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Binomial Theorem — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsBinomial Theorem1 Mark
MCQ
$(\sqrt{3}+1)^{5}-(\sqrt{3}+1)^{5}=$
  • ✓
    $152$
  • B
    $142$
  • C
    $124$
  • D
    $162$
✓

Answer

Correct option: A.
$152$
In the above binomial expansion, the terms at the odd position will get eliminated.
We would be left with
$2({^{5}}\text{C}_{1}(\sqrt{3})^{4}+{^5}\text{C}_{3}(\sqrt{3})^{2}+{^5}\text{C}_{5})$
$=2(5(3^2)+10(3)+1)$
$=2(45+30+1)$
$=2(76)$
$=152$

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