Concept of Elementary Row and Column Operation
« Previous Topic: System of Equations Last Topic in »
For More Updates join with Us
Matrix and Determinant

79437 The value of \(\lambda\), for which the lines \(3 x-4 y=13\), \(8 x-11 y=33\) and \(2 x-3 y+\lambda=0\) are concurrent is

1 -1
2 -7
3 \(\frac{1}{7}\)
4 9
BITSAT-2014
Matrix and Determinant

79438 Let \(\alpha_{1}, \alpha_{2}\) and \(\beta_{1}, \beta_{2}\) be the roots of \(\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}\) \(=0\) and \(p x^{2}+q x+r=0\) respectively. If the system of equations \(\alpha_{1} y+\alpha_{2} z=0\) and \(\beta_{1} y+\beta_{2} z=0\) has a non-trivial solution, then

1 \(\frac{\mathrm{b}^{2}}{\mathrm{q}^{2}}=\frac{\mathrm{ac}}{\mathrm{pr}}\)
2 \(\frac{\mathrm{c}^{2}}{\mathrm{r}^{2}}=\frac{\mathrm{ab}}{\mathrm{pq}}\)
3 \(\frac{\mathrm{a}^{2}}{\mathrm{p}^{2}}=\frac{\mathrm{bc}}{\mathrm{qr}}\)
4 None of these
BITSAT-2016
Matrix and Determinant

79439 If a system of equation \(-a x+y+z=0 ; x-b y+\) \(\mathbf{z}=\mathbf{0} ; \mathbf{x}+\mathbf{y}-\mathbf{c z}=\mathbf{0}(\mathrm{a}, \mathrm{b}, \mathrm{c} \neq-\mathbf{1})\) has a nonzero solution then
\(\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}=\)

1 0
2 1
3 2
4 3
BITSAT-2017
Matrix and Determinant

79440 The rank of the matrix \(\left[\begin{array}{ccc}-1 & 2 & 5 \\ 2 & -4 & a-4 \\ 1 & -2 & a+1\end{array}\right]\) is

1 1 if \(a=6\)
2 2 if \(a=1\)
3 3 if \(a=2\)
4 1 if \(a=4\)
VITEEE-2017
NEET DIGITAL LIBRARY
Matrix and Determinant

79437 The value of \(\lambda\), for which the lines \(3 x-4 y=13\), \(8 x-11 y=33\) and \(2 x-3 y+\lambda=0\) are concurrent is

1 -1
2 -7
3 \(\frac{1}{7}\)
4 9
BITSAT-2014
Matrix and Determinant

79438 Let \(\alpha_{1}, \alpha_{2}\) and \(\beta_{1}, \beta_{2}\) be the roots of \(\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}\) \(=0\) and \(p x^{2}+q x+r=0\) respectively. If the system of equations \(\alpha_{1} y+\alpha_{2} z=0\) and \(\beta_{1} y+\beta_{2} z=0\) has a non-trivial solution, then

1 \(\frac{\mathrm{b}^{2}}{\mathrm{q}^{2}}=\frac{\mathrm{ac}}{\mathrm{pr}}\)
2 \(\frac{\mathrm{c}^{2}}{\mathrm{r}^{2}}=\frac{\mathrm{ab}}{\mathrm{pq}}\)
3 \(\frac{\mathrm{a}^{2}}{\mathrm{p}^{2}}=\frac{\mathrm{bc}}{\mathrm{qr}}\)
4 None of these
BITSAT-2016
Matrix and Determinant

79439 If a system of equation \(-a x+y+z=0 ; x-b y+\) \(\mathbf{z}=\mathbf{0} ; \mathbf{x}+\mathbf{y}-\mathbf{c z}=\mathbf{0}(\mathrm{a}, \mathrm{b}, \mathrm{c} \neq-\mathbf{1})\) has a nonzero solution then
\(\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}=\)

1 0
2 1
3 2
4 3
BITSAT-2017
Matrix and Determinant

79440 The rank of the matrix \(\left[\begin{array}{ccc}-1 & 2 & 5 \\ 2 & -4 & a-4 \\ 1 & -2 & a+1\end{array}\right]\) is

1 1 if \(a=6\)
2 2 if \(a=1\)
3 3 if \(a=2\)
4 1 if \(a=4\)
VITEEE-2017
Join With Us for More Updates
Matrix and Determinant

