# NCERT Mathematics Class 10 Exemplar Ch 1 Real Numbers Part 4

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**EXERCISE 1.4**

1. Show that the cube of a positive integer of the form is an integer and is also of the form .

Answer: The cube of a positive integer of the form is an integer and is also of the forms , , , , and i.e.,.

2. Prove that one and only one out of , and is divisible by 3, where n is any positive integer.

Answer: one and only one out of , and is divisible by 3.

3. Prove that one of any three consecutive positive integers must be divisible by 3.

Answer: One of any three consecutive positive integers must be divisible by 3.

4. For any positive integer n, prove that is divisible by 6.

Answer: By condition I the number is always divisible by 6, where n is any positive integer.

5. Show that one and only one out of , , , and is divisible by 5, where n is any positive integer.

Answer: One and Only one out of , , and is divisible by 5, where n is any positive integer.