Determinants and their Properties
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Matrix and Determinant

78999 The value of \(\left|\begin{array}{lll}441 & 442 & 443 \\ 445 & 446 & 447 \\ 449 & 450 & 451\end{array}\right|\) is :

1 \(441 \times 446 \times 4510\)
2 0
3 \(-1\)
4 \(1\)
Karnataka CET-2004
Matrix and Determinant

79000 If \(x^{3}-2 x^{2}-9 x+18=0\) and \(A=\left|\begin{array}{lll}1 & 2 & 5 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|\) then
the maximum value of \(A\) is

1 96
2 36
3 24
4 120
Karnataka CET-2021
Matrix and Determinant

79001 If \(A\) and \(B\) are matrices of order 3 and \(|A|=5\), \(|B|=3\), then \(|\mathbf{3 A B}|\) is

1 425
2 405
3 565
4 585
Karnataka CET-2021
Matrix and Determinant

79002 The system of linear equations \(x+y+z=6\), \(\mathbf{x}+\mathbf{2 y + 3 z}=\mathbf{1 0}\) and \(\quad \mathbf{x}+\mathbf{2 y}+\mathbf{a z}=\mathbf{b}\) has no solution when

1 \(a=3, b \neq 10\)
2 \(b=3, a \neq 10\)
3 \(\mathrm{a}=2, \mathrm{~b} \neq 3\)
4 \(b=2, a=3\)
Karnataka CET-2015
Matrix and Determinant

79003 If \(a e^{x}+b e^{y}=c ; p e^{x}+q e^{y}=d\) and
\(\Delta_{1}=\left|\begin{array}{ll}\mathbf{a} & \mathbf{b} \\ \mathbf{p} & \mathbf{q}\end{array}\right| ; \Delta_{2}=\left|\begin{array}{ll}\mathbf{c} & \mathbf{b} \\ \mathbf{d} & \mathbf{q}\end{array}\right| ; \Delta_{3}=\left|\begin{array}{ll}\mathbf{a} & \mathbf{c} \\ \mathbf{p} & \mathbf{d}\end{array}\right|\) the value of \((\mathrm{x}, \mathrm{y})\)
is

1 \(\left(\frac{\Delta_{2}}{\Delta_{1}}, \frac{\Delta_{3}}{\Delta_{1}}\right)\)
2 \(\left(\log \frac{\Delta_{2}}{\Delta_{1}}, \log \frac{\Delta_{3}}{\Delta_{1}}\right)\)
3 \(\left(\log \frac{\Delta_{1}}{\Delta_{3}}, \log \frac{\Delta_{1}}{\Delta_{2}}\right)\)
4 \(\left(\log \frac{\Delta_{1}}{\Delta_{2}}, \log \frac{\Delta_{1}}{\Delta_{3}}\right)\)
SRM JEE-2018
NEET DIGITAL LIBRARY
Matrix and Determinant

78999 The value of \(\left|\begin{array}{lll}441 & 442 & 443 \\ 445 & 446 & 447 \\ 449 & 450 & 451\end{array}\right|\) is :

1 \(441 \times 446 \times 4510\)
2 0
3 \(-1\)
4 \(1\)
Karnataka CET-2004
Matrix and Determinant

79000 If \(x^{3}-2 x^{2}-9 x+18=0\) and \(A=\left|\begin{array}{lll}1 & 2 & 5 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|\) then
the maximum value of \(A\) is

1 96
2 36
3 24
4 120
Karnataka CET-2021
Matrix and Determinant

79001 If \(A\) and \(B\) are matrices of order 3 and \(|A|=5\), \(|B|=3\), then \(|\mathbf{3 A B}|\) is

1 425
2 405
3 565
4 585
Karnataka CET-2021
Matrix and Determinant

79002 The system of linear equations \(x+y+z=6\), \(\mathbf{x}+\mathbf{2 y + 3 z}=\mathbf{1 0}\) and \(\quad \mathbf{x}+\mathbf{2 y}+\mathbf{a z}=\mathbf{b}\) has no solution when

1 \(a=3, b \neq 10\)
2 \(b=3, a \neq 10\)
3 \(\mathrm{a}=2, \mathrm{~b} \neq 3\)
4 \(b=2, a=3\)
Karnataka CET-2015
Matrix and Determinant

79003 If \(a e^{x}+b e^{y}=c ; p e^{x}+q e^{y}=d\) and
\(\Delta_{1}=\left|\begin{array}{ll}\mathbf{a} & \mathbf{b} \\ \mathbf{p} & \mathbf{q}\end{array}\right| ; \Delta_{2}=\left|\begin{array}{ll}\mathbf{c} & \mathbf{b} \\ \mathbf{d} & \mathbf{q}\end{array}\right| ; \Delta_{3}=\left|\begin{array}{ll}\mathbf{a} & \mathbf{c} \\ \mathbf{p} & \mathbf{d}\end{array}\right|\) the value of \((\mathrm{x}, \mathrm{y})\)
is

