A) 33
B) 30
C) 34
D) 31
Correct Answer: A
Solution :
\[{{(2000)}^{10}}=1.024\times {{10}^{k}}\] \[\Rightarrow \] \[{{(2\times {{10}^{3}})}^{10}}=\frac{1024}{1000}\times {{10}^{k}}\] \[\Rightarrow \] \[{{2}^{10}}\times {{10}^{30}}=1024\times {{10}^{k-3}}\] \[\Rightarrow \] \[{{2}^{10}}\times {{10}^{30}}={{2}^{10}}\times {{10}^{k-3}}\] \[\Rightarrow \] \[30=k-3\] \[\Rightarrow \] \[k=33\]
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