Differentiation and Integration of Determinant
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Matrix and Determinant

79234 Let \(\Delta=\left|\begin{array}{lll}A x & x^{2} & 1 \\ B y & y^{2} & 1 \\ C z & z^{2} & 1\end{array}\right|\) and \(\Delta_{1}=\left|\begin{array}{ccc}A & B & C \\ x & y & z \\ z y & z x & x y\end{array}\right|\) then

1 \(\Delta_{1}=-\Delta\)
2 \(\Delta_{1}=\Delta\)
3 \(\Delta_{1}=2 \Delta\)
4 \(\Delta_{1} \neq \Delta\)
Karnataka CET-2017
Matrix and Determinant

79235 If \(f(x), g(x)\) and \(h(x)\) are three polynomials of degree 2 and
\(\Delta(\mathbf{x})=\left|\begin{array}{ccc} \mathbf{f}(\mathbf{x}) & \mathbf{g}(\mathbf{x}) & \mathbf{h}(\mathbf{x}) \\ \mathbf{f}^{\prime}(\mathbf{x}) & \mathbf{g}^{\prime}(\mathbf{x}) & \mathbf{h}^{\prime}(\mathbf{x}) \\ \mathbf{f}^{\prime \prime}(\mathbf{x}) & \mathbf{g}^{\prime \prime}(\mathbf{x}) & \mathbf{h}^{\prime \prime}(\mathbf{x}) \end{array}\right|\)
then \(\Delta(x)\) is a polynomial of degree 2 and

1 2
2 3
3 0
4 atmost 3
VITEEE-2010
Matrix and Determinant

79236 If \(C=2 \cos \theta\), then the value of the determinant
\(\Delta=\left|\begin{array}{lll}\mathbf{C} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{C} & \mathbf{1} \\ \mathbf{6} & \mathbf{1} & \mathbf{C}\end{array}\right|\) is

1 \(\frac{\sin 4 \theta}{\sin \theta}\)
2 \(\frac{2 \sin ^{2} 2 \theta}{\sin \theta}\)
3 \(4 \cos ^{2} \theta(2 \cos \theta-1)\)
4 None of the above
BCECE-2012
Matrix and Determinant

79237 The only integral root of the equation
\(\left|\begin{array}{ccc}2-y & 2 & 3 \\ 2 & 5-y & 6 \\ 3 & 4 & 10-y\end{array}\right|=0\) is

1 \(y=3\)
2 \(y=2\)
3 \(y=1\)
4 none of these
AMU-2016
Matrix and Determinant

79238 If
\(=\left|\begin{array}{ccc} 2 \cos x & 1 & 0 \\ x-\frac{\pi}{2} & 2 \cos x & 1 \end{array}\right| \text { then } \quad \mathbf{f}^{\prime}(\pi / 2) \quad \text { is }\)
equal to.

1 0
2 2
3 \(\frac{\pi}{2}\)
4 \(\pi-6\)
AP EAMCET-2010
NEET DIGITAL LIBRARY
Matrix and Determinant

79234 Let \(\Delta=\left|\begin{array}{lll}A x & x^{2} & 1 \\ B y & y^{2} & 1 \\ C z & z^{2} & 1\end{array}\right|\) and \(\Delta_{1}=\left|\begin{array}{ccc}A & B & C \\ x & y & z \\ z y & z x & x y\end{array}\right|\) then

1 \(\Delta_{1}=-\Delta\)
2 \(\Delta_{1}=\Delta\)
3 \(\Delta_{1}=2 \Delta\)
4 \(\Delta_{1} \neq \Delta\)
Karnataka CET-2017
Matrix and Determinant

79235 If \(f(x), g(x)\) and \(h(x)\) are three polynomials of degree 2 and
\(\Delta(\mathbf{x})=\left|\begin{array}{ccc} \mathbf{f}(\mathbf{x}) & \mathbf{g}(\mathbf{x}) & \mathbf{h}(\mathbf{x}) \\ \mathbf{f}^{\prime}(\mathbf{x}) & \mathbf{g}^{\prime}(\mathbf{x}) & \mathbf{h}^{\prime}(\mathbf{x}) \\ \mathbf{f}^{\prime \prime}(\mathbf{x}) & \mathbf{g}^{\prime \prime}(\mathbf{x}) & \mathbf{h}^{\prime \prime}(\mathbf{x}) \end{array}\right|\)
then \(\Delta(x)\) is a polynomial of degree 2 and

1 2
2 3
3 0
4 atmost 3
VITEEE-2010
Matrix and Determinant

79236 If \(C=2 \cos \theta\), then the value of the determinant
\(\Delta=\left|\begin{array}{lll}\mathbf{C} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{C} & \mathbf{1} \\ \mathbf{6} & \mathbf{1} & \mathbf{C}\end{array}\right|\) is

