The values of , for which the following equations x - cos y + ( +… - Vidyadip

MCQ

The values of $\theta, \lambda$ for which the following equations $\sin \theta x - cos\theta y + (\lambda +1)z = 0$; $\cos\theta x + \sin\theta\, y - \lambda z = 0$;$ \lambda x +(\lambda + 1)y + \cos\theta z = 0$ have non trivial solution, is

A
$\theta = n\pi , \lambda \in R - {0}$
B
$\theta = 2n\pi , \lambda $ is any rational number
C
$\theta = (2n + 1)\pi , \lambda \in R+, n \in I$
✓
$\theta = (2n + 1),\frac{\pi }{2} \lambda \in R, n \in I$

✓

Answer

Correct option: D.

$\theta = (2n + 1),\frac{\pi }{2} \lambda \in R, n \in I$

d
for non trivial solution $\left| {\,\begin{array}{*{20}{c}}{\sin \theta }&{ - \cos \theta }&{\lambda + 1}\\{\cos \theta }&{\sin \theta }&{ - \lambda }\\\lambda &{\lambda + 1}&{\cos \theta }\end{array}\,} \right|$ $= 0$ ;

this gives $2$ $\cos\theta (\lambda^2 + \lambda + 1) = 0$

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

If $\begin{bmatrix} 1 & -\tan\theta \\ \tan\theta & 1 \end{bmatrix}\begin{bmatrix} 1 & \tan\theta \\ -\tan\theta & 1 \end{bmatrix}-1=\begin{bmatrix} \text{a} & -\text{b} \\ \text{b} & \text{a} \end{bmatrix},$ then :

The area of a triangle is $5$ and two of its vertices are $A(2, 1), B(3, -2)$. The third vertex which lies on line $y = x + 3$ is-

$\int_0^\infty {\frac{{\log \,(1 + {x^2})}}{{1 + {x^2}}}} \,dx = $

If X is a binomial variate with parameters n and p, where 0 < p < 1 such that $\frac{\text{P(X = r)}}{\text{P(X = n - r})}$ is independent of n and r, then p equals:

If $y = {\left[ {x + \sqrt {{x^2} - 1} } \right]^{15}} + {\left[ {x - \sqrt {{x^2} - 1} } \right]^{15}}$ , then $\left( {{x^2} - 1} \right)\frac{{{d^2}y}}{{d{x^2}}} + x\frac{{dy}}{{dx}}$ is equal to

The function $\text{f(x)}=\frac{\text{x}^3+\text{x}^2-16\text{x}+20}{\text{x}-2}$ is not defind for $x = 2$. in order to make $f(x)$ continuous at $x = 2,$ here $f(2)$ should be defined as:

Let $A=\left(\begin{array}{rrr}1 & -1 & 0 \\ 0 & 1 & -1 \\ 0 & 0 & 1\end{array}\right)$ and $B=7 A^{20}-20 A^{7}+2 I$, where $I$ is an identity matrix of order $3 \times 3$ If $B=\left[b_{i j}\right]$, then $b_{13}$ is equal to $....$

Consider the function $f\left( x \right) = \left| {x - 2} \right| + \left| {x - 5} \right|,x \in R$

Statement $-1 :$ $f'\left( 4 \right) = 0$

Statement $-2 :$ $ f $ is continuous in $ [2,5] $ , differentiable in $ (2,5) $ and $f(2)=f(5).$

Let $\alpha x=\exp \left(x^\beta y^\gamma\right)$ be the solution of the differential equation $2 x^2 y d y-\left(1-x y^2\right) d x=0$, $x >0, y (2)=\sqrt{\log _e 2}$. Then $\alpha+\beta-\gamma$ equals :

The value of $\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\big(\text{x}^3+\text{x}\cos\text{x}+\tan^5\text{x}+1\big)\text{dx},$ is: