Let a, , R. Consider the system of linear equations a x+2 y= 3 x-… - Vidyadip

MCQ

Let $a, \lambda, \mu \in \mathbb{R}$. Consider the system of linear equations

$a x+2 y=\lambda$

$3 x-2 y=\mu$Which of the following statement($s$) is(are) correct?

($A$) If $a=-3$, then the system has infinitely many solutions for all values of $\lambda$ and $\mu$

($B$) If $a \neq-3$, then the system has a unique solution for all values of $\lambda$ and $\mu$

($C$) If $\lambda+\mu=0$, then the system has infinitely many solutions for $a=-3$

($D$) If $\lambda+\mu \neq 0$, then the system has no solution for $a=-3$

A
$A,C$
B
$B,C$
✓
$B,C,D$
D
$B,C,A$

✓

Answer

Correct option: C.

$B,C,D$

c
$\alpha x+2 y=\lambda$

$3 x-2 y=\mu$

$\Delta=\left|\begin{array}{ll}\alpha & 2 \\ 3 & -2\end{array}\right|=-2 \alpha-6$

$\Delta=0, \therefore, \alpha=-3$

$\Delta_1=\left|\begin{array}{ll}\lambda & 2 \\ \mu & -2\end{array}\right|=-2 \lambda-2 \mu=-2(\lambda+\mu)$

$\Delta_2=\left|\begin{array}{ll}-3 & \lambda \\ 3 & \mu\end{array}\right|=-3 \mu-3 \lambda=-3(\lambda-\mu)$

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

Given $A=\left[\begin{array}{ccc}\sqrt{3} & 1 & -1 \\ 2 & 3 & 0\end{array}\right]$ and $B=\left[\begin{array}{ccc}2 & \sqrt{5} & 1 \\ -2 & 3 & \frac{1}{2}\end{array}\right],$ find $A+B$ $=$ ........

The function $\text{f}:[0,\infty)\rightarrow\ \text{R}$ given by $\text{f(x)}=\frac{\text{x}}{\text{x}+1}$ is:

If $f: R \rightarrow R$ be given by $f(\text{x})=(3-\text{x}^3)^{\frac{1}{3}},$ then $fof(x)$ is:

Function $f(x) = {{4{x^2} + 1} \over x}$ is decreasing for interval

If $\text{f(x)}=\log_{\text{x}^2}(\log\text{x}),$ the f(x) at x = e is:

$\int\frac{\text{x}^3}{\text{x}+1}\text{ dx}$ is equal to:

If $ a$ and $b$ are unit vectors such that $a \times b$ is also a unit vector, then the angle between $a$ and $ b$ is

$a.(b × c)$ is equal to

Let $\vec{a}=a_i \hat{i}+a_2 \hat{j}+a_3 \hat{k}$ and $\vec{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$ be two vectors such that $|\vec{a}|=1 ; \quad \vec{a} \cdot \vec{b}=2$ and $|\vec{b}|=4$. If $\vec{c}=2(\vec{a} \times \vec{b})-3 \vec{b}$, then the angle between $\vec{b}$ and $\vec{c}$ is equal to :

For the curve $\sqrt{\text{x}}+\sqrt{\text{y}}=1,\frac{\text{dy}}{\text{dx}}$ at $\Big(\frac{1}{4},\frac{1}{4}\Big)$ is: