Explanation:

This scenario describes a specific type of offense against property under the Indian Penal Code (IPC), where property or valuable security is obtained through intimidation. We need to differentiate between various related offenses. **Analysis of Options:** * **Option (1) Cheating:** Cheating is defined under Section 415 of the IPC. It involves deception, where a person, by deceiving another, fraudulently or dishonestly induces the person so deceived to deliver any property or to consent that any person shall retain any property, or intentionally induces the person so deceived to do or omit to do anything which he would not do or omit if he were not so deceived, and which act or omission causes or is likely to cause damage or harm to that person in body, mind, reputation or property. In the given scenario, 'A' is putting 'B' in fear, not deceiving 'B'. The element of deception is absent. Therefore, this option is incorrect. * **Option (2) Forgery:** Forgery is defined under Section 463 of the IPC. It involves making a false document or false electronic record with intent to cause damage or injury to the public or to any person, or to support any claim or title, or to cause any person to part with property, or to enter into any express or implied contract, or with intent to commit fraud or that fraud may be committed. In this case, 'B' is signing the paper, not 'A' making a false document. 'A' is inducing 'B' to sign, not forging 'B's signature or creating a false document himself. Therefore, this option is incorrect. * **Option (3) Robbery:** Robbery is an aggravated form of either theft or extortion, defined under Section 390 of the IPC. It occurs when, in committing theft, the offender voluntarily causes or attempts to cause to any person death or hurt or wrongful restraint, or fear of instant death or of instant hurt or of instant wrongful restraint. Similarly, extortion becomes robbery if the offender, at the time of committing the extortion, is in the presence of the person put in fear, and commits the extortion by putting that person in fear of instant death, instant hurt, or instant wrongful restraint. The key element for robbery in the context of extortion is the 'instant' nature of the fear. The scenario mentions 'fear of grievous hurt', which is not necessarily instant. Moreover, the act is inducing signing, not taking by force in the immediate presence. Therefore, this option is incorrect. * **Option (4) Extortion:** This is the correct answer. Extortion is defined under Section 383 of the IPC: "Whoever intentionally puts any person in fear of any injury to that person, or to any other, and thereby dishonestly induces the person so put in fear to deliver to any person any property or valuable security, or anything signed or sealed which may be converted into a valuable security, commits 'extortion'." In the given scenario, 'A' intentionally puts 'B' in fear of 'grievous hurt' (an injury). By doing so, 'A' dishonestly induces 'B' to sign a blank paper and deliver it to 'A'. A blank paper, once signed, can be converted into a valuable security (e.g., a promissory note, a cheque, or a deed). All elements of extortion are perfectly met: putting in fear of injury, dishonest inducement, and delivery of something that can become a valuable security. Therefore, 'A' has committed the offense of extortion. In conclusion, 'A's actions perfectly align with the definition of extortion under Section 383 of the Indian Penal Code.