If _1 = | * 20 c b^5 c^6 ( c^3 - b^3 ) & a^4 c^6 ( a^3 - c^3 ) & … - Vidyadip

MCQ

If ${\Delta _1} = \left| {\begin{array}{*{20}{c}}
{{b^5}{c^6}\left( {{c^3} - {b^3}} \right)}&{{a^4}{c^6}\left( {{a^3} - {c^3}} \right)}&{{a^4}{b^5}\left( {{b^3} - {a^3}} \right)} \\
{{b^2}{c^3}\left( {{b^6} - {c^6}} \right)}&{a{c^3}\left( {{c^6} - {a^6}} \right)}&{a{b^2}\left( {{a^6} - {b^6}} \right)} \\
{{b^2}{c^3}\left( {{c^3} - {b^3}} \right)}&{a{c^3}\left( {{a^3} - {c^3}} \right)}&{a{b^2}\left( {{b^3} - {a^3}} \right)}
\end{array}} \right|$ and ${\Delta _2} = \left| {\begin{array}{*{20}{c}}
a&{{b^2}}&{{c^3}} \\
{{a^4}}&{{b^5}}&{{c^6}} \\
{{a^7}}&{{b^8}}&{{c^9}}
\end{array}} \right|$ then ${\Delta _1}{\Delta _2}$ is equal to

✓
$\Delta _2^3$
B
$\Delta _2^2$
C
$\Delta _2^4$
D
None of these

✓

Answer

Correct option: A.

$\Delta _2^3$

a
$\Delta_{1}=\left(\Delta_{2}\right)^{n-1}\{n=3\}$

so, $\Delta_{1}=\Delta_{2}^{2}$

and $\Delta_{1} \Delta_{2}=\Delta_{2}^{2} \cdot \Delta=\Delta_{2}^{2}$

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 area of the smaller region enclosed by the curves $y ^{2}=8 x +4$ and $x^{2}+y^{2}+4 \sqrt{3} x-4=0$ is equal to.

If $\int {f(x)\,dx = f(x)} ,$ then ${\int {\left[ {f(x)} \right]} ^2}\,\,dx$ is

What is the equation of the ellipse with foci $( \pm 2,\;0)$ and eccentricity $ = \frac{1}{2}$

The area of a triangle whose vertices are $A\,(1,\, - 1,\,2),$ $B\,(2,\,1,\, - 1)$ and $C\,(3,\, - 1,\,2)$ is

Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=3 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}$ be three vectors such that $\vec{c}$ is coplanar with $\vec{a}$ and $\vec{b}$. If the vector $\vec{c}$ is perpendicular to $\vec{b}$ and $\vec{a} \cdot \vec{c}=5$, then $|\vec{c}|$ is equal to

If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B,$ then the locus of the foot of perpendicular from $O$ on $AB$ is

If $y = sin^{-1 }\left( {x\sqrt {1\,\, - \,\,x} \,\,\, + \,\,\,\sqrt x \,\,\sqrt {1\, - \,{x^2}} } \right) \&\,\, \frac{{dy}}{{dx}}= \frac{1}{{2\,\sqrt {x\,(1\,\, - \,\,x)} }}+ p$, then $p =$

Let $S=\{z=x+i y:|z-1+i| \geq|z|,|z|<2,|z+i|=$ $|z-1|\}$. Then the set of all values of $x$, for which $w=2 x+i y \in S$ for some $y \in R$, is.

The value of $\int_2^3 {\frac{{x + 1}}{{{x^2}(x - 1)}}dx} $ is

Let $b_i>1$ for $i=1,2, \ldots, 101$. Suppose $\log _e b_1, \log _e b_2, \ldots, \log _e b_{101}$ are in Arithmetic Progression ($A.P$.) with the common difference $\log _e 2$. Suppose $a_1, a_2, \ldots, a_{101}$ are in $A.P$. such that $a_1=b_1$ and $a_{51}=b_{51}$. If $t=b_1+b_2+\cdots+b_{51}$ and $s=a_1+a_2+\cdots+t_{65}$, then