Question

Ex.3. The unit's digit in the expansion of (2137)754 is (1) 1 (2) 3 (4) 9 (3) 7

11th - 12th Class

Maths

Solution

163

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Sol. (4) Expression ( =(2137)^{754} ) Unit's digit in ( 2137=7 ) Now, ( 7^{1}=7,7^{2}=49,7^{3}=343,7^{4}=2401 ) ( 7^{5}=16807, ldots ldots ldots . ) Clearly, after index ( 4, ) the unit's digit follow the same order. Dividing index 754 by 4 we get remainder ( =2 ) ( therefore ) Unit's digit in the expansion of ( (2137)^{754}= ) Unit's digit in the expansion of ( (2137)^{2}=9 )