Ncert solutions mathematics class 10 Solutions for Chapter 1 real numbers

Which of the following expressions 3m or 3m + 1 can be used to represent the square of any positive integer m?

Use Euclid’s division algorithm to find the HCF of 135 and 225

Use Euclid’s division algorithm to find the HCF of 196 and 38220

Use Euclid’s division algorithm to find the HCF of 867 and 255.

Which of the following expressions can be used represent the cube of any positive integer?

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Use Euclid's division lemma to identify the correct statement.

Express 7429 as product of its prime factors.

Express 140 as a product of its prime factors.

Express 3825 as a product of its prime factors.

Express 156 as a product of its prime factors.

Express 5005 as product of its prime factors.

Find the LCM and HCF of 26 and 91 and verify that LCM × HCF = product of the two numbers.

Find the LCM and HCF of 510 and 92 and verify that LCM × HCF = product of the two numbers.

Find the LCM and HCF of 336 and 54 and verify that LCM × HCF = product of the two numbers.

Find the LCM and HCF of12,15 and 21 by applying the prime factorisation method.

7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Given that HCF (306, 657) = 9, find LCM (306, 657).

Find the LCM and HCF of 17,23 and 29 by applying the prime factorisation method.

Find the LCM and HCF of 8, 9 and 25 by applying the prime factorisation method.

State whether the following statement is true or false.

6^n can end with the digit 0 for any natural number n.

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

State whether 3 + 2√5 is irrational or rational. Prove it using contradiction method.

State whether 6 + √2 is irrartional or rational. Prove it using method of contradiction.

State whether 2√5 is irrartional or rational. Prove it using method of contradiction.

State whether 3√3 is irrartional or rational. Prove it using method of contradiction.

State whether √5 is irrational or not. Prove it using contradiction method.

State whether 1/√2 is irrartional or rational. Prove it using method of contradiction.

State whether 7√5 is irrartional or rational. Prove it using method of contradiction.

Write down the decimal expansions of 35/50.

Decide whether 43.123456789 is rational or not. If they are

rational, and of the form, p q what can you say about the prime factors of q? Select all the correct answers.

Decide whether 0.120120012000120000. . . is rational or not. If they are rational,

and of the form, p q what can you say about the prime factors of q?

Decide whether 43.\overline{123456789} is rational or not. If they are rational, and of the form, p q what can you say about the prime factors of q?

Write down the decimal expansions of 6/15.

Without actually performing the long division, state whether 15/ 1600 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Without actually performing the long division, state whether 23/(2^35 ^2) will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Without actually performing the long division, state whether

13/3125 will have a terminating decimal expansion or a non-terminating repeating

decimal expansion.

Without actually performing the long division, state whether 64/455 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Without actually performing the long division, state whether 17/8 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Without actually performing the long division, state whether

29/343 will have a terminating decimal expansion or a non-terminating repeating

decimal expansion.

Without actually performing the long division, state whether 129/(2^25 ^77^5 ) will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Without actually performing the long division, state whether 6/15 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Without actually performing the long division, state whether 35/50 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Without actually performing the long division, state whether 77/210 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Write down the decimal expansions of 13/3125.

Write down the decimal expansions of 17/8.

Write down the decimal expansions of 23/ (2^35 ^2).

Write down the decimal expansions of 15/ 1600.