MCQ
$\left|\begin{array}{cc}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right|=$
- A$(a+b)^2$
- B$(a+b+c+d)^2$
- C$\left(a^2+b^2-c^2-d^2\right)$
- ✓$a^2+b^2+c^2+d^2$
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$(A)$ $f^{\prime \prime}(x)$ exists for all $x \in(0, \infty)$
$(B)$ $f^{\prime}(x)$ exists for all $x \in(0, \infty)$ and $f^{\prime}$ is continuous on $(0, \infty)$, but not differentiable on $(0, \infty)$
$(C)$ there exists $\alpha>1$ such that $\left|f^{\prime}(x)\right|<|f(x)|$ for all $x \in(\alpha, \infty)$
$(D)$ there exists $\beta>0$ such that $|f(x)|+\left|f^{\prime}(x)\right| \leq \beta$ for all $x \in(0, \infty)$