If the division of a natural number n by 5 leaves a remainder of 3, what might be the ones digit of n?

Let n be a natural number. If the division n -:2 leaves a remaineder of 1, what might be the units digit of n ?

Let n be a natural number. If the division n-:2 leaves no remainder, what might be the unites digit of n ?

Let n be a natural number such that the division n-:5 leaves a remainder of 4, and the division n-:2 leaves a remainder of 1. What must be the units digit of n ?

If n is an even number which leaves a remainder of two when divided by five , what is the remainder if (3n + 7) (2n +5) is divided by 10 /

On the set N of all natural numbers, a relation R is defined as follows: AA n,m in N, n R m Each of the natural numbers n and m leaves the remainder less than 5.Show that R is an equivalence relation. Also, obtain the pairwise disjoint subsets determined by R.

On the set N of all natural numbers, a relation R is defined as follows: n R m Each of the natural numbers n and m leaves the same remainder less than 5 when divided by 5. Show that R is an equivalence relation. Also, obtain the pairwise disjoint subsets determined by R .

Write the cubes of 5 natural number which are of form 3n+1(edotg. 4 ,7, 10 ) and verify the following : The cube of a natural number of the form 3n+1 is a natural number of the same form i.e. when divided by 3 it leaves the remainder 1

Number of three digit natural numbers which on dividing by 6 leaves 3 as the remainder, are (a)149 (b) 150 (c) 148 (d) 151

Consider the numbers 4^n , where n is a natural number. Cheek whether there is any value of n for which 4^n ends with the digit zero.

If the positive integer N leaves a remainder of 3 when divided by 7 , which of the folllowing statements would be ture ? I. 4N + 2 is divisible by 14 II. N^(2) - 2 is divisible by 7 III. (N + 3) ( N + 4) is divisible by 7.