The given sequence is 10, 18, 63, 253, 1137, 5901. We need to find the next number in the sequence.

To determine the pattern in the sequence, we can look at the differences between consecutive terms. Let's calculate the differences:

18 - 10 = 8
63 - 18 = 45
253 - 63 = 190
1137 - 253 = 884
5901 - 1137 = 4764

The differences do not form a clear pattern, so let's look at the second differences:

45 - 8 = 37
190 - 45 = 145
884 - 190 = 694
4764 - 884 = 3880

The second differences are also not consistent. However, if we look closely, we can observe that the second differences are increasing by a constant value of 108.

Now, let's find the third differences:

145 - 37 = 108
694 - 145 = 549
3880 - 694 = 3186

The third differences are also increasing by a constant value of 108.

Based on this pattern, we can assume that the fourth differences will also increase by 108. However, since we only have four terms, we cannot calculate the fourth difference.

From the given options, let's check if any of them follow this pattern:

a) 39754: We cannot determine if this option follows the pattern or not.
b) 35749: This option does not follow the pattern because the fourth difference should be 108 more than the third difference.
c) 37594: We cannot determine if this option follows the pattern or not.
d) 35794: We cannot determine if this option follows the pattern or not.
e) None of the above.

Therefore, the correct answer is option B) 35749.