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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
Let $f(x)=\left|\begin{array}{cc}x^2 & \sin x \\ p & -1\end{array}\right|$, where $p$ is a constant. The value of $p$ for which $f^{\prime}(0)=1$ is
  • A
    R
  • B
    1
  • C
    $0$
  • D
    -1
✓

Answer

Given, $f(x)=\left|\begin{array}{cc}x^2 & \sin x \\ p & -1\end{array}\right|=-x^2-p \sin x$
$
\begin{array}{l}
\Rightarrow f^{\prime}(x)=-2 x-p \cos x \\
\text { We have, } f^{\prime}(0)=1 \Rightarrow-2(0)-p \cos (0)=1 \Rightarrow-p=1 \Rightarrow p=-1
\end{array}
$

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