Given Exp. = | 800 | x | 1296 | = 450 |
64 | 36 |
3897 x 999 | = 3897 x (1000 - 1) |
= 3897 x 1000 - 3897 x 1 | |
= 3897000 - 3897 | |
= 3893103. |
(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.
9 + | 3 | + 7 + | 2 | - | ❨ | 9 + | 1 | ❩ | =? |
4 | 17 | 15 |
Given sum |
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∴(6767 + 1) will be divisible by (67 + 1)
∴(6767 + 1) + 66, when divided by 68 will give 66 as remainder.
(217)2 + (183)2 | = (200 + 17)2 + (200 - 17)2 |
= 2 x [(200)2 + (17)2] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)] | |
= 2[40000 + 289] | |
= 2 x 40289 | |
= 80578. |
2056 x 987 | = 2056 x (1000 - 13) |
= 2056 x 1000 - 2056 x 13 | |
= 2056000 - 26728 | |
= 2029272. |
This is an A.P. in which a = 24, d = 6 and l = 96
Let the number of terms in it be n.
Then tn = 96 ⟹ a + (n - 1)d = 96
⟹ 24 + (n - 1) x 6 = 96
⟹ (n - 1) x 6 = 72
⟹ (n - 1) = 12
⟹ n = 13
Required number of numbers = 13.
87) 13601 (156 87 ---- 490 435 ---- 551 522 --- 29 --- Therefore, the required number = 29.
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
∴ P = 1.
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