CLASS 10 SUMS SOLVED

1. sums G.U.H.S
YELLAGONDAPALAYA
ON LINE
Arithmetic
Progression
Vidyagamma

2. [1] ಎರಡು ಅಂಕಿಗಳ ಎಷ್ುು? ಸಂಖ್ಯೆಗಳು 3 ರಂದ ಭಾಗಿಸಲ್ಪಡುತದಯ?
ಪರಹಾರ: 12, 15, 18, …………99
ಇದು ಸಮಾಂತರ ಶಯರೇಢಿಯೇ ? ಹೌದು ಸಮಾಂತರ ಶಯರೇಢಿ , ಇಲ್ಲಿ,
a = 12, d = 3 , an = 99
ಸೂತರ an = a + ( n – 1 ) d ,
99 = 12 + ( n – 1 ) 3 ,
i.e., 99 – 12 = ( n – 1 ) 3 ,
i.e., 87 = (n – 1) 3 ,
i.e., 87 = 3n – 3 ,
i.e., 87 + 3 = 3n
3n = 90
n =
90
3
n = 30
ಎರಡು ಅಂಕಿಗಳ ಎಷ್ುು?
ಸಂಖ್ಯೆಗಳು -- ರಂದ
ಭಾಗಿಸಲ್ಪಡುತದಯ?
[a] 4
[b] 5
[c] 6
[d] 7
[e] 8
ಆದದರಂದ ಎರಡು ಅಂಕಯಗಳ 30 ಸಂಖ್ಯೆಗಳು 3 ರಂದ ಭಾಗಿಸಲ್ಪಡುತೆಯ

3. [2] ಎರಡು ಅಂಕಿಗಳ ಎಷ್ುು? ಸಂಖ್ಯೆಗಳು 3 ರಂದ ಭಾಗಿಸಲ್ಪಡುತದಯ? [ ಪರ್ಾಾಯ ವಿಧಾನ ]
ಪರಹಾರ: 12, 15, 18, …………99
ಇದು ಸಮಾಂತರ ಶಯರೇಢಿಯೇ ? ಹೌದು ಸಮಾಂತರ ಶಯರೇಢಿ , ಇಲ್ಲಿ,
a = 12, d = 3 , an = 99
ಸೂತರ an = a + ( n – 1 ) d ,
99 = 12 + ( n – 1 ) 3 ,
i.e., 99 – 12 = ( n – 1 ) 3 ,
i.e., 87 = (n – 1) 3 ,
i.e., ( n – 1 ) =
87
3
( n – 1 ) = 29
n = 29 + 1
n = 30
ಎರಡು ಅಂಕಿಗಳ ಎಷ್ುು?
ಸಂಖ್ಯೆಗಳು -- ರಂದ
ಭಾಗಿಸಲ್ಪಡುತದಯ?
[a] 4
[b] 5
[c] 6
[d] 7
[e] 8
ಆದದರಂದ ಎರಡು ಅಂಕಯಗಳ 30 ಸಂಖ್ಯೆಗಳು 3 ರಂದ ಭಾಗಿಸಲ್ಪಡುತೆಯ

4. [1] How many two-digits numbers are divisible by 3?
Solutions: The list of two digit numbers divisible by 3 is :
12, 15, 18, …………99
Is this is an A.P? Yes it is , Here, a = 12, d = 3 , an = 99
As an = a + ( n – 1 ) d ,
We have 99 = 12 + ( n – 1 ) 3 ,
i.e., 99 – 12 = ( n – 1 ) 3 ,
i.e., 87 = (n – 1) 3 ,
i.e., 87 = 3n – 3 ,
i.e., 87 + 3 = 3n
3n = 90
n =
90
3
n = 30
How many two-digits
numbers
are divisible by
[a] 4
[b] 5
[c] 6
[d] 7
[e] 8
There are 30 two-digits numbers are divisible by 3

5. [2] How many two-digits numbers are divisible by 3? [ another type]
Formula an = a + ( n – 1 ) d
We have 99 = 12 + ( n – 1 ) 3 ,
i.e., 99 – 12 = ( n – 1 ) 3 ,
i.e., 87 = (n – 1) 3 ,
i.e., ( n – 1 ) =
87
3
( n – 1 ) = 29
n = 29 + 1
n = 30
How many two-digits
numbers
are divisible by
[a] 4
[b] 5
[c] 6
[d] 7
[e] 8
Solutions: The list of two digit numbers divisible by 3 is :
12, 15, 18, …………99
Is this is an A.P? Yes it is , Here, a = 12, d = 3 , an = 99
There are 30 two-digits numbers are divisible by 3

6. [3] ಮೂರು ಅಂಕಿಗಳ ಎಷ್ುು? ಸಂಖ್ಯೆಗಳು 7 ರಂದ ಭಾಗಿಸಲ್ಪಡುತದಯ?
ಪರಹಾರ: 105, 112, 119, …………994
ಇದು ಸಮಾಂತರ ಶಯರೇಢಿಯೇ ? ಹೌದು ಸಮಾಂತರ ಶಯರೇಢಿ , ಇಲ್ಲಿ,
a = 105, d = 7 , an = 994
ಸೂತರ an = a + ( n – 1 ) d ,
We have 994 = 105 + ( n – 1 ) 7 ,
i.e., 994 – 105 = ( n – 1 ) 7 ,
i.e., 889 = (n – 1) 7 ,
i.e., ( n – 1 ) =
889
7
( n – 1 ) = 127
n = 127 + 1
n = 128
ಮೂರು ಅಂಕಿಗಳ ಎಷ್ುು?
ಸಂಖ್ಯೆಗಳು -- ರಂದ
ಭಾಗಿಸಲ್ಪಡುತದಯ?
[a] 4
[b] 5
[c] 6
[d] 9
[e] 8
ಆದದರಂದ ಮೂರು ಅಂಕಯಗಳ 128 ಸಂಖ್ಯೆಗಳು 7 ರಂದ ಭಾಗಿಸಲ್ಪಡುತೆಯ

7. [3] How many three-digits numbers are divisible by 7 ?
Solution: 105, 112, 119, …………994
Is this is an A.P? Yes it is , Here,
a = 105, d = 7 , an = 994
Formula an = a + ( n – 1 ) d ,
We have 994 = 105 + ( n – 1 ) 7 ,
i.e., 994 – 105 = ( n – 1 ) 7 ,
i.e., 889 = (n – 1) 7 ,
i.e., ( n – 1 ) =
889
7
( n – 1 ) = 127
n = 127 + 1
n = 128
How many two-digits
numbers
are divisible by ?
[a] 4
[b] 5
[c] 6
[d] 9
[e] 8
There are 128 three-digits numbers are divisible by 7