Suppose D = | , * 20 c a_1 & b_1 & c_1 a_2 & b_2 & c_2 a_3 & b_3 … - Vidyadip

MCQ

Suppose $D = \left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right|$ and $D' = \left| {\,\begin{array}{*{20}{c}}{{a_1} + p{b_1}}&{{b_1} + q{c_1}}&{{c_1} + r{a_1}}\\{{a_2} + p{b_2}}&{{b_2} + q{c_2}}&{{c_2} + r{a_2}}\\{{a_3} + p{b_3}}&{{b_3} + q{c_3}}&{{c_3} + r{a_3}}\end{array}\,} \right|$, then

A
$D' = D$
B
$D' = D(1 - pqr)$
C
$D' = D(1 + p + q + r)$
✓
$D' = D(1 + pqr)$

✓

Answer

Correct option: D.

$D' = D(1 + pqr)$

d
(d) $D' = D + pqr\,D = D(1 + pqr)$.

Trick : Check by putting $a_1 = b_2 = c_3 = 1$ and all other zero.

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 STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

${\cot ^{ - 1}}\frac{{xy + 1}}{{x - y}} + {\cot ^{ - 1}}\frac{{yz + 1}}{{y - z}} + {\cot ^{ - 1}}\frac{{zx + 1}}{{z - x}} = $

The lines $\frac{\text{x}}{1}=\frac{\text{y}}{2}=\frac{\text{z}}{3}$ and $\frac{\text{x}-1}{-2}=\frac{\text{y}-2}{-4}=\frac{\text{z}-3}{-6}$ are:

If magnitudes of vectors $\vec a,\vec b,\,\vec c$ are $3, 4,$ and $5$ respectively $\vec a\,$ and $\,\vec b + \,\vec c,\, \vec b\,$ and $\,\vec c + \,\vec a,$ $\vec c\,$ and $ \,\vec a + \,\vec b,$ perpendicular to each other, then $\left| {\vec a + \vec b + \vec c} \right|=$

If a function $f(x)$ is such that $f\left( {x + \frac{1}{x}} \right) = {x^2} + \frac{1}{{{x^2}}};$ then $(fof )$ $\sqrt {11} )$ =

In a binomial distribution $B(n\,\,,\,p =$ $\frac{1}{4}$) ,if the probability of at least one success is greater than or equal to$ \frac{9}{{10}}$ then $n$ greater than :

If ${\sin ^{ - 1}}x + {\sin ^{ - 1}}y + {\sin ^{ - 1}}z = \frac{{3\pi }}{2}$, then the value of ${x^{100}} + {y^{100}} + {z^{100}} - \frac{9}{{{x^{101}} + {y^{101}} + {z^{101}}}}$ is equal to

If matrix $A$ is of order $p \times q$ and matrix $B$ is of order $r \times s$ then $A − B$ will exist if :

If the vectors $2i - 3j,\,\,i + j - k$ and $3i - k$ form three concurrent edges of $a $ parallelopiped, then the volume of the parallelopiped is

Choose the correct answer from the given four options:
The area of the region bounded by the y-axis, $\text{y}=\cos\text{x}$ and $\text{y}=\sin\text{x},0\leq\text{x}\leq\frac{\pi}{2}$ is:

$\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sec^2\text{x dx}$ is equal to: