WB JEE 2022 | Matrices and Determinants Question 25 | Mathematics

WB JEE 2022

MCQ (More than One Correct Answer)

-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

$$\Delta$$ is independent of $$\theta$$

$$\Delta$$ is independent of $$\varphi $$

$$\Delta$$ is a constant

$${\left( {{{d\Delta } \over {d\theta }}} \right)_{\theta = {\pi \over 2}}} = 0$$

WB JEE 2021

MCQ (More than One Correct Answer)

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$$\left| {\matrix{ x & {3x + 2} & {2x - 1} \cr {2x - 1} & {4x} & {3x + 1} \cr {7x - 2} & {17x + 6} & {12x - 1} \cr } } \right| = 0$$ is true for

only one value of x

only two value of x

only three values of x

infinitely many value of x

WB JEE 2019

MCQ (More than One Correct Answer)

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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

3, 0, 3

0, 3, 6

1, 0, $$-$$6

3, 3, 6

WB JEE 2018

MCQ (More than One Correct Answer)

-0

In a third order matrix A, a_ij denotes the element in the ith row and jth column. If a_ij = 0 for i = j

= 1 for i > j

= $$-$$ 1 for i < j

Then the matrix is

skew symmetric

symmetric

not invertible

non-singular

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