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OverviewExercise"When ambition ends, happiness begins."
- (Proverb)
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| 31. |
On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?
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Answer: Option B
Explanation:
Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
 x = 5k + 3
 x2 = (5k + 3)2
= (25k2 + 30k + 9)
= 5(5k2 + 6k + 1) + 4
On dividing x2 by 5, we get 4 as remainder.
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| 32. |
How many 3-digit numbers are completely divisible 6 ?
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Answer: Option D
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.
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| 33. |
How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?
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Answer: Option B
Explanation:
Required numbers are 24, 30, 36, 42, ..., 96
This is an A.P. in which a = 24, d = 6 and l = 96
Let the number of terms in it be n.
Then tn = 96 a + (n - 1)d = 96
24 + (n - 1) x 6 = 96
(n - 1) x 6 = 72
(n - 1) = 12
n = 13
Required number of numbers = 13.
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| 34. |
How many of the following numbers are divisible by 3 but not by 9 ?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276 |
Answer: Option B
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.
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| 35. |
| (963 + 476)2 + (963 - 476)2 |
= ? |
| (963 x 963 + 476 x 476) |
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Answer: Option C
Explanation:
| Given Exp. = |
(a + b)2 + (a - b)2 |
= |
2(a2 + b2) |
= 2 |
| (a2 + b2) |
(a2 + b2) |
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| 36. |
How many 3 digit numbers are divisible by 6 in all ?
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Answer: Option C
Explanation:
Required numbers 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,
a + (n - 1)d = 996
102 + (n - 1) x 6 = 996
6 x (n - 1) = 894
(n - 1) = 149
n = 150.
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| 37. |
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) = ?
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Answer: Option D
Explanation:
4 a 3 |
9 8 4 } ==> a + 8 = b ==> b - a = 8
13 b 7 |
Also, 13 b7 is divisible by 11 (7 + 3) - (b + 1) = (9 - b)
(9 - b) = 0
b = 9
(b = 9 and a = 1) (a + b) = 10.
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| 38. |
8597 - ? = 7429 - 4358
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Answer: Option E
Explanation:
7429 Let 8597 - x = 3071
-4358 Then, x = 8597 - 3071
---- = 5526
3071
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| 39. |
The smallest prime number is:
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Answer: Option E
Explanation:
The smallest prime number is 2.
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| 40. |
(12345679 x 72) = ?
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| A. |
88888888 | B. |
888888888 | | C. |
898989898 | D. |
9999999998 |
Answer: Option E
Explanation:
| 12345679 x 72 |
= 12345679 x (70 +2) |
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= 12345679 x 70 + 12345679 x 2 |
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= 864197530 + 24691358 |
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= 888888888 |
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