MCQ
જો $D= \begin{vmatrix}2&\cos\theta&2\\-\cos\theta&2&\cos\theta\\-2&-\cos\theta&2\end{vmatrix},$ તો $D...............$ અંતરાલમાં છે.
- A$\left( {16,\infty } \right)$
- B$\left( {16,20} \right)$
- C$\left[ {12,16} \right]$
- ✓$\left[ {16,20} \right]$
$D=2(4+cos^2\theta)-cos\theta(-2cos\theta+2cos\theta)+2(cos^2\theta+4)$
$=4cos^2\theta+16$
હવે $0 \ \leq cos^2 \theta \leq1$
$\therefore 0\leq4 \ cos^2\theta \leq 4$
$\therefore 16\leq4 \ cos^2\theta+16 \leq 4+16$
$\therefore 16\leq D \ \leq 20$
$\therefore D$ નું મૂલ્ય $[16,20]$
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