Question

Let for $ \mathrm{i}=1,2,3, \mathrm{p}_{\mathrm{i}}(\mathrm{x}) $ be a polynomial of degree 2 in $ \mathrm{x}, \mathrm{p}_{\mathrm{i}}^{\prime}(\mathrm{x}) $ and $ \mathrm{p}_{\mathrm{\prime \prime}}{ }_{\mathrm{\prime}}(\mathrm{x}) $ be the first and second order derivatives of $ \mathrm{p}_{\mathrm{i}}(\mathrm{x}) $ respectively. Let, $$ A(x)=\left[\begin{array}{lll} \mathrm{p}_{1}(\mathrm{x}) & \mathrm{p}_{1}^{\prime}(\mathrm{x}) & \mathrm{p}_{1}^{\prime \prime}(\mathrm{x}) \ \mathrm{p}_{2}(\mathrm{x}) & \mathrm{p}_{2}{ }^{\prime}(\mathrm{x}) & \mathrm{p}_{2}^{\prime \prime}(\mathrm{x}) \ \mathrm{p}_{3}(\mathrm{x}) & \mathrm{p}_{3}{ }^{\prime}(\mathrm{x}) & \mathrm{p}_{3}{ }^{\prime \prime}(\mathrm{x}) \end{array}ight] $$ and $ \mathrm{B}(\mathrm{x})=[\mathrm{A}(\mathrm{x})]^{T} \mathrm{A}(\mathrm{x}) $. Then determinant of $ \mathrm{B}(\mathrm{x}) $ :

Accepted Answer

is a polynomial of degree 6 in $ x $.

Answer

is a polynomial of degree 3 in $ x $.

Answer

is a polynomial of degree 2 in $ \mathrm{x} $.

Answer

does not depend on $ x $

JEE MATHEMATICS MCQ: DIFFERENTIATION

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