Real number Test paper

Real number Test paper  

1. Write whether every positive integer can be of the form 4q + 2, where q is an

integer. Justify your answer.

2. “The product of two consecutive positive integers is divisible by 2”. Is this statement

true or false? Give reasons.

3. “The product of three consecutive positive integers is divisible by 6”. Is this statement

true or false”? Justify your answer.

4. Write whether the square of any positive integer can be of the form 3m + 2, where

m is a natural number. Justify your answer.

5. A positive integer is of the form 3q + 1, q being a natural number. Can you write its

square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m? Justify

your answer.

6. The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75. What is

HCF (525, 3000)? Justify your answer.

7. Explain why 3 × 5 × 7 + 7 is a composite number.

8. Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

9. Without actually performing the long division, find if 987/10500

will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.

10. A rational number in its decimal expansion is 327.7081. What can you say about

the prime factors of q, when this number is expressed in the form p/q ? Give reasons.