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
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 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 $3X + 2Y = I$ and $2X - Y = O$, where $ I$  and $ O $ are unit and null matrices of order $3 $ respectively, then
→
If the maximum value of $a$, for which the function $f_{a}(x)=\tan ^{-1} 2 x-3 a x+7$ is non-decreasing in $\left(-\frac{\pi}{6}, \frac{\pi}{6}\right)$, is $\bar{a}$, then $f_{a}\left(\frac{\pi}{8}\right)$ is equal to
→
Let $\phi(\text{x})=\text{f}(\text{x})+\text{f}(2\text{a}-\text{x})$ and f'(x) > 0 for all $\text{x}\in[0,\text{a}].$ Then, $\phi(\text{x}):$
  1. Increases on [0, a]
  2. Decreases on [0, a]
  3. Increases on [-a, 0]
  4. Decreases on [a, 2a]
→
Let f(x) = (x - a)2 + (x - b)2 + (x - c)2. Then, f(x) has a minimum at x = 
  1. $\frac{\text{a}+\text{b}+\text{c}}{3}$
  2. $\sqrt[3]{\text{a}\text{b}\text{c}}$
  3. $\frac{3}{\frac{1}{\text{a}}+\frac{1}{\text{b}}+\frac{1}{\text{c}}}$
  4. None of these.
→
A tetrahedron of volume $5$  has three of its vertices at the points $A(2,1,-1), \,\,B(3,0,1)$ and $C(2,-1,3).$ If the fourth vertex $D$ lies on the $y-$ axis, then sum of ordinates of all possible points $D$ is-
→
Let $S$ be the set of all twice differentiable functions $f$ from $R$ to $R$ such that $\frac{d^2 f}{d x^2}(x)>0$ for all $x \in(-1,1)$. For $f \in S$, let $X_f$ be the number of points $x \in(-1,1)$ for which $f(x)=x$. Then which of the following statements is(are) true?

($A$) There exists a function $f \in S$ such that $X_f=0$

($B$) For every function $f \in S$, we have $X_f \leq 2$

($C$) There exists a function $f \in S$ such that $X_f=2$

($D$) There does $NOT$ exist any function $f$ in $\mathrm{S}$ such that $\mathrm{X}_f=1$

→
A line $L$ : $y=m x+3$ meets $y$ - axis at $E(0,3)$ and the arc of the parabola $y^2=16 x, 0 \leq y \leq 6$ at the point $F\left(x_0, y_0\right)$. The tangent to the parabola at $F\left(x_0, y_0\right)$ intersects the $y$-axis at $G\left(0, y_1\right)$. The slope $m$ of the line $L$ is chosen such that the area of the triangle EFG has a local maximum

Match List $I$ with List $II$ and select the correct answer using the code given below the lists :

List $I$ List $II$
$P.$ $\quad$m= $1.$ $\quad\frac{1}{2}$
$Q.$ $\quad$Maximum area of $\triangle E F G$ is $2.$ $\quad4$
$R.$ $\quad y_0=$ $3.$ $\quad2$
$S.$ $\quad y_1=$ $4.$ $\quad1$

Codes: $ \quad P \quad Q \quad R \quad S $ 

→
The distance between the point (3, 4, 5) and the point where the line $\frac{\text{x}-3}{\text{1}}=\frac{\text{y}-4}{\text{2}}=\frac{\text{z}-5}{\text{2}}$ meets the plane x + y + z = 17 is:
  1. 1
  2. 2
  3. 3
  4. None of these
→
The function $f(x) = {\sin ^4}x + {\cos ^4}x$ increases, if
→
If the points A and B are (1, 2, -1), and (2, 1, -1) respectively, then $ \vec{ \text{AB }} $ is:
  1. $\hat{\text{i}}+\hat{\text{j}}$
  2. $\hat{\text{i}}-\hat{\text{j}}$
  3. $2\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}$
  4. $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$
→