79437 The value of \(\lambda\), for which the lines \(3 x-4 y=13\), \(8 x-11 y=33\) and \(2 x-3 y+\lambda=0\) are concurrent is

1 -1
2 -7
3 \(\frac{1}{7}\)
4 9
BITSAT-2014
Matrix and Determinant

79438 Let \(\alpha_{1}, \alpha_{2}\) and \(\beta_{1}, \beta_{2}\) be the roots of \(\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}\) \(=0\) and \(p x^{2}+q x+r=0\) respectively. If the system of equations \(\alpha_{1} y+\alpha_{2} z=0\) and \(\beta_{1} y+\beta_{2} z=0\) has a non-trivial solution, then

1 \(\frac{\mathrm{b}^{2}}{\mathrm{q}^{2}}=\frac{\mathrm{ac}}{\mathrm{pr}}\)
2 \(\frac{\mathrm{c}^{2}}{\mathrm{r}^{2}}=\frac{\mathrm{ab}}{\mathrm{pq}}\)
3 \(\frac{\mathrm{a}^{2}}{\mathrm{p}^{2}}=\frac{\mathrm{bc}}{\mathrm{qr}}\)
4 None of these
BITSAT-2016
Matrix and Determinant

79439 If a system of equation \(-a x+y+z=0 ; x-b y+\) \(\mathbf{z}=\mathbf{0} ; \mathbf{x}+\mathbf{y}-\mathbf{c z}=\mathbf{0}(\mathrm{a}, \mathrm{b}, \mathrm{c} \neq-\mathbf{1})\) has a nonzero solution then
\(\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}=\)

1 0
2 1
3 2
4 3
BITSAT-2017
Matrix and Determinant

79440 The rank of the matrix \(\left[\begin{array}{ccc}-1 & 2 & 5 \\ 2 & -4 & a-4 \\ 1 & -2 & a+1\end{array}\right]\) is

1 1 if \(a=6\)
2 2 if \(a=1\)
3 3 if \(a=2\)
4 1 if \(a=4\)
VITEEE-2017
For More Updates join with Us
Matrix and Determinant

79437 The value of \(\lambda\), for which the lines \(3 x-4 y=13\), \(8 x-11 y=33\) and \(2 x-3 y+\lambda=0\) are concurrent is

1 -1
2 -7
3 \(\frac{1}{7}\)
4 9
BITSAT-2014
Matrix and Determinant

79438 Let \(\alpha_{1}, \alpha_{2}\) and \(\beta_{1}, \beta_{2}\) be the roots of \(\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}\) \(=0\) and \(p x^{2}+q x+r=0\) respectively. If the system of equations \(\alpha_{1} y+\alpha_{2} z=0\) and \(\beta_{1} y+\beta_{2} z=0\) has a non-trivial solution, then

1 \(\frac{\mathrm{b}^{2}}{\mathrm{q}^{2}}=\frac{\mathrm{ac}}{\mathrm{pr}}\)
2 \(\frac{\mathrm{c}^{2}}{\mathrm{r}^{2}}=\frac{\mathrm{ab}}{\mathrm{pq}}\)
3 \(\frac{\mathrm{a}^{2}}{\mathrm{p}^{2}}=\frac{\mathrm{bc}}{\mathrm{qr}}\)
4 None of these
BITSAT-2016
Matrix and Determinant

79439 If a system of equation \(-a x+y+z=0 ; x-b y+\) \(\mathbf{z}=\mathbf{0} ; \mathbf{x}+\mathbf{y}-\mathbf{c z}=\mathbf{0}(\mathrm{a}, \mathrm{b}, \mathrm{c} \neq-\mathbf{1})\) has a nonzero solution then
\(\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}=\)

1 0
2 1
3 2
4 3
BITSAT-2017
Matrix and Determinant

79440 The rank of the matrix \(\left[\begin{array}{ccc}-1 & 2 & 5 \\ 2 & -4 & a-4 \\ 1 & -2 & a+1\end{array}\right]\) is

1 1 if \(a=6\)
2 2 if \(a=1\)
3 3 if \(a=2\)
4 1 if \(a=4\)
VITEEE-2017