Answer:
Option D
Explanation:
Key Idea = $(a+b)^{n}+(a-b)^{n}$
= $2(^{n}C_{0}a^{n}+^{n}C_{2}a^{n-2}b^{2}+^{n}C_{4}a^{n-4}b^{4}.....)$
We have,
$(x+\sqrt{x^{3}-1})^{5}+(x-\sqrt{x^{3}-1})^{5},x>1$
= $ 2(^{5}C_{0}x^{5}+^{5}C_{2}x^{3}(\sqrt{x^{3}-1})^{2}+^{5}C_{4}x(\sqrt{x^{3}-1})^{4})$
= $ 2(x^{5}+10x^{3}(x^{3}-1)+5x(x^{3}-1)^{2})$
= $ 2(x^{5}+10x^{6}-10x^{3}+5x^{7}- 10x^4+5x)$
Sum of coefficients of all odd degree terms is 2 (1-10+5+5)=2
