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प्रश्न
How many two-digits numbers are divisible by 3?
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उत्तर
The two-digit numbers divisible by 3 are 12, 15, 18, ..., 99.
Clearly, these number are in AP.
Here, a = 12 and d =15 - 12 = 3
Let this AP contains n terms. Then,
an = 99
⇒ 12 + (n-1) × 3 =99 [an = a + (n-1) d]
⇒ 3n + 9 =99
⇒ 3n = 99 - 9 = 90
⇒ n = 30
Hence, there are 30 two-digit numbers divisible by 3.
संबंधित प्रश्न
If Sn1 denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 ×(5 + 3)]
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