NCERT Solutions For Class 10 Maths Chapter 1 Real Numbers

NCERT Solutions For Class 10 Maths Chapter 1 Real Numbers 

NCERT Solutions For Class 10 Maths Chapter 1 Real Numbers Ex 1.1

Ex 1.1 Class 10 Maths Question 1.

Use Euclid’s Division Algorithm to find the HCF of:
(i) 135 and 225
(ii) 196 and 38220
(iii) 867 and 255
Solution:

Ex 1.1 Class 10 Maths Question 2.

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

Ex 1.1 Class 10 Maths Question 3.
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?
Solution:

Ex 1.1 Class 10 Maths Question 4.
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.
Solution:

Ex 1.1 Class 10 Maths Question 5.
Use Euclid’s Division Lemma to show that the cube of any positive integer is either of the form 9m, 9m + 1 or 9m + 8.
Solution:

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Class 10 Maths Real Numbers

Rational numbers and irrational numbers are taken together form the set of real numbers. The set of real numbers is denoted by R. Thus every real number is either a rational number or an irrational number. In either case, it has a non–terminating decimal representation. In the case of rational numbers, the decimal representation is repeating (including repeating zeroes) and if the decimal representation is non–repeating, it is an irrational number. For every real number, there corresponds a unique point on the number line ‘l’ or we may say that every point on the line ‘l’ corresponds to a real number (rational or irrational).

From the above discussion we may conclude that:
To every real number there corresponds a unique point on the number line and conversely, to every point on the number line there corresponds a real number. Thus we see that there is one–to–one correspondence between the real numbers and points on the number line ‘l’, that is why the number line is called the ‘real number line’.

Maths NCERT Solutions For Class 10 Chapter 1 Ex 1.2

Ex 1.2 Class 10 Maths Question 1.
Express each number as a product of its prime factors:
(i) 140
(ii) 156
(iii) 3825
(iv) 5005
(v) 7429
Solution:

Ex 1.2 Class 10 Maths Question 2.

Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = Product of the two numbers:
(i) 26 and 91
(ii) 510 and 92
(iii) 336 and 54
Solution:

Ex 1.2 Class 10 Maths Question 3.
Find the LCM and HCF of the following integers by applying the prime factorization method:
(i) 12, 15 and 21
(ii) 17, 23 and 29
(iii) 8, 9 and 25
Solution:

Ex 1.2 Class 10 Maths Question 4:
Given that HCF (306, 657) = 9, find LCM (306, 657).

Ex 1.2 Class 10 Maths Question 5.
Check whether 6n can end with the digit 0 for any natural number n.

Ex 1.2 Class 10 Maths Question 6.
Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.

Ex 1.2 Class 10 Maths Question 7.
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?
Solution:

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3

Ex 1.3 Class 10 Maths Question 1.
Prove that √5 is irrational.
Solution:

Ex 1.3 Class 10 Maths Question 2.

Show that 3 + √5 is irrational.
Solution:

Ex 1.3 Class 10 Maths Question 3.
Prove that the following are irrational.

Solution:

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4

Ex 1.4 Class 10 Maths Question 1.
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or non-terminating repeating decimal expansion:

Ex 1.4 Class 10 Maths Question 2.

Write down the decimal expansions of those rational numbers in question 1, which have terminating decimal expansions.

Ex 1.4 Class 10 Maths Question 3.
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 , what can you say about the prime factors of q?
(i) 43. 123456789
(ii) 0.120120012000120000…
(iii) 43. 

Real Numbers Class 10 Extra Questions Maths Chapter 1

Extra Questions for Class 10 Maths Chapter 1 Real Numbers. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.