If [x] denotes the greatest integer ≤ x, then the system of linear equations [sin θ]x + [-cos θ]y = 0 and [cot θ]x + y = 0

Has unique solution if \(\theta \in \left( {\frac{\pi }{2},{\rm{\;}}\frac{{2\pi }}{3}} \right) \cup \left( {\pi ,{\rm{\;}}\frac{{7\pi }}{6}} \right)\).

Have infinitely many solutions if \(\theta \in \left( {\frac{\pi }{2},{\rm{\;}}\frac{{2\pi }}{3}} \right)\) and has a unique solution if \(\theta \in \left( {\pi ,{\rm{\;}}\frac{{7\pi }}{6}} \right)\).

Has unique solution if \(\theta \in \left( {\frac{\pi }{2},{\rm{\;}}\frac{{2\pi }}{3}} \right)\) and have infinitely many solutions if \(\theta \in \left( {\pi ,{\rm{\;}}\frac{{7\pi }}{6}} \right)\).

Have infinitely many solutions if \(\theta \in \left( {\frac{\pi }{2},\;\frac{{2\pi }}{3}} \right) \cup \left( {\pi ,\;\frac{{7\pi }}{6}} \right)\).

If [x] denotes the greatest integer ≤ x, then the system of linea

1.	If [x] denotes the greatest integer ≤ x, then the system of linear equations [sin θ]x + [-cos θ]y = 0 and [cot θ]x + y = 0
A.	Have infinitely many solutions if \(\theta \in \left( {\frac{\pi }{2},{\rm{\;}}\frac{{2\pi }}{3}} \right)\) and has a unique solution if \(\theta \in \left( {\pi ,{\rm{\;}}\frac{{7\pi }}{6}} \right)\).
B.	Has unique solution if \(\theta \in \left( {\frac{\pi }{2},{\rm{\;}}\frac{{2\pi }}{3}} \right) \cup \left( {\pi ,{\rm{\;}}\frac{{7\pi }}{6}} \right)\).
C.	Has unique solution if \(\theta \in \left( {\frac{\pi }{2},{\rm{\;}}\frac{{2\pi }}{3}} \right)\) and have infinitely many solutions if \(\theta \in \left( {\pi ,{\rm{\;}}\frac{{7\pi }}{6}} \right)\).
D.	Have infinitely many solutions if \(\theta \in \left( {\frac{\pi }{2},\;\frac{{2\pi }}{3}} \right) \cup \left( {\pi ,\;\frac{{7\pi }}{6}} \right)\).
Answer» B. Has unique solution if \(\theta \in \left( {\frac{\pi }{2},{\rm{\;}}\frac{{2\pi }}{3}} \right) \cup \left( {\pi ,{\rm{\;}}\frac{{7\pi }}{6}} \right)\).

Discussion

No Comment Found

Related MCQs

If \(A=\left[ \begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ \end{matrix} \right]\) then A-1 is-
If the determinant \(\left| {\begin{array}{*{20}{c}} x&1&3\\ 0&0&1\\ 1&x&4 \end{array}} \right| = 0\) then what is x equal to?
If A and B are square matrices of order 3 such that |A| = -1, |B| = 3 then |3 AB| is equal to -
If B is a non-singular matrix and A is a square matrix, then the value of det (B-1 AB) is equal to
If [x] denotes the greatest integer ≤ x, then the system of linear equations [sin θ]x + [-cos θ]y = 0 and [cot θ]x + y = 0
If a, b, c are real numbers, then the value of the determinant \(\left| {\begin{array}{*{20}{c}} {1 - {\rm{a}}}&{{\rm{a}} - {\rm{b}} - {\rm{c}}}&{{\rm{b}} + {\rm{c}}}\\ {1 - {\rm{b}}}&{{\rm{b}} - {\rm{c}} - {\rm{a}}}&{{\rm{c}} + {\rm{a}}}\\ {1 - {\rm{c}}}&{{\rm{c}} - {\rm{a}} - {\rm{b}}}&{{\rm{a}} + {\rm{b}}} \end{array}} \right|\) is
If the value of the determinant \(\left[ {\begin{array}{*{20}{c}} {\rm{a}}&1&1\\ 1&{\rm{b}}&1\\ 1&1&{\rm{c}} \end{array}} \right]\) is positive, where a ≠ b ≠ c, then the value of abc is
A matrix Mr is defined as \(M_r = \begin{bmatrix} r & r - 1 \\\ r - 1 & r \end{bmatrix} r \in N\), then the value of det (M1) + det(M2) + ... + det(M2015) is
If \(A=\left[ \begin{matrix}{{e}^{t}} & {{e}^{-t}}\text{cos }\!\!~\!\!\text{ }t & {{e}^{-t}}\text{sin }\!\!~\!\!\text{ }t \\{{e}^{t}} & -{{e}^{-t}}\text{cos }\!\!~\!\!\text{ }t-{{e}^{-t}}\text{sin }\!\!~\!\!\text{ }t & -{{e}^{-t}}\text{sin }\!\!~\!\!\text{ }t+{{e}^{-t}}\text{cos }\!\!~\!\!\text{ }t \\{{e}^{t}} & 2{{e}^{-t}}\text{sin }\!\!~\!\!\text{ }t & -2{{e}^{-t}}\text{cos }\!\!~\!\!\text{ }t \\\end{matrix} \right]\) then A is:
Factors of the determinant \(\left| {\begin{array}{*{20}{c}} a&{b + c}&{{a^2}}\\ b&{c + a}&{{b^2}}\\ c&{a + b}&{{c^2}} \end{array}} \right|\)