Binomial Theorem

Maths · Class 11

Simulation · Maths · Class 11

Track the power of x in every term

"Track the power of x in every term" is a free, interactive Class 11 Maths simulation for JEE, built on the NCERT section "The general term" in Binomial Theorem. For (x^p + k/x^q)ⁿ, a number line of x-powers marks the exponent np − (p + q)r of each term Tᵣ₊₁; the term free of x lights up where the exponent hits 0. 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.

Track the power of x in every termMaths · Class 11

What it shows

NCERT §7.2.1

For (x^p + k/x^q)ⁿ, a number line of x-powers marks the exponent np − (p + q)r of each term Tᵣ₊₁; the term free of x lights up where the exponent hits 0.

Controls

5 to try

  • Steppern 3–10
  • Stepperp 1–3
  • Stepperq 1–3
  • Sliderr 0–n
  • Stepperk 1–3

Try this

In (x² + 2/x)⁶ find the term free of x and read 240 (r = 4).

Common mistake

Setting only the power of x² to zero instead of combining powers.

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

4 answers

What does the "Track the power of x in every term" simulation show?
For (x^p + k/x^q)ⁿ, a number line of x-powers marks the exponent np − (p + q)r of each term Tᵣ₊₁; the term free of x lights up where the exponent hits 0.
What mistake does the "Track the power of x in every term" simulation fix?
A common mistake it clears up: setting only the power of x² to zero instead of combining powers.
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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