Which solution should be recommended to ensure that only authorized applications can run on virtual machines in an Azure subscription?

To recommend a solution that ensures only authorized applications can run on virtual machines in an Azure subscription, adaptive application controls in Defender for Cloud is the most suitable option. This feature leverages intelligent capabilities to analyze the applications running on your VMs and create policies based on what's considered authorized or legitimate within your environment.

By utilizing adaptive application controls, administrators can automatically monitor and identify applications that deviate from the approved list, thereby preventing unauthorized software from executing on the virtual machines. This proactive approach not only enhances security but also simplifies management by aligning application usage with organizational compliance requirements.

Other options like application security groups, firewall rules, and identity and access management policies address different aspects of security but do not specifically focus on controlling which applications can run on the VMs. Application security groups facilitate network access control, firewall rules manage inbound and outbound traffic, and identity and access management policies regulate user access rights, but these do not serve the purpose of sanctioning or restricting application execution directly.