When the number (12345678910111213 ... 99100) is divided by 16, what will be the remainder ?

To find remainder mod 16, we only need the last 4 digits (since 10⁴ = 10000 = 625 × 16, so 10⁴ ≡ 0 mod 16). The last 4 digits of the concatenation ending in ...9899100 are '9100'. 9100 ÷ 16 = 568 with remainder 12. Wait: 568 × 16 = 9088, so 9100 − 9088 = 12. So remainder is 12. The answer is (b) 12.