Download App

3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
Let $m$ and $M$ be respectively the minimum and maximum values of

$\left|\begin{array}{ccc}\cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x\end{array}\right|$.

Then the ordered pair $( m , M )$ is equal to

  • ✓
    $(-3,-1)$
  • B
    $(-4,-1)$
  • C
    $(1,3)$
  • D
    $(-3,3)$
✓

Answer

Correct option: A.
$(-3,-1)$
a
$\left|\begin{array}{ccc}\cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x\end{array}\right|$

$R_{1} \rightarrow R_{1}-R_{2}, R_{2} \rightarrow R_{2}-R_{3}$

$\left|\begin{array}{ccc}-1 & 1 & 0 \\ 1 & 0 & -1 \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x\end{array}\right|$

$=-1\left(\sin ^{2} x\right)-1\left(1+\sin 2 x+\cos ^{2} x\right)$

$=-\sin 2 x-2$

$m=-3, M=-1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The differential equation of the ellipse $\frac{\text{x}^{2}}{\text{a}^{2}}+\frac{\text{y}^{2}}{\text{b}^{2}}=\text{C}$ is:
  1. $\frac{\text{y}''}{\text{y}'}+\frac{\text{y}'}{\text{y}}-\frac{1}{\text{x}}=0$
  2. $\frac{\text{y}''}{\text{y}'}+\frac{\text{y}'}{\text{y}}+\frac{1}{\text{x}}=0$
  3. $\frac{\text{y}''}{\text{y}'}-\frac{\text{y}'}{\text{y}}-\frac{1}{\text{x}}=0$
  4. None of these.
→
The volume ( $V$ ) of the casted half cylinder will be
→
The area (in sq. units) of the region $\left\{(x, y): 0 \leq y \leq x^{2}+1,0 \leq y \leq x+1\right.$ $\left.\frac{1}{2} \leq x \leq 2\right\}$ is 
→
The value of ${\cos ^{ - 1}}\left[ {\cot \left\{ {{{\sin }^{ - 1}}\sqrt {\frac{{2 - \sqrt 3 }}{4}}  + {{\cos }^{ - 1}}\frac{{\sqrt {12} }}{4} + {{\sec }^{ - 1}}\sqrt 2 } \right\}} \right]$ is
→
Simplest form of
$\tan ^{-1}\left(\frac{\sqrt{1+\cos x}+\sqrt{1-\cos x}}{\sqrt{1+\cos x}-\sqrt{1-\cos x}}\right)$,$\pi$< x<$\frac{3 \pi}{2}$ is
→
Let $p ( x )$ be a real polynomial of least degree which has a local maximum at $x =1$ and a local minimum at $x=3$. If $p(1)=6 p(3)=2$, then $p^{\prime}(0)$ is
→
If $f\left( x \right) = \int\limits_x^{{x^2}} {\left( {t - 1} \right)\,dt\,\,,\,\,1 \le x \le 3,} $ then global maximum value of $f(x)$ is
→
The solution of  $\frac{\text{d}^2\text{y}}{\text{dx}^2}=0$ represents:
  1. a straight line
  2. a circle
  3. a parabola
  4. a point
→
The distance travelled $s$ (in centi metre) by a particle in $ t $ seconds is given by, $s = {t^3} + 2{t^2} + t.$ The speed of the particle after $1 $ second will be ......... $cm/sec$
→
The area (in sq. units) bounded by the parabola $y = x^2 -1$, the tangent at the point $(2, 3)$ into it and the $y -$ axis is
→