A) Not a prime
B) An even number
C) Not an odd number
D) None of these
Correct Answer: A
Solution :
111?..1 (91 times) = \[1+10+{{10}^{2}}+.....+{{10}^{90}}\] = \[\frac{{{10}^{91}}-1}{10-1}=\frac{{{({{10}^{7}})}^{13}}-1}{10-1}\]= \[\frac{{{t}^{13}}-1}{9}\], where \[t={{10}^{7}}\] = \[\left( \frac{t-1}{9} \right)\,({{t}^{12}}+{{t}^{11}}+.....+t+1)\] = \[\left( \frac{{{10}^{7}}-1}{10-1} \right)\,(1+t+{{t}^{2}}+....+{{t}^{12}})\] \[=(1+10+{{10}^{2}}+....+{{10}^{6}})(1+t+{{t}^{2}}+...+{{t}^{12}})\] \ \[111.....1(91\,\,\text{times)}\] is a composite number.
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