Question

Choose the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}{2}^n=1024,\mathrm{then}{2}^{\left(\frac{n}{2}+2\right)}= \\ \left(\mathrm{a}\right)64\left(\mathrm{b}\right)128\left(\mathrm{c}\right)256\left(\mathrm{d}\right)512 \end{gathered}$$

Answer 1

$$\begin{gathered} \mathrm{As},2^n=1024 \\ \Rightarrow 2^n=2^{10} \\ \mathrm{Comparing}\mathrm{the}\mathrm{exponent}\mathrm{of}\mathrm{both}\mathrm{the}\mathrm{sides},\mathrm{we}\mathrm{get} \\ n=10 \\ \mathrm{Now}, \\ {2}^{\left(\frac{n}{2}+2\right)} \\ =2^{\left(\frac{10}{2}+2\right)} \\ =2^{\left(5+2\right)} \\ =2^7 \\ =128 \end{gathered}$$

Hence, the correct alternative is option (b).