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
MCQ
The value of $\left| {\,\begin{array}{*{20}{c}}a&{a + b}&{a + 2b}\\{a + 2b}&a&{a + b}\\{a + b}&{a + 2b}&a\end{array}\,} \right|$ is equal to
  • A
    $9{a^2}(a + b)$
  • ✓
    $9{b^2}(a + b)$
  • C
    ${a^2}(a + b)$
  • D
    ${b^2}(a + b)$
✓

Answer

Correct option: B.
$9{b^2}(a + b)$
b
(b) Operating ${C_1} \to {C_1} + {C_2} + {C_3}$. We get the value of given determinant as $\left| {\,\begin{array}{*{20}{c}}{3a + 3b}&{a + b}&{a + 2b}\\{3a + 3b}&a&{a + b}\\{3a + 3b}&{a + 2b}&a\end{array}\,} \right|$

= $3\,(a + b)\,\left| {\,\begin{array}{*{20}{c}}1&{a + b}&{a + 2b}\\1&a&{a + b}\\1&{a + 2b}&a\end{array}\,} \right|$

Operate ${R_3} \to {R_3} - {R_1}$, ${R_2} \to {R_2} - {R_1}$

= $3\,(a + b)\,\left| {\,\begin{array}{*{20}{c}}1&{a + b}&{a + 2b}\\0&{ - b}&{ - b}\\0&b&{ - 2b}\end{array}\,} \right|$

$ = 3(a + b)\,(2{b^2} + {b^2}) = 9{b^2}(a + b)$.

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 vertex of a parabola is the point $(a, b)$ and latus rectum is of length $l$. If the axis of the parabola is along the positive direction of $y$ - axis, then its equation is
→
Let $\theta_1, \theta_2, \ldots, \theta_{10}$ be positive valued angles (in radian) such that $\theta_1+\theta_2+\ldots+\theta_{10}=2 \pi$. Define the complex numbers $z_1=e^{i \theta_1}, z_k=z_{k-1} e^{i \theta_k}$ for $k=2,3, \ldots, 10$, where $i=\sqrt{-1}$. Consider the statements $P$ and $Q$ given below :

$P:\left|z_2-z_1\right|+\left|z_3-z_2\right|+\ldots+\left|z_{10}-z_9\right|+\left|z_1-z_{10}\right| \leq 2 \pi$

$Q:\left|z_2^2-z_1^2\right|+\left|z_3^2-z_2^2\right|+\ldots .+\left|z_{10}^2-z_9^2\right|+\left|z_1^2-z_{10}^2\right| \leq 4 \pi$

Then,

→
Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors such that $\vec{b}$ and $\vec{c}$ are non-collinear if $\vec{a}+5 \vec{b}$ is collinear with $\overrightarrow{\mathrm{c}}, \overrightarrow{\mathrm{b}}+6 \overrightarrow{\mathrm{c}}$ is collinear with $\overrightarrow{\mathrm{a}}$ and $\vec{a}+\alpha \vec{b}+\beta \vec{c}=\overrightarrow{0}$, then $\alpha+\beta$ is equal to
→
$\mathop {\lim }\limits_{x \to 0} \frac{{\cos (\sin x) - 1}}{{{x^2}}} = $
→
If the mean deviation about the mean of the numbers $1,2,3, \ldots ., n$, where $n$ is odd, is $\frac{5(n+1)}{n}$, then $n$ is equal to
→
The value of $\frac{{{{\sin }^2}\theta }}{{\sin \theta  - \cos \theta }} - \frac{{\sin \theta  + \cos \theta }}{{{{\tan }^2}\theta  - 1}}$ for all permissible vlaues of $\theta$
→
Let $\alpha $ and $\beta $ be integers satisfying $0 < \beta < \alpha $ .Let $P\left( {\alpha ,\beta } \right),Q$ be the reflection of $P$ in the line $y = x, R$ be the reflection of $Q$ in the $y-$ axis, $S$ be the reflection of $R$ in the $x-$ axis and $T$ be the reflection of $S$ in the $y-$ axis. If the area of convex pentagon $PQRST$ is $187\ sq. units$ , then value of $\alpha  + {\beta ^2}$ is
→
Let $AB$ be a chord of the circle ${x^2} + {y^2} = {r^2}$ subtending a right angle at the centre. Then the locus of the centroid of the $\Delta PAB$ as $P$ moves on the circle is
→
Find the values of $\tan \left(\sin ^{-1} \frac{3}{5}+\cot ^{-1} \frac{3}{2}\right)$
→
If ${i^2} = - 1$, then sum $i + {i^2} + {i^3} + ...$to $1000$ terms is equal to
→