PE 1 - Numbers | Algebra - Number Theory
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The least number which on division by 25 leaves the remainder 15, on division by 35 leaves the remainder 25 and on division by 45 leaves the remainder 35 is
- (a)
1565
- (b)
1575
- (c)
1585
- (d)
1595
- (e)
None of these
Solution
Discuss
ReportA group of students is divided into groups of 3, 4 and 5, and each time one student is left out. The least number of students in the heap is
- (a)
31
- (b)
41
- (c)
51
- (d)
61
- (e)
71
What is the highest power of 288 that divides 35!?
- (a)
2
- (b)
6
- (c)
4
- (d)
5
- (e)
None of these
369 has been divided into three parts such that half of the first part, one-third of the second part and one-fourth of the third part are equal. The largest part is
Seven bells commence tolling together and toll at intervals of 3, 6, 9, 12, 15, 18 and 21 s respectively. In 300 mins, how many times do they toll together?
- (a)
4
- (b)
11
- (c)
10
- (d)
15
- (e)
None of these
When ‘n’ is divided by 5 the remainder is 3. What is the remainder when n2 is divided by 5?
- (a)
2
- (b)
1
- (c)
3
- (d)
4
- (e)
0
The expression + + + ... + for any natural number n, is
- (a)
always less than 1
- (b)
always greater than 2
- (c)
always equal to 1
- (d)
always lies between 1 and 2
- (e)
None of these
The ratio between a two-digit number and the sum of the digits of that number is 4 : 1. If the digit in the unit’s place is twice the digit in the ten’s place, what is that number?
- (a)
48
- (b)
63
- (c)
84
- (d)
Cannot be determined
What is the greatest positive power of 5 that divides 40! exactly?
- (a)
5
- (b)
6
- (c)
7
- (d)
8
- (e)
9