Correct Answer - Option 1 : 40
Given:
The expression is 15 × 25 × 35 × 45 × … × 385
Concept used:
To find the number of zeroes at the end of the product, we need to calculate the number of 2’s and number 5’s or number of pairs of 2 and 5.
2 × 5 = 10 ⇒ Number of zeroes = 1 (number of pair = 1)
The number of pairs of 2 and 5 is same as the number of zeroes at the end of the product
Calculation:
15 × 25 × 35 × 45 × … × 385
In the above expression, number of 2’s is more than the number of 5’s. So we need to calculate the number of 5’s only
Number of 5’s
|
|
No. of 5
|
55
|
(1 × 5)5
|
5
|
105
|
(2 × 5)5
|
5
|
155
|
(3 × 5)5
|
5
|
205
|
(4 × 5)5
|
5
|
255
|
(5 × 5)5
|
10
|
305
|
(6 × 5)5
|
5
|
355
|
(7 × 5)5
|
5
|
Total number of 5’s = 5 + 5 + 5 + 5 + 10 + 5 + 5 =40
There are only 40 pairs of 2 and 5 are possible.
∴ The total number of zeroes is 40.