Download App

STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
If the minimum and the maximum values of the function $f :\left[\frac{\pi}{4}, \frac{\pi}{2}\right] \rightarrow R ,$ defined by : 

$f (\theta)=\left|\begin{array}{ccc}-\sin ^{2} \theta & -1-\sin ^{2} \theta & 1 \\ -\cos ^{2} \theta & -1-\cos ^{2} \theta & 1 \\ 12 & 10 & -2\end{array}\right|$ are $m$ and $M$ respectively, then the ordered pair $( m , M )$ is equal to

  • A
    $(0,4)$
  • B
    $(-4,4)$
  • C
    $(0,2 \sqrt{2})$
  • ✓
    $(-4,0)$
✓

Answer

Correct option: D.
$(-4,0)$
d
$C _{3} \rightarrow C _{3}-\left( C _{1}- C _{2}\right)$

$f(\theta)=\left|\begin{array}{ccc}-\sin ^{2} \theta & -1-\sin ^{2} \theta & 0 \\ -\cos ^{2} \theta & -1-\cos ^{2} \theta & 0 \\ 12 & 10 & -4\end{array}\right|$

$=-4\left[\left(1+\cos ^{2} \theta\right) \sin ^{2} \theta-\cos ^{2} \theta\left(1+\sin ^{2} \theta\right)\right]$

$=-4\left[\sin ^{2} \theta+\sin ^{2} \theta \cos ^{2} \theta-\cos ^{2} \theta-\cos ^{2} \theta \sin ^{2} \theta\right]$

$f(\theta)=4 \cos 2 \theta$

$\theta \in\left[\frac{\pi}{4}, \frac{\pi}{2}\right]$

$2 \theta \in\left[\frac{\pi}{2}, \pi\right]$

$f(\theta) \in[-4,0]$

$( m , M )=(-4,0)$

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 STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int_{\, - \pi /2}^{\,\pi /2} {{{\sin }^4}x{{\cos }^6}x\,dx = } $
→
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

→
If $\times $ is a binary operation on set of integers $I$ defined by $a \times b = 3a + 4b - 2,$ then find the value of $4 \times 5.$
→
The value of $\sin ^{ -1 }{ \left( \cos { \frac { 53\pi }{ 5 } } \right) }=\sin ^{ -1 }{ \left( \cos { \frac { 50\pi+3\pi }{ 5 } } \right) }:$
→
If $N$ be the set of all$-$natural numbers, consider $f : N \rightarrow N$ such that $f(x)=2 x, \forall \ x \in N$, then $f$ is:
→
The projection of the line segment joining the points $(-1, 0, 3)$ and $(2, 5, 1)$ on the line whose direction ratios are $6, 2, 3$ is
→
Let $f(x)$ be a non-negative continous function such that the area bounded by the curve $y = f(x)$, $x -$ axis and the ordinates $x = \frac{\pi }{4}$, $x = \beta > \frac{\pi }{4}$ is $\left( {\beta \sin \beta + \frac{\pi }{4}\cos \beta + \sqrt 2 \beta } \right)$. Then $f\;\left( {\frac{\pi }{2}} \right)$ is
→
For some $a, b, c \in N$, let $f(x)=a x-3$ and $g ( x )= x ^{ b }+ c , x \in R$. If $(\text { fog })^{-1}( x )=\left(\frac{ x -7}{2}\right)^{1 / 3}$ then $(fog) (ac) + (gof) (b)$ is equal to $..........$
→
If $A$ is a singular matrix, then $\text{adj A}$ is:
→
If $ a, b, c$  are three non-coplanar vector, then $\frac{{a\,.\,b \times c}}{{c \times a\,.\,b}} + \frac{{b\,.\,a \times c}}{{c\,.\,a \times b}}$=
→