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
If $\left[ {\begin{array}{*{20}{c}}{2 + x}&3&4\\1&{ - 1}&2\\x&1&{ - 5}\end{array}} \right]$is a singular matrix, then $x$ is
  • A
    $\frac{{13}}{{25}}$
  • ✓
    $ - \frac{{25}}{{13}}$
  • C
    $\frac{5}{{13}}$
  • D
    $\frac{{25}}{{13}}$
✓

Answer

Correct option: B.
$ - \frac{{25}}{{13}}$
b
(b) Given, $\left| {\,\begin{array}{*{20}{c}}{2 + x}&3&4\\1&{ - 1}&2\\x&1&{ - 5}\end{array}\,} \right|\, = 0$

==> $(2 + x)(5 - 2) - 3( - 5 - 2x) + 4(1 + x) = 0$

==> $6 + 3x + 15 + 6x + 4 + 4x = 0$

==> $13x = - 25 \Rightarrow x = - \frac{{25}}{{13}}$.

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 $y=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\ldots .$. , then $\frac{d y}{d x}=$ _________ .
→
Find the area of bounded by $\text{y}=\sin\text{x}$  from $\text{x}=\frac{\pi}{4}$ to $\text{x}=\frac{\pi}{2}:$
  1. $\frac{\sqrt{2-1}}{\sqrt2}$
  2. $\frac{1}{2}$
  3. $\frac{1}{4}$
  4. $\text{none}\text{ of}\text{ these}$
→
If $f: \mathrm{R} \rightarrow \mathrm{R}$ is a twice differentiable function such that $f^{\prime \prime}(x)>0$ for all $x \in \mathrm{R}$, and $f\left(\frac{1}{2}\right)=\frac{1}{2}, f(1)=1$, then
→
Let $y\,(x)$ be a solution of $\frac{{(2 + \sin \,x)\,dy}}{{(1 + y)dx}} = \cos \,\,x.$ If $y(0) = 2,$ then $y\left( {\frac{\pi }{2}} \right)$ equals
→
The domain of the function $f(x)=\frac{1}{\sqrt{[x]^2-3[x]-10}}$ is (where $[x]$ denotes the greatest integer less than or equal to $x$ )
→
$a.(b × c)$  is equal to
→
Consider $5$ independent Bernoulli's trials each with probability of success $p.$ If the probability of at least one failure is greater than or equal to $\frac{{31}}{{32}}$ then $p$ lies in the interval
→
Let $\Omega$ be the set of all $3 \times 3$ symmetric matrices all of whose entries are either $0$ or $1$ . Five of these entries are $1$ and four of them are $0$ .

$1.$ The number of matrices in $\Omega$ is

$(A)$ $12$ $(B)$ $6$ $(C)$ $9$ $(D)$ $3$

$2.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations

$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has a unique solution, is

$(A)$ less than $4$

$(B)$ at least $4$ but less than $7$

$(C)$ at least $7$ but less than $10$

$(D)$ at least $10$

$3.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations

$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ is inconsistent, is

$(A)$ $0$ $(B)$ more than $2$ $(C)$ $2$ $(D)$ $1$

→
If $A = \left[ {\begin{array}{*{20}{c}}1&2\\0&1\end{array}} \right],$then ${A^n} = $
→
Given that $\int_0^\infty {\frac{{{x^2}\,dx}}{{({x^2} + {a^2})({x^2} + {b^2})({x^2} + {c^2})}} = \frac{\pi }{{2(a + b)(b + c)(c + a)}}} ,$ then the value of $\int_0^\infty {\frac{{{x^2}dx}}{{({x^2} + 4)({x^2} + 9)}}} $ is
→