Download App

Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
If $\text{a, b, c}$ are in $A.P$., then the determinant $\begin{vmatrix}\text{x}+2&\text{x}+3&\text{x}+2\text{a}\\\text{x}+3&\text{x}+4&\text{x}+2\text{b}\\\text{x}+4&\text{x}+5&\text{x}+2\text{c}\end{vmatrix}$
  • ✓
    $0$
  • B
    $1$
  • C
    $x$
  • D
    $2x$
✓

Answer

Correct option: A.
$0$
$\begin{vmatrix}\text{x}+2&\text{x}+3&\text{x}+2\text{a}\\\text{x}+3&\text{x}+4&\text{x}+2\text{b}\\\text{x}+4&\text{x}+5&\text{x}+2\text{c}\end{vmatrix}$
$=\begin{vmatrix}0&0&2(\text{a}+\text{c}-2\text{b})\\\text{x}+3&\text{x}+4&\text{x}+2\text{b}\\\text{x}+4&\text{x}+5&\text{x}+2\text{c}\end{vmatrix}$
$[$Applying $R_1 \rightarrow R_1+R_3-R_2, R_1 \rightarrow R_1-R_2]$
$=\begin{vmatrix}0&0&0\\\text{x}+3&\text{x}+4&\text{x}+2\text{b}\\\text{x}+4&\text{x}+5&\text{x}+2\text{c}\end{vmatrix}\ [\because \text{a, b, c}$ are in $A.P.]$
$=0$

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 Determinants→Determinants — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The unit vector perpendicular to the plane passing through points $\text{P}\big(\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}\big),\text{Q}\big(2\hat{\text{i}}-\hat{\text{k}}\big)$ and $\text{R}\big(2\hat{\text{j}}+\hat{\text{k}}\big)$ is :
→
$\int_0^{\pi /2} {\frac{{\cos x - \sin x}}{{1 + \sin x\cos x}}} \,dx = $
→
A rectangular parallelopiped is formed by planes drawn through the point (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is:
→
The area bounded by curve $y = x^2- 1$ and tangents to it at $(2, 3)$ and $y -$ axis is:
→
Choose the correct answer from given four options in each of the Exercise:
If A and B are invertible matrices, then which of the following is not correct?
→
Let $\overrightarrow{ a }=2 \hat{ i }-3 \hat{ j }+4 \hat{ k }$ and $\overrightarrow{ b }=7 \hat{ i }+\hat{ j }-6 \hat{ k }$ If $\overrightarrow{ r } \times \overrightarrow{ a }=\overrightarrow{ r } \times \overrightarrow{ b }, \overrightarrow{ r } \cdot(\hat{ i }+2 \hat{ j }+\hat{ k })=-3,$ then $\overrightarrow{ r } \cdot(2 \hat{ i }-3 \hat{ j }+\hat{ k })$ is equal to
→
The vector $2\,i + j - k$ is perpendicular to $i - 4j + \lambda k,$ if $\lambda = $
→
$\mathop {\lim }\limits_{n \to \infty } \frac{1}{n}\sum\limits_{r = 1}^{2n} {\frac{r}{{\sqrt {{n^2} + {r^2}} }}} $ equals
→
Let x, y be two variables and x > 0, xy = 1, then minimum value of x + y is :
→
The matrix $\text{A}=\begin{bmatrix}0&\text{amp};0&\text{amp};0\\0&\text{amp};4&\text{amp};0\\4&\text{amp};0&\text{amp};0\end{bmatrix}$ is $a$ :
→