Correct Answer: 2

Solution : Given: $x+\frac{1}{x}=2$
Squaring both sides, we get
⇒ $(x+\frac{1}{x})^2=2^2$
⇒ $x^2+\frac{1}{x^2}+2\times x\times\frac{1}{x}=4$
⇒ $x^2+\frac{1}{x^2}=4-2$
⇒ $x^2+\frac{1}{x^2}=2$
Again squaring both sides, we get:
⇒ $(x^2+\frac{1}{x^2})^2=2^2$
⇒ $x^4+\frac{1}{x^4}+2\times x^2\times\frac{1}{x^2}=4$
⇒ $x^4+\frac{1}{x^4}=4-2$
⇒ $x^4+\frac{1}{x^4}=2$
Hence, the correct answer is 2.