Show that one and only one out of p, p + 2 or p + 4 is divisible by 3.

Given below are two pairs of statements. Combine these two statements using if and only if : p : If the sum of digits of a number is divisible by 3, then the number is divisible by 3. q : If a number is divisible by 3, then the sum of its digits is divisible by 3.

Combine the following statements using "if and only if' p: if the sum of digit of a number is divisible by3, then the numebr is divisible by 3.

If P (n) is the statement : "n (n + 1) (n + 2) is divisible by 12”, prove that P(3) and P(4) are true, but P(5) is not true.

Find the product: p xx q^2 xx p^3 xx p ^4

Which one of the following is the zero of p(x) = 3x + 1 on dividing :

If p = – 2, find the value of – 3p^2 + 4p + 7

Consider a number N = 2 1 P 5 3 Q 4. The number of ordered pairs (P,Q) so that the number 'N' is divisible by 44, is

If p is a natural number, then prove that p^(n+1) + (p+1)^(2n-1) is divisible by p^(2) + p +1 for every positive integer n.

Consider a number N=21 P 5 3 Q 4. The number of ordered pairs (P,Q) so that the number' N' is divisible by 9, is