Binomial Theorem

Class 11 · Mathematics

47 questions20 easy12 medium15 hard

Sample Questions

Q1.The identity ⁿC₀ + ⁿC₁ + ... + ⁿCₙ = 2ⁿ can be proved using the binomial theorem by substituting:

  • Ax = 0 in (1+x)ⁿ
  • Bx = 1 in (1+x)ⁿ
  • Cx = –1 in (1+x)ⁿ
  • Dx = 2 in (1+x)ⁿ

Q2.The coefficient of x² in (1+x+x²)⁴ is:

  • A10
  • B13
  • C16
  • D6

Q3.The binomial theorem for (a+b)ⁿ is valid for all n that are:

  • AReal numbers
  • BPositive integers (in NCERT Class 11 scope)
  • CPositive even integers
  • DAny integers

Q4.The term independent of x in the expansion of (x + 1/x)⁶ is:

  • A15
  • B20
  • C10
  • D6

Q5.The value of C₀ + 2C₁ + 3C₂ + ... + (n+1)Cₙ where Cᵣ = ⁿCᵣ is:

  • A(n+2)·2ⁿ⁻¹
  • Bn·2ⁿ⁻¹
  • C(n+1)2ⁿ
  • D2ⁿ⁺¹

Q6.This is a sample question to preview what you'll get in the full practice test...

  • A. Option one
  • B. Option two
  • C. Option three
  • D. Option four
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Concepts Covered

Applications of binomial theoremBinomial coefficientsBinomial theorem statementGeneral termMiddle termParticular termsPascal's triangleProperties of binomial coefficients

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