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Binomial Theorem — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSBinomial Theorem1 Mark
MCQ
(x - 1)4 + 4(x - 1)3 + 6(x - 1)2 + 4(x - 1) + 1 =
    • A
      x4
    • B
      x3
    • C
      x2
    • D
      1
    ✓

    Answer

    1. x4

    Solution:

    Consider the following identity

    (a + 1)4

    = ((a + 1)2)2

    = (a2 + 2a + 1)2

    = a4 + 4a2 + 1 + 4a3 + 4a + 2a2

    = a4 + 4a3 + 6a2 + 4a + 1 ...(i)

    Comparing i with the given question we get

    a = (x - 1)

    Therefore

    (x - 1)4 + 4(x - 1)3 + 6(x - 1)2 + 4(x - 1) + 1

    = (x - 1 + 1)4 from (i)

    = x4.

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