Determinants in 2-D
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Matrix and Determinant

79164 If
\(\left|\begin{array}{lll}
x^{n} & x^{n+2} & x^{n+3} \\ y^{n} & y^{n+2} & y^{n+3} \\ z^{n} & z^{n+2} & z^{n+3} \end{array}\right|=(y-z)(z-x)(x-y)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)\)
then \(\mathbf{n}\) is equal to :

1 2
2 -2
3 -1
4 1
BCECE-2006
Matrix and Determinant

79165 The value of the following
determinant
\(\left|\begin{array}{ccc} 1 & 1 & 1 \\ \mathbf{a} & \mathbf{b} & \mathbf{c} \\ \mathbf{a}^{3} & \mathbf{b}^{3} & \mathbf{c}^{3} \end{array}\right| \text { is : }\)

1 \((a-b)(b-c)(c-a)(a+b+c)\)
2 \(a b c(a+b)(b+c)(c+a)\)
3 \((a-b)(b-c)(c-a)\)
4 none of the above
BCECE-2004
Matrix and Determinant

79166 The value of the determinant \(\left|\begin{array}{lll}x & a & b+c \\ x & b & c+a \\ x & c & a+b\end{array}\right|=0\)
if :

1 \(x=a\)
2 \(x=b\)
3 \(x=c\)
4 \(x\) has any value
BCECE-2003
Matrix and Determinant

79167 If \(f(x)=\left(\begin{array}{lll}\left(1+a^{2}\right) x & 1+b^{2} x & \left(1+c^{2}\right) x\end{array} \quad\right.\) and
\(\left(1+a^{2}\right) x \quad\left(1+b^{2}\right) x \quad 1+c^{2} x\)
\(a^{2}+b^{2}+c^{2}=-2\), then what is the degree of the polynomial \(f(x)\) ?

1 0
2 1
3 2
4 3
SCRA-2009
Matrix and Determinant

79168 What is the value of the determinant if \(b^{2}-a c\) \(<0\) and \(a>0\) ?

1 Positive
2 Negative
3 Zero
4 sign cannot be determined
SCRA-2012
NEET DIGITAL LIBRARY
Matrix and Determinant

79164 If
\(\left|\begin{array}{lll}
x^{n} & x^{n+2} & x^{n+3} \\ y^{n} & y^{n+2} & y^{n+3} \\ z^{n} & z^{n+2} & z^{n+3} \end{array}\right|=(y-z)(z-x)(x-y)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)\)
then \(\mathbf{n}\) is equal to :

1 2
2 -2
3 -1
4 1
BCECE-2006
Matrix and Determinant

79165 The value of the following
determinant
\(\left|\begin{array}{ccc} 1 & 1 & 1 \\ \mathbf{a} & \mathbf{b} & \mathbf{c} \\ \mathbf{a}^{3} & \mathbf{b}^{3} & \mathbf{c}^{3} \end{array}\right| \text { is : }\)

1 \((a-b)(b-c)(c-a)(a+b+c)\)
2 \(a b c(a+b)(b+c)(c+a)\)
3 \((a-b)(b-c)(c-a)\)
4 none of the above
BCECE-2004
Matrix and Determinant

79166 The value of the determinant \(\left|\begin{array}{lll}x & a & b+c \\ x & b & c+a \\ x & c & a+b\end{array}\right|=0\)
if :

1 \(x=a\)
2 \(x=b\)
3 \(x=c\)
4 \(x\) has any value
BCECE-2003
Matrix and Determinant

79167 If \(f(x)=\left(\begin{array}{lll}\left(1+a^{2}\right) x & 1+b^{2} x & \left(1+c^{2}\right) x\end{array} \quad\right.\) and
\(\left(1+a^{2}\right) x \quad\left(1+b^{2}\right) x \quad 1+c^{2} x\)
\(a^{2}+b^{2}+c^{2}=-2\), then what is the degree of the polynomial \(f(x)\) ?

1 0
2 1
3 2
4 3
SCRA-2009
Matrix and Determinant

79168 What is the value of the determinant if \(b^{2}-a c\) \(<0\) and \(a>0\) ?

1 Positive
2 Negative
3 Zero
4 sign cannot be determined
SCRA-2012
Join With Us for More Updates
Matrix and Determinant

79164 If
\(\left|\begin{array}{lll}
x^{n} & x^{n+2} & x^{n+3} \\ y^{n} & y^{n+2} & y^{n+3} \\ z^{n} & z^{n+2} & z^{n+3} \end{array}\right|=(y-z)(z-x)(x-y)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)\)
then \(\mathbf{n}\) is equal to :

1 2
2 -2
3 -1
4 1
BCECE-2006
Matrix and Determinant

79165 The value of the following
determinant
\(\left|\begin{array}{ccc} 1 & 1 & 1 \\ \mathbf{a} & \mathbf{b} & \mathbf{c} \\ \mathbf{a}^{3} & \mathbf{b}^{3} & \mathbf{c}^{3} \end{array}\right| \text { is : }\)

1 \((a-b)(b-c)(c-a)(a+b+c)\)
2 \(a b c(a+b)(b+c)(c+a)\)
3 \((a-b)(b-c)(c-a)\)
4 none of the above
BCECE-2004
Matrix and Determinant

79166 The value of the determinant \(\left|\begin{array}{lll}x & a & b+c \\ x & b & c+a \\ x & c & a+b\end{array}\right|=0\)
if :

1 \(x=a\)
2 \(x=b\)
3 \(x=c\)
4 \(x\) has any value
BCECE-2003
Matrix and Determinant

79167 If \(f(x)=\left(\begin{array}{lll}\left(1+a^{2}\right) x & 1+b^{2} x & \left(1+c^{2}\right) x\end{array} \quad\right.\) and
\(\left(1+a^{2}\right) x \quad\left(1+b^{2}\right) x \quad 1+c^{2} x\)
\(a^{2}+b^{2}+c^{2}=-2\), then what is the degree of the polynomial \(f(x)\) ?

