Yes, candidates with a degree in Metallurgical Engineering can apply for the GATE EE (Electrical Engineering) exam. However, it is important to understand the eligibility criteria and the syllabus of the GATE EE exam before applying. Here are the details:

Eligibility Criteria:
To be eligible for the GATE EE exam, candidates must meet the following criteria:
1. Educational Qualification: Candidates should have a bachelor's degree in Engineering/Technology or a master's degree in any relevant science subject.
2. Qualifying Degree: Candidates with a degree in Metallurgical Engineering are considered eligible as it falls under the category of Engineering/Technology.
3. Year of Passing: Candidates should have completed their degree or be in the final year of their degree program.
4. Age Limit: There is no age limit to apply for the GATE exam.

Syllabus for GATE EE Exam:
The GATE EE syllabus covers various subjects related to Electrical Engineering. The syllabus is divided into different sections, and candidates with a degree in Metallurgical Engineering can prepare for the following subjects/topics:
1. Engineering Mathematics: This section covers topics such as linear algebra, calculus, differential equations, probability, and statistics.
2. Electric Circuits: Candidates need to have knowledge of circuit analysis techniques, network theorems, and AC/DC circuits.
3. Electromagnetic Fields: This section includes topics like electrostatics, magnetostatics, Maxwell's equations, electromagnetic waves, and waveguides.
4. Signals and Systems: Candidates should have an understanding of continuous-time and discrete-time signals, Fourier series, Laplace transforms, Z-transforms, and linear time-invariant systems.
5. Electrical Machines: This section covers topics like transformers, DC machines, synchronous machines, and induction machines.
6. Power Systems: Candidates need to study power generation, transmission, and distribution systems, as well as power factor correction and economic operation.
7. Control Systems: This section includes topics like feedback principles, transfer functions, block diagrams, and stability analysis.

Conclusion:
Candidates with a degree in Metallurgical Engineering can apply for the GATE EE exam by meeting the eligibility criteria. They need to study the syllabus specific to the Electrical Engineering discipline to prepare for the exam. GATE is a prestigious exam that opens up opportunities for higher studies and job opportunities in the field of Electrical Engineering.