JEE MAIN - Mathematics (2017 - 8th April Morning Slot - No. 2)
If (27)999 is divided by 7, then the remainder is :
1
2
3
6
Explanation
We have,
$${{{{\left( {27} \right)}^{999}}} \over 7}$$
= $${{{{\left( {28 - 1} \right)}^{999}}} \over 7}$$
= $${{28\,\lambda - 1} \over 7}$$
= $${{28\,\lambda - 7 + 7 - 1} \over \lambda }$$
= $${{7\left( {4\lambda - 1} \right) + 6} \over 7}$$
$$\therefore\,\,\,$$ Remainder = 6
$${{{{\left( {27} \right)}^{999}}} \over 7}$$
= $${{{{\left( {28 - 1} \right)}^{999}}} \over 7}$$
= $${{28\,\lambda - 1} \over 7}$$
= $${{28\,\lambda - 7 + 7 - 1} \over \lambda }$$
= $${{7\left( {4\lambda - 1} \right) + 6} \over 7}$$
$$\therefore\,\,\,$$ Remainder = 6
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