Question

The value of $\frac{2^{2001}+2^{1999}}{2^{2000}-2^{1998}}$, is __________.

• A. $2$
• B. $\frac{10}{3}$
• C. $2^{1000}+1$
• D. $10$

Answer 1

Answer: (B)

$\frac{10}{3}$

Given expression is $\frac{2^{2001}+2^{1999}}{2^{2000}-2^{1998}}=f$

$\Rightarrow f=\frac{2^{2001}+2^{1999}}{2^{2000}-2^{1998}}=\frac{2^{1999}\times (2^2+1)}{2^{1998}\times (2^2-1)}=\frac{2\times 5}{3}=\frac{10}{3}$

Option (B) is correct.