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- Question
If n is a natural number, then (6n2 + 6n) is always divisible by:
Options- A. 6 only
- B. 6 and 12 both
- C. 12 only
- D. by 18 only
- Correct Answer
- 6 and 12 both
Explanation
(6 n 2 + 6 n ) = 6 n ( n + 1), which is always divisible by 6 and 12 both, since n ( n + 1) is always even. - 1. If (64)2 - (36)2 = 20 x x, then x =?
Options- A. 70
- B. 120
- C. 180
- D. 140
- E. None of these Discuss
- 2. {(476 + 424)2 - 4 x 476 x 424} =?
Options- A. 2906
- B. 3116
- C. 2704
- D. 2904
- E. None of these Discuss
- 3. 1397 x 1397 =?
Options- A. 1951609
- B. 1981709
- C. 18362619
- D. 2031719
- E. None of these Discuss
- 4. The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?
Options- A. 240
- B. 270
- C. 295
- D. 360 Discuss
- 5. 5358 x 51 =?
Options- A. 273258
- B. 273268
- C. 273348
- D. 273358 Discuss
- 6. Which of the following numbers will completely divide (4915 - 1)?
Options- A. 8
- B. 14
- C. 46
- D. 50 Discuss
- 7. The unit digit in the product (784 x 618 x 917 x 463) is:
Options- A. 2
- B. 3
- C. 4
- D. 5 Discuss
- 8. Which natural number is nearest to 9217, which is completely divisible by 88?
Options- A. 9152
- B. 9240
- C. 9064
- D. 9184
- E. None of these Discuss
- 9. 107 x 107 + 93 x 93 =?
Options- A. 19578
- B. 19418
- C. 20098
- D. 21908
- E. None of these Discuss
- 10. On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will the remainder?
Options- A. 0
- B. 1
- C. 2
- D. 3 Discuss
Numbers problems
Search Results
Correct Answer: 140
Explanation:
20 x x = (64 + 36)(64 - 36) = 100 x 28
| ⟹ x = | 100 x 28 | = 140 |
| 20 |
Correct Answer: 2704
Explanation:
| Given Exp. | = [(a + b)2 - 4ab], where a = 476 and b = 424 |
| = [(476 + 424)2 - 4 x 476 x 424] | |
| = [(900)2 - 807296] | |
| = 810000 - 807296 | |
| = 2704. |
Correct Answer: 1951609
Explanation:
| 1397 x 1397 | = (1397)2 |
| = (1400 - 3)2 | |
| = (1400)2 + (3)2 - (2 x 1400 x 3) | |
| = 1960000 + 9 - 8400 | |
| = 1960009 - 8400 | |
| = 1951609. |
Correct Answer: 270
Explanation:
Let the smaller number be x . Then larger number = ( x + 1365).
∴ x + 1365 = 6x + 15
⟹ 5x = 1350
⟹ x = 270
∴Smaller number = 270.
Correct Answer: 273258
Explanation:
| 5358 x 51 | = 5358 x (50 + 1) |
| = 5358 x 50 + 5358 x 1 | |
| = 267900 + 5358 | |
| = 273258. |
Correct Answer: 8
Explanation:
( x n - 1) will be divisibly by ( x + 1) only when n is even.
(4915 - 1) = {(72)15 - 1} = (730 - 1), which is divisible by (7 +1), i.e., 8.
Correct Answer: 2
Explanation:
Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2
Correct Answer: 9240
Explanation:
On dividing we get,
88) 9217 (104
88
----
417
352
----
65
----
Therefore, Required number = 9217 + (88 - 65) // Because (88 - 65) < 65.
= 9217 + 23
= 9240.
Correct Answer: 20098
Explanation:
| 107 x 107 + 93 x 93 | = (107)2 + (93)2 |
| = (100 + 7)2 + (100 - 7)2 | |
| = 2 x [(100)2 + 72] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2) ] | |
| = 20098 |
Correct Answer: 1
Explanation:
Number = 269 x 68 + 0 = 18292
67) 18292 (273
134
----
489
469
----
202
201
---
1
---
Therefore, Required remainder = 1
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