Question

If D = $\left| \begin{matrix} e^{x} & \sin x & 1 \\ \cos x & \mathcal{l}n(1 + x^{2}) & 1 \\ x & x^{2} & 1 \end{matrix} \right|$ = a + bx + cx² then the value of b is

• A. 0
• B. –1
• C. –2
• D. None of these

Answer 1

Answer: (B)

–1

Answer 2

D'= $\left| \begin{matrix} e^{x} & \sin x & 1 \

• \sin x & \mathcal{l}n(1 + x^{2}) & 1 \ 1 & x^{2} & 1 \end{matrix} \right|$+$\left| \begin{matrix} e^{x} & \cos x & 1 \ \cos x & \frac{2x}{1 + x^{2}} & 1 \ x & 2x & 1 \end{matrix} \right|$ + 0 = b + 2cx

Now use x = 0

b = $\left| \begin{matrix} 1 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 0 & 1 \end{matrix} \right|$ + $\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 0 & 1 \\ 0 & 0 & 1 \end{matrix} \right|$ = – 1