1 \(\left(\frac{\Delta_{2}}{\Delta_{1}}, \frac{\Delta_{3}}{\Delta_{1}}\right)\)
2 \(\left(\log \frac{\Delta_{2}}{\Delta_{1}}, \log \frac{\Delta_{3}}{\Delta_{1}}\right)\)
3 \(\left(\log \frac{\Delta_{1}}{\Delta_{3}}, \log \frac{\Delta_{1}}{\Delta_{2}}\right)\)
4 \(\left(\log \frac{\Delta_{1}}{\Delta_{2}}, \log \frac{\Delta_{1}}{\Delta_{3}}\right)\)
SRM JEE-2018
Join With Us for More Updates
Matrix and Determinant

78999 The value of \(\left|\begin{array}{lll}441 & 442 & 443 \\ 445 & 446 & 447 \\ 449 & 450 & 451\end{array}\right|\) is :

1 \(441 \times 446 \times 4510\)
2 0
3 \(-1\)
4 \(1\)
Karnataka CET-2004
Matrix and Determinant

79000 If \(x^{3}-2 x^{2}-9 x+18=0\) and \(A=\left|\begin{array}{lll}1 & 2 & 5 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|\) then
the maximum value of \(A\) is

1 96
2 36
3 24
4 120
Karnataka CET-2021
Matrix and Determinant

79001 If \(A\) and \(B\) are matrices of order 3 and \(|A|=5\), \(|B|=3\), then \(|\mathbf{3 A B}|\) is

1 425
2 405
3 565
4 585
Karnataka CET-2021
Matrix and Determinant

79002 The system of linear equations \(x+y+z=6\), \(\mathbf{x}+\mathbf{2 y + 3 z}=\mathbf{1 0}\) and \(\quad \mathbf{x}+\mathbf{2 y}+\mathbf{a z}=\mathbf{b}\) has no solution when

1 \(a=3, b \neq 10\)
2 \(b=3, a \neq 10\)
3 \(\mathrm{a}=2, \mathrm{~b} \neq 3\)
4 \(b=2, a=3\)
Karnataka CET-2015
Matrix and Determinant

79003 If \(a e^{x}+b e^{y}=c ; p e^{x}+q e^{y}=d\) and
\(\Delta_{1}=\left|\begin{array}{ll}\mathbf{a} & \mathbf{b} \\ \mathbf{p} & \mathbf{q}\end{array}\right| ; \Delta_{2}=\left|\begin{array}{ll}\mathbf{c} & \mathbf{b} \\ \mathbf{d} & \mathbf{q}\end{array}\right| ; \Delta_{3}=\left|\begin{array}{ll}\mathbf{a} & \mathbf{c} \\ \mathbf{p} & \mathbf{d}\end{array}\right|\) the value of \((\mathrm{x}, \mathrm{y})\)
is

1 \(\left(\frac{\Delta_{2}}{\Delta_{1}}, \frac{\Delta_{3}}{\Delta_{1}}\right)\)
2 \(\left(\log \frac{\Delta_{2}}{\Delta_{1}}, \log \frac{\Delta_{3}}{\Delta_{1}}\right)\)
3 \(\left(\log \frac{\Delta_{1}}{\Delta_{3}}, \log \frac{\Delta_{1}}{\Delta_{2}}\right)\)
4 \(\left(\log \frac{\Delta_{1}}{\Delta_{2}}, \log \frac{\Delta_{1}}{\Delta_{3}}\right)\)
SRM JEE-2018
For More Updates join with Us
Matrix and Determinant

78999 The value of \(\left|\begin{array}{lll}441 & 442 & 443 \\ 445 & 446 & 447 \\ 449 & 450 & 451\end{array}\right|\) is :

1 \(441 \times 446 \times 4510\)
2 0
3 \(-1\)
4 \(1\)
Karnataka CET-2004
Matrix and Determinant

79000 If \(x^{3}-2 x^{2}-9 x+18=0\) and \(A=\left|\begin{array}{lll}1 & 2 & 5 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|\) then
the maximum value of \(A\) is

1 96
2 36
3 24
4 120
Karnataka CET-2021
Matrix and Determinant

79001 If \(A\) and \(B\) are matrices of order 3 and \(|A|=5\), \(|B|=3\), then \(|\mathbf{3 A B}|\) is

1 425
2 405
3 565
4 585
Karnataka CET-2021
Matrix and Determinant

79002 The system of linear equations \(x+y+z=6\), \(\mathbf{x}+\mathbf{2 y + 3 z}=\mathbf{1 0}\) and \(\quad \mathbf{x}+\mathbf{2 y}+\mathbf{a z}=\mathbf{b}\) has no solution when

