The number of real values of for which the system of linear equat… - Vidyadip

MCQ

The number of real values of $\lambda $ for which the system of linear equations $2x + 4y - \lambda z = 0$ ;$4x + \lambda y + 2z = 0$ ; $\lambda x + 2y+ 2z = 0$ has infinitely many solutions, is

A
$0$
✓
$1$
C
$2$
D
$3$

✓

Answer

Correct option: B.

$1$

b
Since the given system of linear equations has infinitely many solutions.

$\therefore \begin{array}{*{20}{c}}
2&4&{ - \lambda }\\
4&\lambda &2\\
\lambda &2&2
\end{array} = 0$

$ \Rightarrow {\lambda ^3} + 4\lambda - 40 = 0$

$\lambda $ has only $1$ real root.

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

The distance of the point $B\,(i + 2j + 3k)$ from the line which is passing through $A\,(4i + 2j + 2k)$ and which is parallel to the vector $\overrightarrow C = 2i + 3j + 6k$ is

Equation of curve through point $(1,\,0)$which satisfies the differential equation $(1 + {y^2})dx - xydy = 0$, is

Consider an arithmetic series and a geometric series having four initial terms from the set $\{11,8,21,16,26,32,4\}$ If the last terms of these series are the maximum possible four digit numbers, then the number of common terms in these two series is equal to .......

Statement $-1$ : If two tangents are drawn to an ellipse from a single point and if they are perpendicular to each other, then locus of that point is always a circle

Statement $-2$ : For an ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ , locus of that point from which two perpendicular tangents are drawn, is $x^2 + y^2 = (a + b)^2$ .

Let $\alpha$ and $\beta$ be the roots of $x^{2}-3 x+p=0$ and $\gamma$ and $\delta$ be the roots of $x^{2}-6 x+q=0 .$ If $\alpha$ $\beta, \gamma, \delta$ form a geometric progression. Then ratio $(2 q+p):(2 q-p)$ is

If $y = \sqrt {\sec x + \sqrt {\sec x + \sqrt {\sec x + ......\infty } } } \,,$ then value of $\int\limits_0^{\pi /3} {\left( {(2y - 1)\frac{{dy}}{{dx}}} \right)} \,dx$ is equal to $(\sec x > 0)$ -

A point moves in such a way that its distance from origin is always $4$. Then the locus of the point is

The means of five observations is $4$ and their variance is $5.2$. If three of these observations are $1, 2$ and $6$, then the other two are

If $\frac{d y}{d x}+\frac{2^{x-y}\left(2^{y}-1\right)}{2^{x}-1}=0, x, y>0, y(1)=1$, then $y (2)$ is equal to

Let $3, a , b , c$ be in $A.P$. and $3, a -1, b+1, c +9$ be in $G.P$. Then, the arithmetic mean of $a , b$ and $c$ is :