(3+1)^ 5 -(3+1)^ 5 = - Vidyadip

MCQ

$(\sqrt{3}+1)^{5}-(\sqrt{3}+1)^{5}=$

A
152
B
142
C
124
D
162

✓

Answer

152

Solution:

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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