(i) Passive Voice: The original uses present perfect ("have signed"), so passive must use has/have been + past participle. Subject is singular ("agreement"), so "has been."
Correct: (b) This agreement has been signed in haste by both the partners.
(ii) Indirect Speech: Change direct to reported: "can" → "could", "you" → "her", "this" → "that", speaker remains "I."
Correct: (a) I asked my sister what I could do for her in that matter.
(iii) No sooner...than: For past events, use past perfect ("had left") with inversion. "Than" follows immediately.
Correct: (b) No sooner had he left the house than he met with an accident.