If mRn={(m,n):(m-n) is divisible by 5} then find `(3Rn)cap(5Rn)`

If mRn=[(m,n):m-n is divisible by 5}is the relation with N set,find (3Rn)cap(5Rn)

5^(2n+1)+3^(4n+2) (n in N) is divisible by

10^(n)+3*4^(2)+5 is always divisible by the number -

Applying the principle mathematical induction (P.M.I.) show that 5^(2n+2)-24n-25 is always divisible by 576 where n is a natural number.

Show that by mathematical induction, 3.5^(2n+1) + 2^(3n+1) is divisible by 17, when n > =0 is an integer.

Prove that 2.7^(n)+ 3.5^(n)-5 is divisible by 24 for all n in N

10^(n) +3.4 ^(n+2)+5 is always divisible by (for all n in N) -

The contrapositives of few conditional statements are given below , find the conditional statements : If the sum of digits in a positive integer n is not divisible by 3 , then the integer n is not divisible by 3 .

If .^(n)C_(5)=.^(n)C_(3) , then find .^(n)C_(4) .

If f and g are two functions defined on N , such that f(n)= {{:(2n-1if n is even), (2n+2 if n is odd):} and g(n)=f(n)+f(n+1) Then range of g is (A) {m in N : m= multiple of 4 } (B) { set of even natural numbers } (C) {m in N : m=4k+3,k is a natural number (D) {m in N : m= multiple of 3 or multiple of 4 }