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Yes, both Asana and Zoho Desk offer a Free Trial.
Asana is designed for Large Enterprises, Medium Business and Small Business.
Zoho Desk is designed for Large Enterprises, Medium Business and Small Business.
Pricing for Asana Starts at $6.92/user/month when monthly whereas for Zoho Desk Starts at $7/user/month when yearly.
Some top alternatives to Asana includes Quickbase , Smartsheet, ClickUp, Jira, Basecamp, Trello, Wrike, ProofHub, Zoho Projects, monday.com, Teamwork, ProjectManager.com, Microsoft Project, Quick Base and Height.
Some top alternatives to Zoho Desk includes Zendesk Support, Tidio Helpdesk, ManageEngine ServiceDesk Plus, Jira Service Desk, HelpDesk, SysAid, Desky, ReadyDesk, Sitehelpdesk, Trakdesk, HESK and BoldDesk.