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
Question
If $\left| {\,\begin{array}{*{20}{c}}{x - 1}&3&0\\2&{x - 3}&4\\3&5&6\end{array}\,} \right| = 0$, then $x =$
✓

Answer

d
(d) Given equation reduces to $(x - 1)\,(6x - 38) = 0$

==> $3{x^2} - 22x + 19 = 0 \Rightarrow (x - 1)(3x - 19) = 0$

==> $x = 1,\,19/3$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let a line $l$ pass through the origin and be perpendicular to the lines

$l_1: \overrightarrow{ r }=(\hat{ i }-11 \hat{ j }-7 \hat{ k })+\lambda(\hat{ i }+2 \hat{ j }+3 \hat{ k }), \lambda \in R$

and $l_2: \overrightarrow{ r }=(-\hat{ i }+\hat{ k })+\mu(2 \hat{ i }+2 \hat{ j }+\hat{ k }), \mu \in R$.

If $P$ is the point of intersection of $l$ and $l_1$, and $Q (\alpha$ $, \beta, \gamma)$ is the foot of perpendicular from $P$ on $l_2$, then $9(\alpha+\beta+\gamma)$ is equal to $..........$.

→
$\left| {\,\begin{array}{*{20}{c}}1&{1 + ac}&{1 + bc}\\1&{1 + ad}&{1 + bd}\\1&{1 + ae}&{1 + be}\end{array}\,} \right| = $
→
If $\lim _{x \rightarrow 0} \frac{a x^2 e^x-b \log _e(1+x)+c x e^{-x}}{x^2 \sin x}=1$, then $16\left(a^2+b^2+c^2\right)$ is equal  to ...........................
→
Let $A=\left[\begin{array}{cc}1 & \frac{1}{51} \\ 0 & 1\end{array}\right]$. If $B=\left[\begin{array}{cc}1 & 2 \\ -1 & -1\end{array}\right] A \left[\begin{array}{cc}-1 & -2 \\ 1 & 1\end{array}\right]$ then the sum of all the elements of the matrix $\sum \limits_{n=1}^{50} B^n$ is equal to
→
Integral curve satisfying $y' = \frac{{{x^2} + {y^2}}}{{{x^2} - {y^2}}},\;y(1) = 2$ has the slope at the point $(1, 0)$ of the curve, equal to
→
If $a \ne p,b \ne q,c \ne r$ and $\left| {\,\begin{array}{*{20}{c}}p&b&c\\{p + a}&{q + b}&{2c}\\a&b&r\end{array}\,} \right|$ =$ 0$, then $\frac{p}{{p - a}} + \frac{q}{{q - b}} + \frac{r}{{r - c}} = $
→
If for some $\alpha, \beta ; \alpha \leq \beta, \alpha+\beta=8$ and $\sec ^{2}\left(\tan ^{-1} \alpha\right)+\operatorname{cosec}^{2}\left(\cot ^{-1} \beta\right)=36$, then $\alpha^{2}+\beta$ is ______________ .
→
If domain of the function $\log _e\left(\frac{6 x^2+5 x+1}{2 x-1}\right)+\cos ^{-1}\left(\frac{2 x^2-3 x+4}{3 x-5}\right)$ is $(\alpha, \beta) \cup(\gamma, \delta]$, then $18\left(\alpha^2+\beta^2+\gamma^2+\delta^2\right)$ is equal to $....$.
→
Let the function $f: R \rightarrow R$ be defined by

$f(t)=\left\{\begin{array}{cc}(-1)^{n+1} 2, & \text { if } t=2 n-1, n \in N , \\ \frac{(2 n+1-t)}{2} f(2 n-1)+\frac{(t-(2 n-1))}{2} f(2 n+1), & \text { if } 2 n-1 < t < 2 n+1, n \in N \end{array}\right.$

Define $g(x)=\int_1^x f(t) d t, x \in(1, \infty)$. Let $\alpha$ denote the number of solutions of the equation $g(x)=0$ in the interval $(1,8]$ and $\beta=\lim _{x \rightarrow 1+} \frac{g(x)}{x-1}$. Then the value of $\alpha+\beta$ is equal to. . . . . .

→
If $y=y(x)$ is the solution of the differential equation,$\sqrt{4-x^{2}} \frac{d y}{d x}=\left(\left(\sin ^{-1}\left(\frac{x}{2}\right)\right)^{2}-y\right) \sin ^{-1}\left(\frac{x}{2}\right)$,$-2 \leq x \leq 2, y(2)=\left(\frac{\pi^{2}-8}{4}\right)$, then $\mathrm{y}^{2}(0)$ is equal to _______________ .
→