A) An irrational number
B) 0
C) A natural number
D) None of these
Correct Answer: C
Solution :
[c] \[\sqrt{5}\left[ {{\left( \sqrt{5}+1 \right)}^{50}}-{{\left( \sqrt{5}-1 \right)}^{50}} \right]\] \[=2\sqrt{5}\left[ ^{50}{{C}_{1}}{{\left( \sqrt{5} \right)}^{49}}+{{\,}^{50}}{{C}_{3}}{{\left( \sqrt{5} \right)}^{47}}+.... \right]\] \[=2\left[ ^{50}{{C}_{1}}{{\left( \sqrt{5} \right)}^{50}}+{{\,}^{50}}{{C}_{3}}{{\left( \sqrt{5} \right)}^{48}}+.... \right]\] = a natural number
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