| If \[{{(2000)}^{10}}=1.024\times {{10}^{k}},\]then the value of k is [SSC (CPO) 2011] |
A) 33
B) 30
C) 34
D) 31
Correct Answer: A
Solution :
| (a) \[{{(2000)}^{10}}=1024\times {{10}^{k}}\] |
| \[\Rightarrow \]\[{{(2\times 1000)}^{10}}=1.024\times {{10}^{k}}\] \[\Rightarrow \]\[{{(2\times {{10}^{3}})}^{10}}=\frac{1024}{1000}\times {{10}^{k}}\] |
| \[\Rightarrow \]\[{{2}^{10}}\times {{10}^{30}}=1024\times {{10}^{k-3}}\] \[[\because {{(PQ)}^{n}}={{P}^{n}}\times {{Q}^{n}}]\] |
| \[\Rightarrow \]\[{{2}^{10}}\times {{10}^{30}}={{2}^{10}}\times {{10}^{k-3}}\] |
| On comparing the powers, we get \[30=k-3\]\[\Rightarrow \]\[k=33\] |
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