Are there any Job Opportunities in Indian Army after completion of 12th class in Science stream???

Yes, you have Job Opportunities in Indian Army after passing 12th class in Science stream, you can get this opportunity through NDA Entrance Exam which is conducted by UPSC

Eligibility for NDA Entrance Exam

Educational Qualifications:

For Army wing --
Must have passed Class XII or equivalent examination from any of the recognized Board or a University

For Air Force and Naval Wings --
Must have passed class XII or equilvalent with Physics and Mathematics from any of the recognized Board or a University

Nationality:
You must either be:
a citizen of India, or
a subject of Bhutan, or
a subject of Nepal, or
a Tibetan refugee who came over to India before the 1st January, 1962 with the intention of permanently settling in India, or
a person of Indian origin who has migrated from Pakistan, Burma, Sri Lanka and East African Countries of Kenya, Uganda, the United Republic of Tanzania, Zambia, Malawi, Zaire and Ethiopia and Vietnam with the intention of permanently settling in India.

Age Limits, Sex and Marital
-You must have attained the age of 16 1/2 years and must not have attained the age 19 years
-You must be an unmarried male Citizen