Assertion : If ∆ (x) = | array ll f _ 1 ( x ) & f _ 2 ( x ) g _ 1 ( x ) & g _ 2 ( x )…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
Assertion : If ∆ (x) =\(\left|\begin{array}{ll}
\mathrm{f}_{1}(\mathrm{x}) & \mathrm{f}_{2}(\mathrm{x}) \\
\mathrm{g}_{1}(\mathrm{x}) & \mathrm{g}_{2}(\mathrm{x})
\end{array}\right|\), then
∆’ (x) ≠ \(\left|\begin{array}{ll} \mathrm{f}_{1}^{\prime}(\mathrm{x}) & \mathrm{f}_{2}^{\prime}(\mathrm{x}) \\ \mathrm{g}_{1}^{\prime}(\mathrm{x}) & \mathrm{g}_{2}^{\prime}(\mathrm{x}) \end{array}\right|\)
Reason : \(\frac{d}{d}\left\{f(x) g(x) \neq \frac{d}{d} f(x) \frac{d}{d} g(x)\right.\)
∆’ (x) ≠ \(\left|\begin{array}{ll} \mathrm{f}_{1}^{\prime}(\mathrm{x}) & \mathrm{f}_{2}^{\prime}(\mathrm{x}) \\ \mathrm{g}_{1}^{\prime}(\mathrm{x}) & \mathrm{g}_{2}^{\prime}(\mathrm{x}) \end{array}\right|\)
Reason : \(\frac{d}{d}\left\{f(x) g(x) \neq \frac{d}{d} f(x) \frac{d}{d} g(x)\right.\)
- If both assertion and reason are correct and reason is the correct explanation of assertion.
- If both assertion and reason are true but reason is not the correct explanation of assertion.
- If assertion is true but reason is false.
- If assertion is false but reason is true.
Answer
(A) If both assertion and reason are correct and reason is the correct explanation of assertion.
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