Download App

STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
MCQ
If matrix $A = \left[ {\begin{array}{*{20}{c}}
{\sin \theta }&{\cos ec\theta }&1\\
{\cos ec\theta }&1&{\sin \theta }\\
1&{\sin \theta }&{\cos ec\theta }
\end{array}} \right]$ is a non invertible matrix, then possible value of $'\theta'$ is 

$($ where $n \in I)$

  • A
    $n\pi  + {( - 1)^n}\frac{\pi }{4}$
  • B
    $n\pi  + {( - 1)^n}\frac{\pi }{3}$
  • C
    $n\pi  + {( - 1)^n}\frac{\pi }{6}$
  • ✓
    $2n\pi+\frac{\pi}{2}$
✓

Answer

Correct option: D.
$2n\pi+\frac{\pi}{2}$
d
$|A|=0 \Rightarrow$  either  $\sin \theta  = \cos ec\theta  = 1$

$\Rightarrow \theta=2 n \pi+\frac{\pi}{2}$ or $\sin \theta  + \cos ec\theta  + 1 = 0$

Not possible.

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

Let $I_{n}(x)=\int_{0}^{x} \frac{1}{\left(t^{2}+5\right)^{n}} d t, n=1,2,3, \ldots .$ Then
→
If the product of roots of the equation, $m{x^2} + 6x + (2m - 1) = 0$ is $-1$, then the value of $m$ will be
→
$\cos 20^\circ \cos 40^\circ \cos 80^\circ = $
→
If the set of natural numbers is partitioned into subsets ${S_1} = \left\{ 1 \right\},\;{S_2} = \left\{ {2,\;3} \right\},\;{S_3} = \left\{ {4,\;5,\;6} \right\}$ and so on. Then the sum of the terms in ${S_{50}}$ is
→
If $f(x)$ satisfies the relation $f\left( {\frac{{5x - 3y}}{2}} \right) = \frac{{5f(x) - 3f(y)}}{2}\forall x,y\, \in \,R$ and $f(0)=1, f'(0)=2$ then the period of $sin(f(x))$ is 
→
Let $A = \{1, 2, 3, 4\}$ and $R$ be a relation in $A$ given by $R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)\}$. Then $R$ is
→
Let $S$ be a set containing n elements and we select $2$ subsets $A$ and $B$ of $S$ at random then the probability that $A \cup B = S$ and $A \cap B = \phi $ is
→
Any circle through the points of intersection of the lines $x + \sqrt 3\, y = 1$ and $\sqrt 3\, x -y = 2$ if intersects these lines at points $P$ and $Q$, then the angle subtended by the arc $PQ$ at its centre is- ............. $^o$
→
The condition of the curves $a{x^2} + b{y^2} = 1$and $a'{x^2} + b'{y^2} = 1$ to intersect each other orthogonally, is
→
If the difference between the roots of the equation $x^2 + ax + b = 0$ is equal to the difference between the roots of the equation $x^2 + bx + a = 0 (a \ne  b)$ , then 
→