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Binomial Theorem — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSBinomial Theorem1 Mark
MCQ
The value of $(\sqrt{5}+1)^{5}-(\sqrt{5}-1)^{5} $ is:
  • A
    252
  • B
    352
  • C
    452
  • D
    532
✓

Answer

  1. 352

Solution:

Given, $(\sqrt{5}+1)^{5}-(\sqrt{5}-1)^{5} $

$=(\sqrt{5}+1)^{5}-(\sqrt{5}-1)^{5} $

The even terms will get eliminated.

Hence, we get

2[5C0​ + 5C2​5 + 5C4​52]

= 2 [1 + 50 + 125]

= 2 [176]

= 352.

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