1 \(\frac{\sin 4 \theta}{\sin \theta}\)
2 \(\frac{2 \sin ^{2} 2 \theta}{\sin \theta}\)
3 \(4 \cos ^{2} \theta(2 \cos \theta-1)\)
4 None of the above
BCECE-2012
Matrix and Determinant

79237 The only integral root of the equation
\(\left|\begin{array}{ccc}2-y & 2 & 3 \\ 2 & 5-y & 6 \\ 3 & 4 & 10-y\end{array}\right|=0\) is

1 \(y=3\)
2 \(y=2\)
3 \(y=1\)
4 none of these
AMU-2016
Matrix and Determinant

79238 If
\(=\left|\begin{array}{ccc} 2 \cos x & 1 & 0 \\ x-\frac{\pi}{2} & 2 \cos x & 1 \end{array}\right| \text { then } \quad \mathbf{f}^{\prime}(\pi / 2) \quad \text { is }\)
equal to.

1 0
2 2
3 \(\frac{\pi}{2}\)
4 \(\pi-6\)
AP EAMCET-2010
Join With Us for More Updates
Matrix and Determinant

79234 Let \(\Delta=\left|\begin{array}{lll}A x & x^{2} & 1 \\ B y & y^{2} & 1 \\ C z & z^{2} & 1\end{array}\right|\) and \(\Delta_{1}=\left|\begin{array}{ccc}A & B & C \\ x & y & z \\ z y & z x & x y\end{array}\right|\) then

1 \(\Delta_{1}=-\Delta\)
2 \(\Delta_{1}=\Delta\)
3 \(\Delta_{1}=2 \Delta\)
4 \(\Delta_{1} \neq \Delta\)
Karnataka CET-2017
Matrix and Determinant

79235 If \(f(x), g(x)\) and \(h(x)\) are three polynomials of degree 2 and
\(\Delta(\mathbf{x})=\left|\begin{array}{ccc} \mathbf{f}(\mathbf{x}) & \mathbf{g}(\mathbf{x}) & \mathbf{h}(\mathbf{x}) \\ \mathbf{f}^{\prime}(\mathbf{x}) & \mathbf{g}^{\prime}(\mathbf{x}) & \mathbf{h}^{\prime}(\mathbf{x}) \\ \mathbf{f}^{\prime \prime}(\mathbf{x}) & \mathbf{g}^{\prime \prime}(\mathbf{x}) & \mathbf{h}^{\prime \prime}(\mathbf{x}) \end{array}\right|\)
then \(\Delta(x)\) is a polynomial of degree 2 and

1 2
2 3
3 0
4 atmost 3
VITEEE-2010
Matrix and Determinant

79236 If \(C=2 \cos \theta\), then the value of the determinant
\(\Delta=\left|\begin{array}{lll}\mathbf{C} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{C} & \mathbf{1} \\ \mathbf{6} & \mathbf{1} & \mathbf{C}\end{array}\right|\) is

1 \(\frac{\sin 4 \theta}{\sin \theta}\)
2 \(\frac{2 \sin ^{2} 2 \theta}{\sin \theta}\)
3 \(4 \cos ^{2} \theta(2 \cos \theta-1)\)
4 None of the above
BCECE-2012
Matrix and Determinant

79237 The only integral root of the equation
\(\left|\begin{array}{ccc}2-y & 2 & 3 \\ 2 & 5-y & 6 \\ 3 & 4 & 10-y\end{array}\right|=0\) is

1 \(y=3\)
2 \(y=2\)
3 \(y=1\)
4 none of these
AMU-2016
Matrix and Determinant

79238 If
\(=\left|\begin{array}{ccc} 2 \cos x & 1 & 0 \\ x-\frac{\pi}{2} & 2 \cos x & 1 \end{array}\right| \text { then } \quad \mathbf{f}^{\prime}(\pi / 2) \quad \text { is }\)
equal to.

1 0
2 2
3 \(\frac{\pi}{2}\)
4 \(\pi-6\)
AP EAMCET-2010
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Matrix and Determinant

79234 Let \(\Delta=\left|\begin{array}{lll}A x & x^{2} & 1 \\ B y & y^{2} & 1 \\ C z & z^{2} & 1\end{array}\right|\) and \(\Delta_{1}=\left|\begin{array}{ccc}A & B & C \\ x & y & z \\ z y & z x & x y\end{array}\right|\) then

1 \(\Delta_{1}=-\Delta\)
2 \(\Delta_{1}=\Delta\)
3 \(\Delta_{1}=2 \Delta\)
4 \(\Delta_{1} \neq \Delta\)
Karnataka CET-2017
Matrix and Determinant

