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- Question
The sum of first 45 natural numbers is:
Options- A. 1035
- B. 1280
- C. 2070
- D. 2140
- 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.
- 1.
854 x 854 x 854 - 276 x 276 x 276 =? 854 x 854 + 854 x 276 + 276 x 276
Options- A. 1130
- B. 578
- C. 565
- D. 1156
- E. None of these Discuss
- 2. The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?
Options- A. 12⁄35
- B. 1⁄35
- C. 35⁄8
- D. 7⁄32 Discuss
- 3. If 1400 x x = 1050. Then, x =?
Options- A. 1⁄4
- B. 3⁄5
- C. 2⁄3
- D. 3⁄4
- E. None of these Discuss
- 4. Which one of the following numbers is completely divisible by 45?
Options- A. 181560
- B. 331145
- C. 202860
- D. 2033555
- E. None of these Discuss
- 5. A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) =?
Options- A. 10
- B. 11
- C. 12
- D. 15 Discuss
- 6. 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
- 7. What is the unit digit in (4137)754?
Options- A. 1
- B. 3
- C. 7
- D. 9 Discuss
- 8. How many 3-digit numbers are completely divisible 6?
Options- A. 149
- B. 150
- C. 151
- D. 166 Discuss
- 9. What is the unit digit in {(6374)1793 x (625)317 x (341491)}?
Options- A. 0
- B. 2
- C. 3
- D. 5 Discuss
- 10. (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 Discuss
Numbers problems
Search Results
Correct Answer: 578
Explanation:
| Given Exp. = | (a3 - b3) | = (a - b) = (854 - 276) = 578 |
| (a2 + ab + b2) |
Correct Answer: 12⁄35
Explanation:
Let the numbers be a and b . Then, a + b = 12 and ab = 35.
| ∴ | a + b | = | 12 | ⟹ | ❨ | 1 | + | 1 | ❩ | = | 12 |
| ab | 35 | b | a | 35 |
| ∴ Sum of reciprocals of given numbers = | 12 |
| 35 |
Correct Answer: 3⁄4
Explanation:
| 1400 x x = 1050 ⟹ x = | 1050 | = | 3 |
| 1400 | 4 |
Correct Answer: 202860
Explanation:
45 = 5 x 9, where 5 and 9 are co-primes.
Unit digit must be 0 or 5 and sum of digits must be divisible by 9.
Among given numbers, such number is 202860.
Correct Answer: 10
Explanation:
4 a 3 | 9 8 4 } ==> a + 8 = b ==> b - a = 8 13 b 7 |Also, 13 b 7 is divisible by 11 ⟹ (7 + 3) - ( b + 1) = (9 - b )
⟹ (9 - b) = 0
⟹ b = 9
∴ (b = 9 and a = 1) ⟹ (a + b) = 10.
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: 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: 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: 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: n is any natural number
Explanation:
For every natural number n , ( x n - a n ) is completely divisible by ( x - a ).
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