1 0
2 1
3 2
4 3
SCRA-2009
Matrix and Determinant

79168 What is the value of the determinant if \(b^{2}-a c\) \(<0\) and \(a>0\) ?

1 Positive
2 Negative
3 Zero
4 sign cannot be determined
SCRA-2012
For More Updates join with Us
Matrix and Determinant

79164 If
\(\left|\begin{array}{lll}
x^{n} & x^{n+2} & x^{n+3} \\ y^{n} & y^{n+2} & y^{n+3} \\ z^{n} & z^{n+2} & z^{n+3} \end{array}\right|=(y-z)(z-x)(x-y)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)\)
then \(\mathbf{n}\) is equal to :

1 2
2 -2
3 -1
4 1
BCECE-2006
Matrix and Determinant

79165 The value of the following
determinant
\(\left|\begin{array}{ccc} 1 & 1 & 1 \\ \mathbf{a} & \mathbf{b} & \mathbf{c} \\ \mathbf{a}^{3} & \mathbf{b}^{3} & \mathbf{c}^{3} \end{array}\right| \text { is : }\)

1 \((a-b)(b-c)(c-a)(a+b+c)\)
2 \(a b c(a+b)(b+c)(c+a)\)
3 \((a-b)(b-c)(c-a)\)
4 none of the above
BCECE-2004
Matrix and Determinant

79166 The value of the determinant \(\left|\begin{array}{lll}x & a & b+c \\ x & b & c+a \\ x & c & a+b\end{array}\right|=0\)
if :

1 \(x=a\)
2 \(x=b\)
3 \(x=c\)
4 \(x\) has any value
BCECE-2003
Matrix and Determinant

79167 If \(f(x)=\left(\begin{array}{lll}\left(1+a^{2}\right) x & 1+b^{2} x & \left(1+c^{2}\right) x\end{array} \quad\right.\) and
\(\left(1+a^{2}\right) x \quad\left(1+b^{2}\right) x \quad 1+c^{2} x\)
\(a^{2}+b^{2}+c^{2}=-2\), then what is the degree of the polynomial \(f(x)\) ?

1 0
2 1
3 2
4 3
SCRA-2009
Matrix and Determinant

79168 What is the value of the determinant if \(b^{2}-a c\) \(<0\) and \(a>0\) ?

1 Positive
2 Negative
3 Zero
4 sign cannot be determined
SCRA-2012
NEET DIGITAL LIBRARY
Matrix and Determinant

79164 If
\(\left|\begin{array}{lll}
x^{n} & x^{n+2} & x^{n+3} \\ y^{n} & y^{n+2} & y^{n+3} \\ z^{n} & z^{n+2} & z^{n+3} \end{array}\right|=(y-z)(z-x)(x-y)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)\)
then \(\mathbf{n}\) is equal to :

1 2
2 -2
3 -1
4 1
BCECE-2006
Matrix and Determinant

79165 The value of the following
determinant
\(\left|\begin{array}{ccc} 1 & 1 & 1 \\ \mathbf{a} & \mathbf{b} & \mathbf{c} \\ \mathbf{a}^{3} & \mathbf{b}^{3} & \mathbf{c}^{3} \end{array}\right| \text { is : }\)

1 \((a-b)(b-c)(c-a)(a+b+c)\)
2 \(a b c(a+b)(b+c)(c+a)\)
3 \((a-b)(b-c)(c-a)\)
4 none of the above
BCECE-2004
Matrix and Determinant

79166 The value of the determinant \(\left|\begin{array}{lll}x & a & b+c \\ x & b & c+a \\ x & c & a+b\end{array}\right|=0\)
if :

1 \(x=a\)
2 \(x=b\)
3 \(x=c\)
4 \(x\) has any value
BCECE-2003
Matrix and Determinant

79167 If \(f(x)=\left(\begin{array}{lll}\left(1+a^{2}\right) x & 1+b^{2} x & \left(1+c^{2}\right) x\end{array} \quad\right.\) and
\(\left(1+a^{2}\right) x \quad\left(1+b^{2}\right) x \quad 1+c^{2} x\)
\(a^{2}+b^{2}+c^{2}=-2\), then what is the degree of the polynomial \(f(x)\) ?

1 0
2 1
3 2
4 3
SCRA-2009
Matrix and Determinant

79168 What is the value of the determinant if \(b^{2}-a c\) \(<0\) and \(a>0\) ?

1 Positive
2 Negative
3 Zero
4 sign cannot be determined
SCRA-2012