I want to run two jobs parallelly on the same Slave. Job 1 is Functional Testing jobs doesn't require Browser and Job 2 is Selenium Job which requires Browser for testing.
As for running the job on the same slave, you can use the option
Restrict where this project can be run, assuming you have the jenkins slave configured in your setup.
For running the jobs in parallel (are you trying to do this via Jenkinsfile or via freestyle jobs?). For jenkinsfile, you can use the parallel stages feature as described here. For freestyle jobs, I would suggest adding one more job (for example
setup job) and use this job to trigger your two jobs at the same time. Here are few screenshots showing one of my pipeline triggering jobs in parallel.