The answer is: A
Explanation
The correct option is A: I promise to pay B or order Rs. 10,000/- on demand.
This is a promissory note because it satisfies the definition given in Section 4 of the Negotiable Instruments Act, 1881. It is an instrument in writing, containing an unconditional undertaking, signed by the maker (A), to pay a certain sum of money (Rs. 10,000/-) only to, or to the order of, a certain person (B) or to the bearer of the instrument.
Option B: Mr. B! I.Owe.You Rs. 10,000/- is not a promissory note because it does not contain an express promise to pay. It is merely an acknowledgement of debt.
Option C: I promise to pay B Rs. 10,000/- and such other sums which shall be due to him is not a promissory note because it does not contain a certain sum of money. The amount payable is uncertain and depends on future events.
Option D: I promise to pay B on his request Rs. 10,000/- on the death of X is not a promissory note because it contains a conditional promise. The payment is subject to the occurrence of the death of X and the request of B.