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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.Sn = n [2a + (n - 1)d] = 45 x [2 x 1 + (45 - 1) x 1] = ❨ 45 x 46 ❩ = (45 x 23) 2 2 2 = 45 x (20 + 3)
= 45 x 20 + 45 x 3
= 900 + 135
= 1035.
Shorcut Method:
Sn = n(n + 1) = 45(45 + 1) = 1035. 2 2 - 1. 3251 + 587 + 369 -? = 3007
Options- A. 1250
- B. 1300
- C. 1375
- D. 1200
- E. None of these Discuss
- 2. It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Options- A. (216 + 1)
- B. (216 - 1)
- C. (7 x 223)
- D. (296 + 1) Discuss
- 3. -84 x 29 + 365 =?
Options- A. 2436
- B. 2801
- C. -2801
- D. -2071
- E. None of these Discuss
- 4. The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
Options- A. 3⁄5
- B. 3⁄10
- C. 4⁄5
- D. 4⁄3 Discuss
- 5. Which of the following is a prime number?
Options- A. 33
- B. 81
- C. 93
- D. 97 Discuss
- 6. The difference between the place values of two sevens in the numeral 69758472 is
Options- A. 0
- B. 6993
- C. 699930
- D. None of these Discuss
- 7. If the number 653 xy is divisible by 90, then (x + y) =?
Options- A. 2
- B. 3
- C. 4
- D. 6 Discuss
- 8. The smallest 3 digit prime number is:
Options- A. 101
- B. 103
- C. 109
- D. 113 Discuss
- 9. The difference between the place value and the face value of 6 in the numeral 856973 is
Options- A. 973
- B. 6973
- C. 5994
- D. None of these Discuss
- 10. Which one of the following can't be the square of natural number?
Options- A. 32761
- B. 81225
- C. 42437
- D. 20164
- E. None of these Discuss
Numbers problems
Search Results
Correct Answer: 1200
Explanation:
3251 Let 4207 - x = 3007 + 587 Then, x = 4207 - 3007 = 1200 + 369 ---- 4207 ----
Correct Answer: (296 + 1)
Explanation:
Let 2 32 = x . Then, (2 32 + 1) = ( x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
Correct Answer: -2071
Explanation:
| Given Exp. | = -84 x (30 - 1) + 365 |
| = -(84 x 30) + 84 + 365 | |
| = -2520 + 449 | |
| = -2071 |
Correct Answer: 4⁄5
Explanation:
| Let the required fraction be x. Then | 1 | - x = | 9 |
| x | 20 |
| ∴ | 1 - x2 | = | 9 |
| x | 20 |
⟹ 20 - 20x2 = 9x
⟹ 20x2 + 9x - 20 = 0
⟹ 20x2 + 25x - 16x - 20 = 0
⟹ 5x(4x + 5) - 4(4x + 5) = 0
⟹ (4x + 5)(5x - 4) = 0
| x = | 4 |
| 5 |
Correct Answer: 97
Explanation:
Clearly, 97 is a prime number.
Correct Answer: 699930
Explanation:
Required difference = (700000 - 70) = 699930
Correct Answer: 4
Explanation:
90 = 10 x 9
Clearly, 653xy is divisible by 10, so y = 0
Now, 653x0 is divisible by 9.
So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.
Hence, (x + y) = (4 + 0) = 4.
Correct Answer: 101
Explanation:
The smallest 3-digit number is 100, which is divisible by 2.
∴ 100 is not a prime number.
√101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
∴101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
Correct Answer: 5994
Explanation:
(Place value of 6) - (Face value of 6) = (6000 - 6) = 5994
Correct Answer: 42437
Explanation:
The square of a natural number never ends in 7.
∴42437 is not the square of a natural number.
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