Download App

3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
Let $\lambda $ be a real number for which the system of linear equations $x + y + z = 6$
 ; $4x + \lambda y - \lambda z = \lambda - 2$ ; $3x + 2y -4z = -5$ Has indefinitely many solutions. Then $\lambda $ is a root of the quadratic equation
  • ✓
    ${\lambda ^2} - \lambda  - 6\, = 0$
  • B
    ${\lambda ^2} - 3\lambda  - 4 = 0$
  • C
    ${\lambda ^2} + 3\lambda  - 4 = 0$
  • D
    ${\lambda ^2} + \lambda  - 6 = 0$
✓

Answer

Correct option: A.
${\lambda ^2} - \lambda  - 6\, = 0$
a
$D=0$

$\left| {\begin{array}{*{20}{c}}
1&1&1\\
4&\lambda &\lambda \\
3&2&{ - 4}
\end{array}} \right| = 0 \Rightarrow \lambda  = 3$

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 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If the point of minima of the function, $f(x) = 1 + a^2x -x^3 $ satisfy the inequality $\frac{{{x^2} + x + 2}}{{{x^2} + 5x + 6}} < 0$, then $'a'$ must lie in the interval
→
Consider the function. $f(x)=\left\{\begin{array}{cc} \frac{a\left(7 x-12-x^2\right)}{b\left|x^2-7 x+12\right|} & , x<3 \\ 2^{\frac{\sin (x-3)}{x-[x]}} & , x>3 \\ b & , x=3 \end{array}\right.$ Where $[\mathrm{x}]$ denotes the greatest integer less than or equal to $x$. If $S$ denotes the set of all ordered pairs $(a, b)$ such that $f(x)$ is continuous at $x=3$, then the number of elements in $\mathrm{S}$ is :
→
If $\text{f(x)}=\begin{cases}\text{ax}^2+\text{b},&0\leq\text{x}<1\\4,&\text{x}=1\\\text{x}+3,&1<\text{x}\leq2\end{cases}$ then the value of (a, b) for which f(x) cannot be continuous at x = 1, is:
  1. (2, 2)
  2. (3, 1)
  3. (4, 0)
  4. (5, 2)
→
$2x + 3y + 4z = 9$,$4x + 9y + 3z = 10,$$5x + 10y + 5z = 11$ then the value of $ x$ is
→
$\int_{}^{} {\frac{{x - 1}}{{(x - 3)(x - 2)}}dx = } $
→
If $a=2i+j+2k$  and $b=5i-3j+k,$  then the projection of $b $ on  $ a $ is
→
If $\int {\frac{{dx}}{{x + {x^7}}}}  = p(x)$ then, $\int {\frac{{{x^6}}}{{x + {x^7}}}} dx$ is equal to
→
If A and B are two events such that $\text{P(A)}=\frac{3}{8},\text{P(B)}=\frac{5}{4}.$ and $\text{P}(\text{A}|\text{B})\times\text{P}(\overline{\text{A}}\cap\text{B})$ is equals to.
  1. $\frac{2}{5}$
  2. $\frac{3}{8}$
  3. $\frac{3}{20}$
  4. $\frac{6}{25}$
→
Given that the inverse trigonometric functions take principal values only. Then, the number of real values of $x$ which satisfy $\sin ^{-1}\left(\frac{3 x}{5}\right)+\sin ^{-1}\left(\frac{4 x}{5}\right)=\sin ^{-1} x$ is equal to:
→
Minimum distance between parabola $y^2 = 8x$ and its image with respect to line $x + y + 4 = 0$ is-
→