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
Let $a, b, c, d$ be in arithmetic progression with common difference $\lambda$. If

$\left|\begin{array}{lll} x+a-c & x+b & x+a \\ x-1 & x+c & x+b \\ x-b+d & x+d & x+c \end{array}\right|=2$

then value of $\lambda^{2}$ is equal to $.....$

  • A
    $4$
  • ✓
    $1$
  • C
    $9$
  • D
    $16$
✓

Answer

Correct option: B.
$1$
b
$\left|\begin{array}{lll}x+a-c & x+b & x+a \\ x-1 & x+c & x+b \\ x-b+d & x+d & x+c\end{array}\right|=2$

$C_{2} \rightarrow C_{2}-C_{3}$

$\left|\begin{array}{ccc}x-2 \lambda & \lambda & x+a \\ x-1 & \lambda & x+b \\ x+2 \lambda & \lambda & x+C\end{array}\right|=2$

$\mathrm{R}_{2} \rightarrow \mathrm{R}_{2}-\mathrm{R}_{1}, \mathrm{R}_{3} \rightarrow \mathrm{R}_{3}-\mathrm{R}_{1}$

$\Rightarrow\left|\begin{array}{ccc}x-2 \lambda & 1 & x+a \\ 2 \lambda-1 & 0 & \lambda \\ 4 \lambda & 0 & 2 \lambda\end{array}\right|=2$

$\Rightarrow 1\left(4 \lambda-4 \lambda^{2}+2 \lambda\right)=2 \Rightarrow \lambda^{2}=1$

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

The area of the region bounded by the parabola y = x2 + 1 and the staight line x + y = 3 is given by:
  1. $\frac{45}{7}$
  2. $\frac{25}{4}$
  3. $\frac{\pi}{18}$
  4. $\frac{9}{2}$ 
→
$\int \frac{(x-3) e^x}{(x-1)^3} d x=$ _________ + C.
→
The value of $\int\frac{\cos\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$ is:
  1. $2\cos\sqrt{\text{x}}+\text{C}$
  2. $\sqrt{\frac{\cos\text{x}}{\text{x}}}+\text{C}$
  3. $\sin\sqrt{\text{x}}+\text{C}$
  4. $2\sin\sqrt{\text{x}}+\text{C}$
→
If $a=i+j$  and $b=2i-k$  are two vectors, then the point of intersection of two lines $r \times a = b \times a$  and $r \times a = a \times b$ is
→
The general solution of the differential equation $x\left(1-y^2\right) d x+y\left(1-x^2\right) d y=0$ is
→
If A is square matrix of order 3, then ∣​Adj(AdjA2)​∣​ =
  1. |A|2
  2. |A|4
  3. |A|8
  4. |A|16
→
$\int_{}^{} {\sqrt {1 + \cos x} \;dx} $ equals
→
If $\text{A}=\begin{bmatrix} 2 & -1 \\ 3 & -2 \end{bmatrix},$ then An =

  1. $\text{A}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix},$ if n is an even natural number

  2. $\text{A}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix},$ if n is an odd natural number

  3. $\text{A}=\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix},\text{if n}\in\text{N}$

  4. None of these.

→
A function $y=f(x)$ satisfies $f(x) \sin 2 x+\sin x-\left(1+\cos ^2 x\right) f^{\prime}(x)=0$ with condition $f(0)=0$. Then $f\left(\frac{\pi}{2}\right)$ is equal to
→
Let $\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{b}=2 \hat{i}-2 \hat{j}-2 \hat{k}$ and $\overrightarrow{ c }=-\hat{ i }+4 \hat{ j }+3 \hat{ k }$. If $\overrightarrow{ d }$ is a vector perpendicular to both $\vec{b}$ and $\overrightarrow{ c }$ and $\overrightarrow{ a } \cdot \overrightarrow{ d }=18$, Then $|\overrightarrow{ a } \times \overrightarrow{ d }|^2$ is equal to $..........$.
→