Requirements analysis should be the best thing to compare against the business case when determining whether a project in the design phase will meet organizational objectives, because it defines the functional and non-functional specifications of the project deliverables that should satisfy the business needs and expectations. Requirements analysis can help evaluate whether the project design is aligned with the business case and whether it can achieve the desired outcomes and benefits. Implementation plan, project budget provisions, and project plan are also important aspects of a project in the design phase, but they are not as relevant as requirements analysis for comparing against the business case. References: CISA Review Manual (Digital Version), Chapter 4, Section 4.2.1

Backup procedures for an organization's critical data are considered to be corrective controls, as they are designed to restore normal operations after a disruption or failure. Corrective controls aim to minimize the impact of an incident and prevent recurrence. Directive, detective and compensating controls are not related to backup procedures. Directive controls are intended to guide or instruct users to follow policies and procedures. Detective controls are intended to identify and report incidents or violations. Compensating controls are intended to mitigate the risk of a missing or ineffective primary control. References: CISA Review Manual (Digital Version), Chapter 2, Section 2.11

Capacity management tools are primarily used to ensure that available resources are used efficiently and effectively to meet the current and future demands of the business. Capacity management tools can help monitor, analyze and optimize the performance and utilization of IT resources such as CPU, memory, disk, network, etc. The other options are not the primary purpose of capacity management tools, although they may be related or derived from them. References:
* ISACA, CISA Review Manual, 27th Edition,chapter 4, section 4.32
* ISACA, COBIT 2019 Framework: Introduction and Methodology, section 3.2