1 \(a=3, b \neq 10\)
2 \(b=3, a \neq 10\)
3 \(\mathrm{a}=2, \mathrm{~b} \neq 3\)
4 \(b=2, a=3\)
Karnataka CET-2015
Matrix and Determinant

79003 If \(a e^{x}+b e^{y}=c ; p e^{x}+q e^{y}=d\) and
\(\Delta_{1}=\left|\begin{array}{ll}\mathbf{a} & \mathbf{b} \\ \mathbf{p} & \mathbf{q}\end{array}\right| ; \Delta_{2}=\left|\begin{array}{ll}\mathbf{c} & \mathbf{b} \\ \mathbf{d} & \mathbf{q}\end{array}\right| ; \Delta_{3}=\left|\begin{array}{ll}\mathbf{a} & \mathbf{c} \\ \mathbf{p} & \mathbf{d}\end{array}\right|\) the value of \((\mathrm{x}, \mathrm{y})\)
is

1 \(\left(\frac{\Delta_{2}}{\Delta_{1}}, \frac{\Delta_{3}}{\Delta_{1}}\right)\)
2 \(\left(\log \frac{\Delta_{2}}{\Delta_{1}}, \log \frac{\Delta_{3}}{\Delta_{1}}\right)\)
3 \(\left(\log \frac{\Delta_{1}}{\Delta_{3}}, \log \frac{\Delta_{1}}{\Delta_{2}}\right)\)
4 \(\left(\log \frac{\Delta_{1}}{\Delta_{2}}, \log \frac{\Delta_{1}}{\Delta_{3}}\right)\)
SRM JEE-2018
NEET DIGITAL LIBRARY
Matrix and Determinant

78999 The value of \(\left|\begin{array}{lll}441 & 442 & 443 \\ 445 & 446 & 447 \\ 449 & 450 & 451\end{array}\right|\) is :

1 \(441 \times 446 \times 4510\)
2 0
3 \(-1\)
4 \(1\)
Karnataka CET-2004
Matrix and Determinant

79000 If \(x^{3}-2 x^{2}-9 x+18=0\) and \(A=\left|\begin{array}{lll}1 & 2 & 5 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|\) then
the maximum value of \(A\) is

1 96
2 36
3 24
4 120
Karnataka CET-2021
Matrix and Determinant

79001 If \(A\) and \(B\) are matrices of order 3 and \(|A|=5\), \(|B|=3\), then \(|\mathbf{3 A B}|\) is

1 425
2 405
3 565
4 585
Karnataka CET-2021
Matrix and Determinant

79002 The system of linear equations \(x+y+z=6\), \(\mathbf{x}+\mathbf{2 y + 3 z}=\mathbf{1 0}\) and \(\quad \mathbf{x}+\mathbf{2 y}+\mathbf{a z}=\mathbf{b}\) has no solution when

1 \(a=3, b \neq 10\)
2 \(b=3, a \neq 10\)
3 \(\mathrm{a}=2, \mathrm{~b} \neq 3\)
4 \(b=2, a=3\)
Karnataka CET-2015
Matrix and Determinant

79003 If \(a e^{x}+b e^{y}=c ; p e^{x}+q e^{y}=d\) and
\(\Delta_{1}=\left|\begin{array}{ll}\mathbf{a} & \mathbf{b} \\ \mathbf{p} & \mathbf{q}\end{array}\right| ; \Delta_{2}=\left|\begin{array}{ll}\mathbf{c} & \mathbf{b} \\ \mathbf{d} & \mathbf{q}\end{array}\right| ; \Delta_{3}=\left|\begin{array}{ll}\mathbf{a} & \mathbf{c} \\ \mathbf{p} & \mathbf{d}\end{array}\right|\) the value of \((\mathrm{x}, \mathrm{y})\)
is

1 \(\left(\frac{\Delta_{2}}{\Delta_{1}}, \frac{\Delta_{3}}{\Delta_{1}}\right)\)
2 \(\left(\log \frac{\Delta_{2}}{\Delta_{1}}, \log \frac{\Delta_{3}}{\Delta_{1}}\right)\)
3 \(\left(\log \frac{\Delta_{1}}{\Delta_{3}}, \log \frac{\Delta_{1}}{\Delta_{2}}\right)\)
4 \(\left(\log \frac{\Delta_{1}}{\Delta_{2}}, \log \frac{\Delta_{1}}{\Delta_{3}}\right)\)
SRM JEE-2018