Real Numbers

Real Number | Chapter-1 | NCERT Solutions Maths | Class 10

Reliable Education Group May 11, 2022

Real Numbers

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p q what can you say about the prime factors of q?

Reliable Education Group May 10, 2022

Real Numbers

Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.

Reliable Education Group May 10, 2022

Real Numbers

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

Reliable Education Group May 10, 2022

Real Numbers

Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2

Reliable Education Group May 10, 2022

Real Numbers

Prove that 3 + 2√5 + is irrational.

Reliable Education Group May 10, 2022

Real Numbers

Prove that √5 is irrational.

Reliable Education Group May 10, 2022

Real Numbers

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

Reliable Education Group May 10, 2022

Real Numbers

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

Reliable Education Group May 10, 2022

Real Numbers

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?

Reliable Education Group May 10, 2022

Real Numbers

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

Reliable Education Group May 10, 2022

Real Numbers

Find the LCM and HCF of the following integers by applying the prime factorisation method.

Reliable Education Group May 10, 2022

Real Numbers

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

Reliable Education Group May 10, 2022

Real Numbers

Express each number as a product of its prime factors:

Reliable Education Group May 10, 2022

Real Numbers

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

Reliable Education Group May 10, 2022

Real Numbers

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?

Reliable Education Group May 10, 2022

Real Numbers

Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

Reliable Education Group May 10, 2022

Real Numbers

Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

Reliable Education Group May 10, 2022

Real Numbers

Use Euclid’s division algorithm to find the HCF of:

Reliable Education Group May 10, 2022