(112 x 54) = 112 x | ❨ | 10 | ❩ | 4 | = | 112 x 104 | = | 1120000 | = 70000 |
2 | 24 | 16 |
106 x 106 - 94 x 94 | = (106)2 - (94)2 |
= (106 + 94)(106 - 94) [Ref: (a2 - b2) = (a + b)(a - b) ] | |
= (200 x 12) | |
= 2400. |
Given Exp. = | (1000)9 | = | (103)9 | = | (10)27 | = 10(27-24) = 103 = 1000 |
1024 | 1024 | 1024 |
But, unit digit in (74)26 = 1
∴ Unit digit in 7105 = (1 x 7) = 7
∴ 10 x Quotient = 230 ⟹ = | 230 | = 23 |
10 |
Dividend = (Divisor x Quotient) + Remainder
= (230 x 23) + 46
= 5290 + 46
= 5336.
x = 357 x y + 39
= (17 x 21 x y) + (17 x 2) + 5
= 17 x (21y + 2) + 5)
∴Required remainder = 5.
587 x 999 | = 587 x (1000 - 1) |
= 587 x 1000 - 587 x 1 | |
= 587000 - 587 | |
= 586413. |
∴Sum = | n | (a + l) | = | 50 | x (51 + 100) = (25 x 151) = 3775. |
2 | 2 |
Unit digit in 358 = Unit digit in [(34)14 x 32]
= Unit digit in [Unit digit in (81)14 x 32]
= Unit digit in [(1)14 x 32]
= Unit digit in (1 x 9)
= Unit digit in (9)
= 9
Unit digit in (795 - 358) = Unit digit in (343 - 9) = Unit digit in (334) = 4.
So, Option B is the answer.
The smallest 5-digit number = 10000. 41) 10000 (243 82 --- 180 164 ---- 160 123 --- 37 --- Required number = 10000 + (41 - 37) = 10004.
4500 x x = 3375 ⟹ x = | = | 3 | |
4 |
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