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- Question
(xn - an) is completely divisible by (x - a), when
Options- A. n is any natural number
- B. n is an even natural number
- C. n is and odd natural number
- D. n is prime
- Correct Answer
- n is any natural number
Explanation
For every natural number n , ( x n - a n ) is completely divisible by ( x - a ). - 1. What is the unit digit in {(6374)1793 x (625)317 x (341491)}?
Options- A. 0
- B. 2
- C. 3
- D. 5 Discuss
- 2. How many 3-digit numbers are completely divisible 6?
Options- A. 149
- B. 150
- C. 151
- D. 166 Discuss
- 3. What is the unit digit in (4137)754?
Options- A. 1
- B. 3
- C. 7
- D. 9 Discuss
- 4. n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4?
Options- A. 3
- B. 2
- C. 1
- D. 0 Discuss
- 5. The sum of first 45 natural numbers is:
Options- A. 1035
- B. 1280
- C. 2070
- D. 2140 Discuss
- 6. (22 + 42 + 62 + ... + 202) =?
Options- A. 770
- B. 1155
- C. 1540
- D. 385 x 385 Discuss
- 7. 8796 x 223 + 8796 x 77 =?
Options- A. 2736900
- B. 2638800
- C. 2658560
- D. 2716740
- E. None of these Discuss
- 8. How many of the following numbers are divisible by 3 but not by 9?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
Options- A. 5
- B. 6
- C. 7
- D. None of these Discuss
- 9. (12345679 x 72) =?
Options- A. 88888888
- B. 888888888
- C. 898989898
- D. 9999999998 Discuss
- 10. If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:
Options- A. 3
- B. 2
- C. 1
- D. 5
- E. None of these Discuss
Numbers problems
Search Results
Correct Answer: 0
Explanation:
Unit digit in (6374) 1793 = Unit digit in (4) 1793
= Unit digit in [(42)896 x 4]
= Unit digit in (6 x 4) = 4
Unit digit in (625)317 = Unit digit in (5)317 = 5
Unit digit in (341)491 = Unit digit in (1)491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
Correct Answer: 150
Explanation:
3-digit number divisible by 6 are: 102, 108, 114,... , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n. Then tn = 996.
∴ a + (n - 1)d = 996
⟹ 102 + (n - 1) x 6 = 996
⟹ 6 x (n - 1) = 894
⟹ (n - 1) = 149
⟹ n = 150
∴ Number of terms = 150.
Correct Answer: 9
Explanation:
Unit digit in (4137) 754 = Unit digit in {[(4137) 4 ] 188 x (4137) 2 }
=Unit digit in { 292915317923361 x 17114769 }
= (1 x 9) = 9
Correct Answer: 2
Explanation:
Let n = 4 q + 3. Then 2 n = 8 q + 6 = 4(2 q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
Correct Answer: 1035
Explanation:
Let S n = (1 + 2 + 3 + ... + 45)
This is an A.P. in which a = 1, d = 1, n = 45 and l = 45
| ∴Sn = | n | (a + l) | = | 45 | x (1 + 45) = (45 x 23) = 1035 |
| 2 | 2 |
Required sum = 1035.
Correct Answer: 1540
Explanation:
(2 2 + 4 2 + 6 2 + ... + 20 2 ) = (1 x 2) 2 + (2 x 2) 2 + (2 x 3) 2 + ... + (2 x 10) 2
= (22 x 12) + (22 x 22) + (22 x 32) + ... + (22 x 102)
= 22 x [12 + 22 + 32 + ... + 102]
| [ | Ref: (12 + 22 + 32 + ... + n2) = | 1 | n(n + 1)(2n + 1) | ] | |
| 6 |
| = | ❨ | 4 x | 1 | x 10 x 11 x 21 | ❩ |
| 6 |
= (4 x 5 x 77)
= 1540.
Correct Answer: 2638800
Explanation:
| 8796 x 223 + 8796 x 77 | = 8796 x (223 + 77) [Ref: By Distributive Law ] |
| = (8796 x 300) | |
| = 2638800 |
Correct Answer: 6
Explanation:
Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s
2133 → 9 (X)
2343 → 12 (/)
3474 → 18 (X)
4131 → 9 (X)
5286 → 21 (/)
5340 → 12 (/)
6336 → 18 (X)
7347 → 21 (/)
8115 → 15 (/)
9276 → 24 (/)
Required number of numbers = 6.
Correct Answer: 888888888
Explanation:
| 12345679 x 72 | = 12345679 x (70 +2) |
| = 12345679 x 70 + 12345679 x 2 | |
| = 864197530 + 24691358 | |
| = 888888888 |
Correct Answer: 3
Explanation:
Given number = 97215 x 6
(6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11.
∴ x = 3
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