a) 2

b) 4

c) 6

d) 8

correct answer is: b) 4

Formula use:
a^2+b^2=\left(a+b\right)^2-2.a.b
a^3+b^3=\left(a+b\right)^3-3.a.b\left(a+b\right)

Explanation

Here, given expression is :
\left(x^2+\large\frac{1}{x^2}\right)\normalsize\left(x^3+\large\frac{1}{x^3}\right)
\rightarrow\large\{\normalsize\left(x+\large\frac{1}{x}\right)^2\normalsize-2.x.\large\frac{1}{x}\}\{\normalsize\left(x+\large\frac{1}{x}\right)^3\normalsize-3.x.\large\frac{1}{x}\normalsize\left(x+\large\frac{1}{x}\right)\large\}
According to the question : x+\large\frac{1}{x}\normalsize=2
\therefore\{\left(2\right)^2-2\times1\}\{\left(2\right)^3-3\times1\times2\}
\rightarrow\left(4-2\right)\left(8-6\right)
\rightarrow\left(2\times2\right)
\therefore 4
Ans: 4.