79235 If \(f(x), g(x)\) and \(h(x)\) are three polynomials of degree 2 and
\(\Delta(\mathbf{x})=\left|\begin{array}{ccc} \mathbf{f}(\mathbf{x}) & \mathbf{g}(\mathbf{x}) & \mathbf{h}(\mathbf{x}) \\ \mathbf{f}^{\prime}(\mathbf{x}) & \mathbf{g}^{\prime}(\mathbf{x}) & \mathbf{h}^{\prime}(\mathbf{x}) \\ \mathbf{f}^{\prime \prime}(\mathbf{x}) & \mathbf{g}^{\prime \prime}(\mathbf{x}) & \mathbf{h}^{\prime \prime}(\mathbf{x}) \end{array}\right|\)
then \(\Delta(x)\) is a polynomial of degree 2 and

1 2
2 3
3 0
4 atmost 3
VITEEE-2010
Matrix and Determinant

79236 If \(C=2 \cos \theta\), then the value of the determinant
\(\Delta=\left|\begin{array}{lll}\mathbf{C} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{C} & \mathbf{1} \\ \mathbf{6} & \mathbf{1} & \mathbf{C}\end{array}\right|\) is

1 \(\frac{\sin 4 \theta}{\sin \theta}\)
2 \(\frac{2 \sin ^{2} 2 \theta}{\sin \theta}\)
3 \(4 \cos ^{2} \theta(2 \cos \theta-1)\)
4 None of the above
BCECE-2012
Matrix and Determinant

79237 The only integral root of the equation
\(\left|\begin{array}{ccc}2-y & 2 & 3 \\ 2 & 5-y & 6 \\ 3 & 4 & 10-y\end{array}\right|=0\) is

1 \(y=3\)
2 \(y=2\)
3 \(y=1\)
4 none of these
AMU-2016
Matrix and Determinant

79238 If
\(=\left|\begin{array}{ccc} 2 \cos x & 1 & 0 \\ x-\frac{\pi}{2} & 2 \cos x & 1 \end{array}\right| \text { then } \quad \mathbf{f}^{\prime}(\pi / 2) \quad \text { is }\)
equal to.

1 0
2 2
3 \(\frac{\pi}{2}\)
4 \(\pi-6\)
AP EAMCET-2010
NEET DIGITAL LIBRARY
Matrix and Determinant

79234 Let \(\Delta=\left|\begin{array}{lll}A x & x^{2} & 1 \\ B y & y^{2} & 1 \\ C z & z^{2} & 1\end{array}\right|\) and \(\Delta_{1}=\left|\begin{array}{ccc}A & B & C \\ x & y & z \\ z y & z x & x y\end{array}\right|\) then

1 \(\Delta_{1}=-\Delta\)
2 \(\Delta_{1}=\Delta\)
3 \(\Delta_{1}=2 \Delta\)
4 \(\Delta_{1} \neq \Delta\)
Karnataka CET-2017
Matrix and Determinant

79235 If \(f(x), g(x)\) and \(h(x)\) are three polynomials of degree 2 and
\(\Delta(\mathbf{x})=\left|\begin{array}{ccc} \mathbf{f}(\mathbf{x}) & \mathbf{g}(\mathbf{x}) & \mathbf{h}(\mathbf{x}) \\ \mathbf{f}^{\prime}(\mathbf{x}) & \mathbf{g}^{\prime}(\mathbf{x}) & \mathbf{h}^{\prime}(\mathbf{x}) \\ \mathbf{f}^{\prime \prime}(\mathbf{x}) & \mathbf{g}^{\prime \prime}(\mathbf{x}) & \mathbf{h}^{\prime \prime}(\mathbf{x}) \end{array}\right|\)
then \(\Delta(x)\) is a polynomial of degree 2 and

1 2
2 3
3 0
4 atmost 3
VITEEE-2010
Matrix and Determinant

79236 If \(C=2 \cos \theta\), then the value of the determinant
\(\Delta=\left|\begin{array}{lll}\mathbf{C} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{C} & \mathbf{1} \\ \mathbf{6} & \mathbf{1} & \mathbf{C}\end{array}\right|\) is

1 \(\frac{\sin 4 \theta}{\sin \theta}\)
2 \(\frac{2 \sin ^{2} 2 \theta}{\sin \theta}\)
3 \(4 \cos ^{2} \theta(2 \cos \theta-1)\)
4 None of the above
BCECE-2012
Matrix and Determinant

79237 The only integral root of the equation
\(\left|\begin{array}{ccc}2-y & 2 & 3 \\ 2 & 5-y & 6 \\ 3 & 4 & 10-y\end{array}\right|=0\) is

1 \(y=3\)
2 \(y=2\)
3 \(y=1\)
4 none of these
AMU-2016
Matrix and Determinant

79238 If
\(=\left|\begin{array}{ccc} 2 \cos x & 1 & 0 \\ x-\frac{\pi}{2} & 2 \cos x & 1 \end{array}\right| \text { then } \quad \mathbf{f}^{\prime}(\pi / 2) \quad \text { is }\)
equal to.

1 0
2 2
3 \(\frac{\pi}{2}\)
4 \(\pi-6\)
AP EAMCET-2010