AP EAMCET · Maths · Functions
If \([x]\) denotes the greatest integer function on \(x\), then the number of positive integral divisors of \(\left[(2+\sqrt{3})^5\right]\) is
- A 6
- B 4
- C 2
- D 8
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
\begin{aligned} & (2+\sqrt{3})^5={ }^5 C_0 \cdot 2^5 \cdot(\sqrt{3})^0+{ }^5 C_1 \cdot 2^4 \cdot(\sqrt{3}) \\ & { }^5 C_2 \cdot 2^3(\sqrt{3})^2+{ }^5 C_3 \cdot 2^2 \cdot(\sqrt{3})^3 \\ & +{ }^5 C_4 \cdot 2 \cdot(\sqrt{3})^4+{ }^5 C_5 \cdot 2^0(\sqrt{3})^5 \\ & =32+80…
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