1
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0

If $$\mathrm{a}_{\mathrm{i}}, \mathrm{b}_{\mathrm{i}}, \mathrm{c}_{\mathrm{i}} \in \mathbb{R}(\mathrm{i}=1,2,3)$$ and $$x \in \mathbb{R}$$ and $$\left|\begin{array}{lll}\mathrm{a}_1+b_1 x & a_1 x+b_1 & c_1 \\ \mathrm{a}_2+b_2 x & a_2 x+b_2 & c_2 \\ \mathrm{a}_3+b_3 x & a_3 x+b_3 & c_3\end{array}\right|=0$$, then

A
$$x=1$$
B
$$x=-1$$
C
$$\left|\begin{array}{ccc}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right|=0$$
D
$$x=2$$
2
WB JEE 2022
MCQ (More than One Correct Answer)
+2
-0

Let $$\Delta = \left| {\matrix{ {\sin \theta \cos \phi } & {\sin \theta \sin \phi } & {\cos \theta } \cr {\cos \theta \cos \phi } & {\cos \theta \sin \phi } & { - \sin \theta } \cr { - \sin \theta \sin \phi } & {\sin \theta \cos \phi } & 0 \cr } } \right|$$. Then

A
$$\Delta$$ is independent of $$\theta$$
B
$$\Delta$$ is independent of $$\varphi$$
C
$$\Delta$$ is a constant
D
$${\left( {{{d\Delta } \over {d\theta }}} \right)_{\theta = {\pi \over 2}}} = 0$$
3
WB JEE 2021
MCQ (More than One Correct Answer)
+2
-0
$$\left| {\matrix{ x & {3x + 2} & {2x - 1} \cr {2x - 1} & {4x} & {3x + 1} \cr {7x - 2} & {17x + 6} & {12x - 1} \cr } } \right| = 0$$ is true for
A
only one value of x
B
only two value of x
C
only three values of x
D
infinitely many value of x
4
WB JEE 2019
MCQ (More than One Correct Answer)
+2
-0
Let $$A = \left[ {\matrix{ 3 & 0 & 3 \cr 0 & 3 & 0 \cr 3 & 0 & 3 \cr } } \right]$$. Then, the roots of the equation det $$(A - \lambda {I_3})$$ = 0 (where I3 is the identity matrix of order 3) are
A
3, 0, 3
B
0, 3, 6
C
1, 0, $$-$$6
D
3, 3, 6
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