There is no entrance exam for admission in BSc Statistics Hons in Delhi University. Every year DU releases its cutoff for admissions in its colleges. BSc Stats hons require PCM aggregate. So yes you are eligible.

With a degree in B.Sc. Statistics are eligible to apply for various jobs in Banking, IT, Quality control etc. You can even take up Actuarial Science as a specialization and join in various financial and share trading companies. With good flair and knowledge in Statistics, are in huge demand in the present scenario.

A student with Masters or Ph.D. in Statistics can apply for jobs such as a business analyst, statistics lecturer, professor etc. They can also go for jobs like software engineer, investigative officer, statistics analyst, researcher etc. 

In the government sector, UPSC carries out entrance exam as to recruit candidates to the Indian Statistical Services. So the scope is good.

All the best!