Hello Payalpriya,

Yes, you can apply for CDS after doing graduation from private Institute as the eligibility criteria 

for different courses are-

• IMA(Indian Military Academy)-Degree of a recognized University,Age-19 to 24,Unmarried.
• Indian Naval Academy-degree in Engineering from recognized University,Age-19 to24,Unmarried.
• Air Force Academy-Degree from recognized University (with physics and maths at 10+2) or Engineering Degree,age 20 to 24,unmarried.
• Officer Training Academy-Degree from recognized University,age 19 to 25,Unmarried or married.
• Officer Training Academy(women,non-technical)-Degreefrom recognized University,age 19 to 25,Unmarried/widow or Divorcee.

You can also visit the careers360 link regarding it-

https://competition.careers360.com/articles/cds-eligibility-criteria

Thank You.

Hope it was helpful.