other Exam Numerical Ability

find remainder when 19^8+18^7+17^6+16^5+15^4+14^3+13^2+12^1+11^0 divided by 11

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Ans is 9
first divide 19^8/11=19%11*19%.........8 times
19%11=8
so 8*8*8*8*8*8*8%11
=64%11*64%11*64%11*64%11
=9*9*9*9%11=5
so 19^8%11=5.
Use same formula for remainning
final we get
(5+6+5+1+3+5+4+1+1)%11
31%11=9
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other Other Question

If three times the larger of two numbers is divided by the smaller number, we get 4 as the quotient and 3 as the remainder. Also, if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as the remainder. Find the difference between these numbers. 5^2n-6n+8 is always divisible by
a)9
b)8
c)5
d)6