Question

(a,b) Unit digit in ( left(7^{95}right) )
( = ) Unit digit in ( left[left(7^{4}right)^{23} times 7^{3}right] )
( = ) Unit digit in ( 7^{3} ) (as unit digit in ( 7^{4}=1 ) )
( = ) Unit digit in 343 Unit digit in ( 3^{58}= ) Unit digit in ( left(3^{4}right)^{4} times 3^{2} ) [as unit digit ( left.3^{4}=1right] ) = Unit digit is 9 So unit digit in ( left(7^{95}-3^{58}right) ) ( = ) Unit digit in ( (343-9) ) ( = ) Unit digit in ( 334=4 ) Unit digit in ( left(7^{95}+3^{58}right)= ) Unit digit in ( (343+9) )
( = ) Unit digit in ( 352=2 )
So the product is ( 4 times 2=8 )

# The product of unit digit in (795 – 358) and (795 +358) is (a) cube of 2 (b) lies between 6 and 10 (c) 6 (d) lies between 3 and 6

Solution