Step 1: Historical Background.
Bakshi Ghulam Muhammad was an important political leader of Jammu and Kashmir. He became the Prime Minister of Jammu and Kashmir after Sheikh Abdullah was dismissed in 1953.
Step 2: Tenure Details.
He remained in office from 1953 to 1963. During his tenure, several developmental works were undertaken in the state.
Step 3: Analysis of the options.
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(A) 1948--53: Incorrect.
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(B) 1950--61: Incorrect.
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(C) 1953--63: Correct.
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(D) 1955--66: Incorrect.
Step 4: Conclusion.
Thus, the tenure of Bakshi Ghulam Muhammad was from 1953 to 1963.
Final Answer:} 1953--63.