If C = 2 , then the value of the determinant = | , * 20 c C&1&0 1… - Vidyadip

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $-9 $ is a root of the equation $\left| {\,\begin{array}{*{20}{c}}x&3&7\\2&x&2\\7&6&x\end{array}\,} \right| = 0$ then the other two roots are

The sine and cosine curves intersects infinitely many times giving bounded regions of equal areas. The area of one of such region is

The tangent to the hyperbola $xy = c^2$ at the point $P$ intersects the $x-$ axis at $T$ and the $y-$ axis at $T'$. The normal to the hyperbola at $P$ intersects the $ x-$ axis at $N$ and the $y-$ axis at $N'$. The areas of the triangles $PNT$ and $PN'T' $ are $ \Delta$ and $ \Delta ' $ respectively, then $\frac{1}{\Delta }\,\, + \,\,\frac{1}{{\Delta '}}\,$ is

The integral $\int {\frac{{xdx}}{{2 - {x^2} + \sqrt {2 - {x^2}} }}} $ equals

The lowest integer which is greater than $\left(1+\frac{1}{10^{100}}\right)^{10^{100}}$ is $.....$

If ${\mathop{\rm Im}\nolimits} \left( {\frac{{2z + 1}}{{iz + 1}}} \right) = - 3,$ then locus of $z$ is :-

$\int \limits_{\pi / 6}^{\pi / 3} \tan ^{3} x \cdot \sin ^{2} 3 x\left(2 \sec ^{2} x \cdot \sin ^{2} 3 x+3 \tan x \cdot \sin 6 x\right) d x$ is equal to

If $x,y,z$ are in $A.P.$ and ${\tan ^{ - 1}}x,{\tan ^{ - 1}}y$ and ${\tan ^{ - 1}}z$ are also in other $A.P.$ then . . .

Let $f(x) = [x]\sin \left( {\frac{\pi }{{[x + 1]}}} \right)$, where $[.]$ denotes the greatest integer function. The domain of $f$ is ….and the points of discontinuity of $f$ in the domain are

Let $A \equiv (\lambda + 2, 1 - 2\lambda , \lambda + 2)$ and $B \equiv (2k + 1, k, k +1)$ and $ \lambda , k \in R.$ Then minimum distance between $A$ and $B$ is -