If $[x]$ denotes the greatest integer $ \leq x$, then the system of linear equations
$[sin \,\theta ] x + [-cos\,\theta ] y = 0$
$[cot \,\theta ] x + y = 0$
If $[x]$ denotes the greatest integer $ \leq x$, then the system of linear equations
$[sin \,\theta ] x + [-cos\,\theta ] y = 0$
$[cot \,\theta ] x + y = 0$
- [JEE MAIN 2019]
- A
have infinitely many solutions if $\theta \in \left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right)$ and and has a unique solution if $\theta \in \left( {\pi ,\frac{{7\pi }}{6}} \right)$
- B
have infinitely many solutions if $\theta \in \left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right) \cup \left( {\pi ,\frac{{7\pi }}{6}} \right)$
- C
has a unique solution if $\theta \in \left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right)$ and and have infinitely many solutions if $\theta \in \left( {\pi ,\frac{{7\pi }}{6}} \right)$
- D
has a unique solution if $\theta \in \left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right) \cup \left( {\pi ,\frac{{7\pi }}{6}} \right)$
Similar Questions
If $a$, $b$, $c$, $d$, $e$, $f$ are in $G.P$., then the value of $\left| {\begin{array}{*{20}{c}}
{{a^2}}&{{d^2}}&x \\
{{b^2}}&{{e^2}}&y \\
{{c^2}}&{{f^2}}&z
\end{array}} \right|$ depends on
If $a$, $b$, $c$, $d$, $e$, $f$ are in $G.P$., then the value of $\left| {\begin{array}{*{20}{c}}
{{a^2}}&{{d^2}}&x \\
{{b^2}}&{{e^2}}&y \\
{{c^2}}&{{f^2}}&z
\end{array}} \right|$ depends on
The value of $k \in R$, for which the following system of linear equations
$3 x-y+4 z=3$
$x+2 y-3 x=-2$
$6 x+5 y+k z=-3$
has infinitely many solutions, is:
The value of $k \in R$, for which the following system of linear equations
$3 x-y+4 z=3$
$x+2 y-3 x=-2$
$6 x+5 y+k z=-3$
has infinitely many solutions, is:
- [JEE MAIN 2021]
The number of $\theta \in(0,4 \pi)$ for which the system of linear equations
$3(\sin 3 \theta) x-y+z=2$, $3(\cos 2 \theta) x+4 y+3 z=3$, $6 x+7 y+7 z=9$ has no solution is.
The number of $\theta \in(0,4 \pi)$ for which the system of linear equations
$3(\sin 3 \theta) x-y+z=2$, $3(\cos 2 \theta) x+4 y+3 z=3$, $6 x+7 y+7 z=9$ has no solution is.
- [JEE MAIN 2022]
If a system of the equation ${(\alpha + 1)^3}x + {(\alpha + 2)^3}y - {(\alpha + 3)^3} = 0$ and $(\alpha + 1)x + (\alpha + 2)y - (\alpha + 3) = 0,x + y - 1 = 0$ is constant. what is the value of $\alpha $
If a system of the equation ${(\alpha + 1)^3}x + {(\alpha + 2)^3}y - {(\alpha + 3)^3} = 0$ and $(\alpha + 1)x + (\alpha + 2)y - (\alpha + 3) = 0,x + y - 1 = 0$ is constant. what is the value of $\alpha $
Consider the system of equations
$ x-2 y+3 z=-1 $ ; $ -x+y-2 z=k $ ; $ x-3 y+4 z=1$
$STATEMENT -1$ : The system of equations has no solution for $\mathrm{k} \neq 3$. and
$STATEMENT - 2$ : The determinant $\left|\begin{array}{ccc}1 & 3 & -1 \\ -1 & -2 & \mathrm{k} \\ 1 & 4 & 1\end{array}\right| \neq 0$, for $\mathrm{k} \neq 3$.
Consider the system of equations
$ x-2 y+3 z=-1 $ ; $ -x+y-2 z=k $ ; $ x-3 y+4 z=1$
$STATEMENT -1$ : The system of equations has no solution for $\mathrm{k} \neq 3$. and
$STATEMENT - 2$ : The determinant $\left|\begin{array}{ccc}1 & 3 & -1 \\ -1 & -2 & \mathrm{k} \\ 1 & 4 & 1\end{array}\right| \neq 0$, for $\mathrm{k} \neq 3$.
- [IIT 2008]