. There are n + 1 terms, the powers always add to n, and bars equally far from the ends are equal. JEE Main asked 54 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).

From the lesson The general term in Binomial Theorem. Change the values and watch what happens.

Find any term of (a + b)ⁿMaths · Class 11

In JEE Main

42 shifts analysed

54 questions from Binomial Theorem across the 42 JEE Main shifts Lumi has analysed (2017–2026).

See the past questions

The idea behind it

NCERT §7.2.1

  • The term with k = r in Σ nCk aⁿ⁻ᵏ bᵏ is nCr aⁿ⁻ʳ bʳ. Counting terms from 1, it is the (r + 1)th term: Tᵣ₊₁ = nCr aⁿ⁻ʳ bʳ.
  • Any single term can be written without the full expansion. In (x + 2)⁶ the 4th term has r = 3: 6C3 x³ 2³ = 20 × 8 x³ = 160x³, which matches the full expansion.
  • To find the coefficient of a given power, write the power of x in Tᵣ₊₁ in terms of r and solve for r. In (2x + 1)⁷ the term in x⁴ needs 7 − r = 4, so r = 3 and the coefficient is 7C3 × 2⁴ = 35 × 16 = 560.
  • Always include the number carried by each part of the binomial: a = 2x brings 2 raised to the power of x, and b = −y brings a sign (−1)ʳ.
  • When a = x² and b = 2/x the powers of x combine: in (x² + 2/x)⁶, Tᵣ₊₁ = 6Cr 2ʳ x¹²⁻³ʳ. The term free of x has 12 − 3r = 0, so r = 4 and it equals 6C4 × 2⁴ = 15 × 16 = 240.
  • The largest binomial coefficient of row n sits in the middle: nC(n/2) for even n (for n = 6 it is 20), and the two equal middle ones for odd n.

Questions

3 answers

What does the "Find any term of (a + b)ⁿ" simulation show?
The bars are the binomial coefficients of (a + b)ⁿ. Slide r to pick a term: b comes from r of the n brackets and a from the rest, so the term is nCr aⁿ⁻ʳ bʳ.
Does JEE Main ask questions from Binomial Theorem?
Yes. JEE Main asked 54 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
Is this simulation free?
Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "The general term" in Binomial Theorem (Class 11 Maths).

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