NCERT Class 10th Math chapter 1 Exercise 1.2 Question Answer. NCERT Solution for Class 10 Maths Chapter 1 Exercise 1.2 of real numbers NCERT Solution for CBSE, HBSE, RBSE and Up Board and all other chapters of class 10 math.
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NCERT Class 10 Math chapter 1 Real Numbers Exercise 1.2 Question Answer Solution.
Class 10 Math Chapter 1 Ex. 1.2 Question Answer
1. Express each number as a product of its prime factors:
(i) 140
Ans. 140 = 10 × 14 = 2 × 5 × 2 × 7 = 22 × 5 × 7
Therefore,
Prime factorization of 140 = 22 × 51 × 71
(ii) 156
Ans. 156 = 4 × 39 = 2 ×2 ×3 ×13 = 22 × 3 ×13
Therefore,
Prime factorization of 156 = 22 × 31 ×131
(iii) 3825
Ans. 3825 = 5 × 765 = 5 × 5 × 153 = 5 × 5 × 9 × 17 = 32 × 52 × 171
Therefore,
Prime factorization of 3825 = 32 × 52 × 171
(iv) 5005
Ans. 5005 = 5 × 1001 = 5 × 7 × 143 = 5 × 7 × 11 × 13
Therefore,
Prime factorization of 5005 = 51 × 71 × 111 × 131
(v) 7429
Ans. 7429 = 17 × 437 = 17 × 19 × 23
Therefore,
Prime factorization of 7429 = 171 × 191 × 231
2. Find the LCM and HCM of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
(i) 26 and 91
Ans. Prime factorization of
26 = 2 × 13
91 = 7 × 13
HCF(26, 91) = 13
LCM(26, 91) = 2 × 7 × 13 = 182
Now verifying LCM × HCF = product of the two numbers
LCM × HCF = 13 × 182 = 2366
Product of two numbers = 26 × 91 = 2366
L.H.S = R.H.S
Hence verified.
(ii) 510 and 92
Ans. Prime factorization of
510 = 10 × 51 = 2 × 5 × 3 × 17 = 2 × 3 × 5 × 17
92 = 4 × 23 = 22 × 23
HCF(510, 92) = 2
LCM(510, 92) = 22 × 3 × 5 × 17 × 23 = 23,460
Now verifying LCM × HCF = product of the two numbers
LCM × HCF = 2 × 23,460 = 46,920
Product of two numbers = 510 × 92 =46,920
L.H.S = R.H.S
Hence verified.
(iii) 336 and 54
Ans. Prime factorization of
336 = 4 × 84 =4 × 4 × 21 = 24 × 3 × 7
54 = 2 × 27 = 2 × 33
HCF(336, 54) = 2 × 3 = 6
LCM(336, 54) = 24 × 33 × 7 = 3,024
Now verifying LCM × HCF = product of the two numbers
LCM × HCF = 6 × 3024 = 18,144
Product of two numbers = 336 × 54 = 18,144
L.H.S = R.H.S
Hence verified.
3. Find the LCM and HCF of following integers by applying the prime factorization method.
(i) 12, 15 and 21
Ans. Prime factorization of
12 = 2 × 6 = 2 × 2 × 3 = 22 × 3
15 = 3 × 5
21 = 3 × 7
Now,
HCF(12, 15, 21) = 3
LCM(12, 15, 21) = 22 × 3 × 5 × 7 = 420
(ii) 17, 23 and 29
Ans. Prime factorization of
17 = 1 × 17
23 = 1 × 23
29 = 1 × 29
Now,
HCF(17, 23, 29) = 1
LCM(17, 23, 29) = 1 × 17 × 23 × 29 = 11,339
(iii) 8, 9 and 25
Ans. Prime factorization of
8 = 2 × 2 × 2 =1 × 23
9 = 3 × 3 = 1 × 32
25 = 5 × 5 = 1× 52
Now,
HCF(8, 9, 25) = 1
LCM(8, 9, 25) = 23 × 32 × 52 = 8 × 9 × 25 = 200 × 9 = 1800
4. Given that HCF(306, 657) = 9, find LCM(306, 657).
Ans. As we know that
a × b = LCM × HCF, where a and b are any two numbers.
Applying it
306 × 657 = LCM × 9
Rearranging
LCM = 34 × 657 = 22,338
5. Check whether 6n can end with the digit 0 for any natural number n.
Ans. Let put be the first natural no 1 we get 61 = 6
Now putting n = 2 we get 62 = 36
Now putting n = 3 we get 63 = 216
In every case while we putting any natural value we always get a number ends with 6.
Therefore,
6n can never be end with digit 0 for any natural number n.
6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 are composite numbers.
Ans. Composite numbers are those numbers which having more than two factors.
7 × 11 × 13 + 13 (taking 13 common)
we get 13(7 × 11 +1) = 13 × 78 = 13 × 3 × 26 = 2 × 3 × 132
It has more than 2 factors therefore it is a composite number.
7 × 6 × 5 × 4 × 3 × 2 × 1
This term also has more than 2 factors. Therefore it is also a composite number.
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?
Ans. Time taken by Sonia to drive one round = 18 min
Time taken by Ravi to drive one round = 12 min
After how many minutes will they meet again in starting point is basically we have to find the LCM of both.
Prime Factorization of
12 = 22 ×3
18 = 2 × 32
LCM(12, 18) = 22 × 32 = 36
Therefore,
After 36 minutes both Ravi and Sonia meet again at the starting point.