Determinants in 2-D
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Matrix and Determinant

79152 The number of the distinct real roots of the
equation \(\left|\begin{array}{lll}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0\), in the interval
\(-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}\) is

1 4
2 3
3 1
4 2
BCECE-2011
Matrix and Determinant

79153 The value of determinant \(\left|\begin{array}{lll}1 / a & b c & a^{3} \\ 1 / b & c a & b^{3} \\ 1 / c & a b & c^{3}\end{array}\right|\)

1 \(a^{2} b^{2} c^{2}(a-b)(b-c)(c-a)
2 ~ 0\)
3 \((a-b)(b-c)(c-a)\)
4 None of the above
UPSEE-2016
Matrix and Determinant

79154 If the determinant \(\Delta=\left|\begin{array}{ccc}3 & -2 & \sin 3 \theta \\ -7 & 8 & \cos 2 \theta \\ -11 & 14 & 2\end{array}\right|=0\),
then the value of \(\sin \theta\) is

1 \(\frac{1}{3}\) orl
2 \(\frac{1}{\sqrt{2}}\) or \(\frac{\sqrt{3}}{2}\)
3 0 or \(\frac{1}{2}\)
4 None of these
UPSEE-2014
Matrix and Determinant

79155 If \(\left|\begin{array}{ccc}a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x\end{array}\right|=0\), then \(x\) is equal to

1 \(0,2 a\)
2 \(a\), \(2 a\)
3 0 , \(3 a\)
4 none of these
[JCECE-2007]
NEET DIGITAL LIBRARY
Matrix and Determinant

79152 The number of the distinct real roots of the
equation \(\left|\begin{array}{lll}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0\), in the interval
\(-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}\) is

1 4
2 3
3 1
4 2
BCECE-2011
Matrix and Determinant

79153 The value of determinant \(\left|\begin{array}{lll}1 / a & b c & a^{3} \\ 1 / b & c a & b^{3} \\ 1 / c & a b & c^{3}\end{array}\right|\)

1 \(a^{2} b^{2} c^{2}(a-b)(b-c)(c-a)
2 ~ 0\)
3 \((a-b)(b-c)(c-a)\)
4 None of the above
UPSEE-2016
Matrix and Determinant

79154 If the determinant \(\Delta=\left|\begin{array}{ccc}3 & -2 & \sin 3 \theta \\ -7 & 8 & \cos 2 \theta \\ -11 & 14 & 2\end{array}\right|=0\),
then the value of \(\sin \theta\) is

1 \(\frac{1}{3}\) orl
2 \(\frac{1}{\sqrt{2}}\) or \(\frac{\sqrt{3}}{2}\)
3 0 or \(\frac{1}{2}\)
4 None of these
UPSEE-2014
Matrix and Determinant

79155 If \(\left|\begin{array}{ccc}a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x\end{array}\right|=0\), then \(x\) is equal to

1 \(0,2 a\)
2 \(a\), \(2 a\)
3 0 , \(3 a\)
4 none of these
[JCECE-2007]
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Matrix and Determinant

79152 The number of the distinct real roots of the
equation \(\left|\begin{array}{lll}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0\), in the interval
\(-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}\) is

1 4
2 3
3 1
4 2
BCECE-2011
Matrix and Determinant

79153 The value of determinant \(\left|\begin{array}{lll}1 / a & b c & a^{3} \\ 1 / b & c a & b^{3} \\ 1 / c & a b & c^{3}\end{array}\right|\)

1 \(a^{2} b^{2} c^{2}(a-b)(b-c)(c-a)
2 ~ 0\)
3 \((a-b)(b-c)(c-a)\)
4 None of the above
UPSEE-2016
Matrix and Determinant

79154 If the determinant \(\Delta=\left|\begin{array}{ccc}3 & -2 & \sin 3 \theta \\ -7 & 8 & \cos 2 \theta \\ -11 & 14 & 2\end{array}\right|=0\),
then the value of \(\sin \theta\) is

1 \(\frac{1}{3}\) orl
2 \(\frac{1}{\sqrt{2}}\) or \(\frac{\sqrt{3}}{2}\)
3 0 or \(\frac{1}{2}\)
4 None of these
UPSEE-2014
Matrix and Determinant

79155 If \(\left|\begin{array}{ccc}a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x\end{array}\right|=0\), then \(x\) is equal to

1 \(0,2 a\)
2 \(a\), \(2 a\)
3 0 , \(3 a\)
4 none of these
[JCECE-2007]
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Matrix and Determinant

79152 The number of the distinct real roots of the
equation \(\left|\begin{array}{lll}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0\), in the interval
\(-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}\) is

1 4
2 3
3 1
4 2
BCECE-2011
Matrix and Determinant

79153 The value of determinant \(\left|\begin{array}{lll}1 / a & b c & a^{3} \\ 1 / b & c a & b^{3} \\ 1 / c & a b & c^{3}\end{array}\right|\)

1 \(a^{2} b^{2} c^{2}(a-b)(b-c)(c-a)
2 ~ 0\)
3 \((a-b)(b-c)(c-a)\)
4 None of the above
UPSEE-2016
Matrix and Determinant

79154 If the determinant \(\Delta=\left|\begin{array}{ccc}3 & -2 & \sin 3 \theta \\ -7 & 8 & \cos 2 \theta \\ -11 & 14 & 2\end{array}\right|=0\),
then the value of \(\sin \theta\) is

1 \(\frac{1}{3}\) orl
2 \(\frac{1}{\sqrt{2}}\) or \(\frac{\sqrt{3}}{2}\)
3 0 or \(\frac{1}{2}\)
4 None of these
UPSEE-2014
Matrix and Determinant

79155 If \(\left|\begin{array}{ccc}a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x\end{array}\right|=0\), then \(x\) is equal to

1 \(0,2 a\)
2 \(a\), \(2 a\)
3 0 , \(3 a\)
4 none of these
[JCECE-2007]