1
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
$${\left( {{{d\Delta } \over {d\theta }}} \right)_{\theta = {\pi \over 2}}} = 0$$
2
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
3
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
4
WB JEE 2018
MCQ (More than One Correct Answer)
+2
-0 In a third order matrix A, aij denotes the element in the ith row and jth column. If aij = 0 for i = j

= 1 for i > j

= $$-$$ 1 for i < j

Then the matrix is
A
skew symmetric
B
symmetric
C
not invertible
D
non-singular
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Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
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