Class 10th NCERT Maths Complete Exercise 1.1 solution in 2025 [HBSE/CBSE Board]
Class 10th NCERT Maths Complete Exercise 1.1 solution in 2025 [HBSE/CBSE Board]
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Class-10th Math Complete Exercise-1.1 Solution |
Class-10th
Chapter-1 (Real Numbers)
Exercise- 1.1
Que-1 Express each number as a prime factors:-
(i) 140
Solution-
Prime Factor of 140 = 2 x 2 x 5 x 7
(ii) 156
Prime Factor of 156 = 2 x 2 x 3 x 13
(iii) 3825
Solution-
Prime Factor of 3825 = 3 x 3 x 5 x 5 x 17
(iv) 7429
Solution-
Prime Factor of 7429 = 17 x 19 x 23
(v) 5005
Prime Factor of 5005 = 5 x 7 x 11 x 13Que-2 Find the LCM and HCF off the following pairs of integers and verify that LCM x HCF = Product of the two numbers.
(i) 26 and 91
26 = 2x13
91 = 7x13
HCF = 13
LCM = 2x7x13 = 182
LCM x HCF = Product of the two numbers
182x13 = 26x91
2366 = 2366
(ii) 510 and 92
510 = 2x3x5x17
92 = 2x2x23
HCF = 2
LCM = 2x2x3x5x17x23 = 23460
LCM x HCF = Product of the two numbers
23460x2 = 510x92
46920 = 46920
(iii) 336 and 54
336 = 2x2x2x2x3x7
54 = 2x3x3x3
HCF = 2x3 = 6
LCM = 2x2x2x2x3x3x3x7 = 3024
LCM x HCF = Product of the two numbers
3024x6 = 336x54
18144 = 18144
Que- 3 Find the LCM and HCF of the following in teasers by applying the prime factorisation method.
(i) 12, 15 and 21
12 = 2x2x3
15 = 3x5
21 = 3x7
HCF = 3
LCM = 2x2x3x5x7 = 420
(ii) 17, 23 and 29
17 = 1x17
23 = 1x23
29 = 1x29
HCF = 1
LCM = 1x17x23x29 = 11339
(iii) 8, 9 and 25
Solution-
8 = 2x2x2x1
9 = 3x3x1
25 = 5x5x1
HCF = 1
LCM = 2x2x2x3x3x5x5
= 8x9x25 = 1800
Que. 4 Give that HCF(306,657) = 9, Find LCM(306,657).
Solution-
First number = 306
Second number = 657
HCF(306,657) = 9
LCM(306,657) = ?
We Know that- LCM x HCF = Product of the numbers
LCM x 9 = 306x657
LCM = 306x657
9
LCM = 34x657
LCM = 22338
Que-5 Check whether 6n can end with the digit 0 for any natural number n.
Since 5 is not a prime factor of 6
Therefore, 6n can not end with zero.
Que- 6 Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 a composite numbers.
Let,
x = 7 x 11 x 13 + 13
= 13 [7 x 11 x 1 + 1]
= 13 [78]
= 13 x 2 x 3 x 13
= 2 x 3 x 13 x 13
y = 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5
= 5 [7 x 6 x 1 x 4 x 3 x 2 x 1 + 1]
= 5 [1009]
= 5 x 1009
Both numbers, x and y have factors other than one
Therefore, these numbers are composite numbers.
Que-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?
The minimum time they will meet is the LCM of 12 and 18
12 = 2x2x3
18 = 2x3x3
LCM(12 and 18) = 2x2x3x3
= 36
Sonia and Ravi meet at starting point after 36 minutes.
