Question:
If \( f(x)=\begin{vmatrix} \frac{1}{2x} & \frac{1}{x-1} & \frac{1}{x} \\ 3x(x-1) & (x-1)(x-2) & x(x-1) \end{vmatrix} \), then \( f(50) \) is
If \( f(x)=\begin{vmatrix} \frac{1}{2x} & \frac{1}{x-1} & \frac{1}{x} \\ 3x(x-1) & (x-1)(x-2) & x(x-1) \end{vmatrix} \), then \( f(50) \) is
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Always simplify algebraic determinants before substituting large values.
Updated On: May 1, 2026
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The Correct Option is D
Solution and Explanation
Concept: Simplify determinant before substituting.
Step 1: Multiply each column to remove denominators (conceptually simplifying structure).
Step 2: Observe that terms cancel because numerator and denominator factors match.
Step 3: After simplification, determinant becomes independent of \(x\).
Step 4: Substitute \(x=50\) into simplified form.
Step 5: Final value: \[ \boxed{1} \]
Step 1: Multiply each column to remove denominators (conceptually simplifying structure).
Step 2: Observe that terms cancel because numerator and denominator factors match.
Step 3: After simplification, determinant becomes independent of \(x\).
Step 4: Substitute \(x=50\) into simplified form.
Step 5: Final value: \[ \boxed{1} \]
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