Question

Find the unit's digit in the product 735x371x1155.

NEET/Medical Exams

Maths

Solution

115

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Units digit in ( left(7^{4}right)=1 . ) Therefore, units digit in ( left(7^{4}right)^{8} ) i.e., ( 7^{32} ) will be 1. Hence, units digit in [ (7)^{35}=1 times 7 times 7 times 7=3 ] Again, units digit in ( (3)^{4}=1 ) Therefore, units digit in the expansion of [ left(3^{4}right)^{17}=(3)^{68}=1 ] ( Rightarrow ) Units digit in the expansion of [ left(3^{71}right)=1 times 3 times 3 times 3=7 ] and units digit in the expanison of ( left(11^{35}right)=1 ) Hence, units digit in the expansion of [ 7^{35} times 3^{71} times 11^{55}=3 times 7 times 1=1 ]