exercise 1.1 class 10 maths
1. Express each number as a product of its prime factors:
(i) 140
140 = 2 x 2 x 5 x 7
= 2² x 5 x 7
(ii) 156
= 2 x 2 x 3 x 13
=2² x 3 x 13
(iii) 3825
= 3 x 3 x 5 x 5 x 17
= 3² x 5² x 17
(iv) 5005
= 5 x 7 x 11 x 13
(iv) 7429
17 x 19 x 23
2. Find the LCM and HCF of following pair of integers and verify that LCM X HCF = product of the two numbers.
(i) 26 and 91
(ii) 510 and 92
(ii) 336 and 54
3. Find the LCM and HCF of the following integers by applying the prime factorisation method.
(i) 12,15 and 21
12 = 2 x 2 x 3
15 = 3 x 5
21 = 3 x 7
HCF (12,15,21) = 3 ( for HCF we take minimum power of the common factor)
LCM (12,15,21) = 2² X 3 X 5 X 7 = 420 ( for LCM we take highest power of every factor)
(ii) 17, 23 and 29
HCF (17,23,29) = 1
LCM (17,23,29) = 17 X 23 X 29
(iii) 8 ,9 and 25
8= 2 X 2 X 2
9= 3 X 3
25=5 X 5
HCF (8,9,25) = 1
LCM(8,9,25) = 2³ X 3² X 5² = 1800
4. Given that HCF (306,657) =9, find LCM (306,657).
5. Check whether 6n can end with the digit 0 for any natural number n.
For a number to end with a digit zero, it must be divisible by 10, which means it must have 10 as a factor in its prime factorization. but 3×2 is the prime factorisation of 6 .Therefore, the prime factorization of any power of 6 is (2 x 3) to the power of n. Since 10 is equal to 2 x 5, for any power of 6 to end in zero, it must have 5 as a factor in its prime factorization. However, since the prime factorization of 6 only contains 2 and 3, there is no way to obtain a factor of 5.Therefore, 6 raised to any power n will not end with the digit zero.
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.
Sol. 7 x 11 x 13 + 13
= 13 ( 7 x 11 + 1) which is a composite number because it has a factor 13.
7 x 6 x 5 x 4 x 3 x 2x 1 + 5
= 5 ( 7 x 6 x 4 x 3 x 2 x 1 + 1) which is a composite number because it has a factor 5.
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 the 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 ?
Sol. Time taken by Sonia to drive one round of the fied = 18 minutes
Time taken by Ravi to drive one round of the field = 12 minutes
Time after which they meet at the starting point= LCM ( 18,12)
18 = 2 x 3²
12 = 2² x 3
LCM(12,18) = 2² x 3² = 36
hence after 36 minutes Sonia and Ravi meet at the starting point.
Ncert Solutions Class 10 Maths Exercise 1.1 https://10thmathsguide.com/exercise-11-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 1.2
Ncert Solutions Class 10 Maths Exercise 2.1 https://10thmathsguide.com/exercise-21-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 2.2
Ncert Solutions Class 10 Maths Exercise 3.1 https://10thmathsguide.com/exercise-31-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 3.2 https://10thmathsguide.com/exercise-32-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 3.3 https://10thmathsguide.com/exercise-33-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 4.1 https://10thmathsguide.com/exercise-41-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 4.2 https://10thmathsguide.com/exercise-42-class-10-maths/
Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/
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