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 $C = 2\cos \theta $, then the value of the determinant $\Delta = \left| {\,\begin{array}{*{20}{c}}C&1&0\\1&C&1\\6&1&C\end{array}\,} \right|$ is
  • A
    $\frac{{\sin 4\theta }}{{\sin \theta }}$
  • B
    $\frac{{2{{\sin }^2}2\theta }}{{\sin \theta }}$
  • C
    $4{\cos ^2}\theta \,(2\cos \theta - 1)$
  • ✓
    None of these
✓

Answer

Correct option: D.
None of these
d
(d) $\Delta = \left| {\,\begin{array}{*{20}{c}}C&1&0\\1&C&1\\6&1&C\end{array}\,} \right|\, = C[{C^2} - 1] - 1[C - 6]$

==> $\Delta = 2\cos \theta (4{\cos ^2}\theta - 1) - (2\cos \theta - 6)$
==> $\Delta = 8{\cos ^3}\theta - 4\cos \theta + 6$.

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

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two collinear vectors, then which of the follwoing are incorrect?
→
Matrices A and B will be inverse of each other only if:
→
If $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1-\sin 2 x} d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}$, where $\alpha, \beta$ and $\gamma$ are rational numbers, then $3 \alpha+4 \beta-\gamma$ is equal to ..........

 

→
The correct evaluation of $\int_0^{\pi /2} {\left| {\,\sin \left( {x - \frac{\pi }{4}} \right)\,} \right|\,dx} $ is
→
A bag containe 5 black, 4white balls and 3 red balls. if a ball is selected randomwise, the probability that it is black or red ball is,
→
The ratio of the areas between the curves $\text{y}=\cos\text{x}$ and $\text{y}=\cos2\text{x}$ and $x-$ axis from $x = 0$ to $x = 0$ to $\text{x}=\frac{\pi}{3}$
→
If $A \ne O$ and $B \ne O$ are $ n × n$ matrix such that $AB = O,$ then
→
An urn contains $5$ red and $2$ green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is
→
Which of the following is not a convex set?
→
Area of circle $x^2+y^2=4$ :
→