**Yes, you can apply for GATE (Graduate Aptitude Test in Engineering) after completing your B.Sc. (PCM) degree.** GATE is a national level entrance examination conducted by the Indian Institute of Technology (IITs) and the Indian Institute of Science (IISc) for admission to postgraduate programs in engineering, technology, and architecture.

**Eligibility Criteria for GATE after B.Sc. (PCM):**
To be eligible for GATE, you need to fulfill the following criteria:
1. Educational Qualification: You must have a minimum of a bachelor's degree in Engineering/Technology/Architecture in the relevant field or a master's degree in any branch of Science/Mathematics/Statistics/Computer Applications or equivalent.
2. B.Sc. (PCM): As you have a B.Sc. degree in PCM (Physics, Chemistry, Mathematics), you are eligible to apply for GATE in specific disciplines related to your degree, such as Physics, Chemistry, Mathematics, etc.

**Application Process for GATE:**
The application process for GATE typically involves the following steps:
1. Online Registration: Visit the official GATE website and complete the online registration by providing the required personal and academic details.
2. Application Form Filling: Fill in the application form with accurate information, including your educational qualifications, personal details, and choice of examination center.
3. Upload Documents: Upload scanned copies of your photograph, signature, and other required documents as per the specifications provided by the conducting authority.
4. Application Fee Payment: Pay the application fee online through the available payment methods, such as credit/debit card, net banking, or e-challan.
5. Submit Application: After completing the above steps, review your application and submit it online.
6. Admit Card: Once your application is accepted, you can download your admit card from the official website within the specified dates.

**Preparation for GATE:**
Preparing for GATE requires a strategic approach and dedication. Here are a few tips to help you with your preparation:
1. Understand the Syllabus: Familiarize yourself with the GATE syllabus specific to your chosen discipline and identify the topics you need to focus on.
2. Study Material: Gather relevant study materials such as textbooks, reference books, and online resources to cover the syllabus comprehensively.
3. Make a Study Plan: Create a study plan that includes daily/weekly targets and allocate sufficient time for each subject.
4. Practice Previous Year Question Papers: Solve previous year GATE question papers to get acquainted with the exam pattern and to improve your time management skills.
5. Mock Tests: Take online mock tests to assess your preparation level and identify areas that require improvement.
6. Seek Guidance: If needed, consider joining coaching classes or seeking guidance from subject experts to enhance your understanding of complex topics.

Remember, GATE is a highly competitive exam, and consistent and focused preparation is crucial to achieve a good score. Good luck with your GATE preparation!