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## MCQ (More than One Correct Answer)

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Let $$\Delta = \left| {\matrix{ {\sin \theta \cos \phi } & {\sin \theta \sin \phi } & {\cos \theta } \cr {\cos ... WB JEE 2022$$\left| {\matrix{ x & {3x + 2} & {2x - 1} \cr {2x - 1} & {4x} & {3x + 1} \cr {7x - 2} & {17x + 6} & {12x -...
WB JEE 2021
Let $$A = \left[ {\matrix{ 3 &amp; 0 &amp; 3 \cr 0 &amp; 3 &amp; 0 \cr 3 &amp; 0 &amp; 3 \cr } } \right... WB JEE 2019 In a third order matrix A, aij denotes the element in the ith row and jth column. If aij = 0 for i = j= 1 for i &gt; j= ... WB JEE 2018 ## MCQ (Single Correct Answer) More The solution of$$\det (A - \lambda {I_2}) = 0$$be 4 and 8 and$$A = \left( {\matrix{ 2 & 2 \cr x & y \cr }...
WB JEE 2022
If $$A = \left( {\matrix{ 1 & 1 \cr 0 & i \cr } } \right)$$ and $${A^{2018}} = \left( {\matrix{ a & b \c... WB JEE 2022 If$$p = \left[ {\matrix{ 1 & \alpha & 3 \cr 1 & 3 & 3 \cr 2 & 4 & 4 \cr } } \right]$$is the adjoint ... WB JEE 2022 If$$\Delta (x) = \left| {\matrix{ {x - 2} & {{{(x - 1)}^2}} & {{x^3}} \cr {x - 1} & {{x^2}} & {{{(x + 1)}^3}} ...
WB JEE 2022
Under which of the following condition(s) does(do) the system of equations $$\left( {\matrix{ 1 & 2 & 4 \cr 2 & ... WB JEE 2022 The determinant$$\left| {\matrix{ {{a^2} + 10} & {ab} & {ac} \cr {ab} & {{b^2} + 10} & {bc} \cr {ac} & {bc...
WB JEE 2021
Let T and U be the set of all orthogonal matrices of order 3 over R and the set of all non-singular matrices of order 3 ...
WB JEE 2021
If an (> 0) be the nth term of a G.P. then$$\left| {\matrix{ {\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} ... WB JEE 2021 Let A and B two non singular skew symmetric matrices such that AB = BA, then A2B2(ATB)$$-$$1(AB$$-$$1)T is equal to ... WB JEE 2021 Let$$A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & {\cos t} & {\sin t} \cr 0 & { - \sin t} & {\cos t} \cr } }...
WB JEE 2021
If M is a 3 $$\times$$ 3 matrix such that (0, 1, 2) M = (1 0 0), (3, 4 5) M = (0, 1, 0), then (6 7 8) M is equal to
WB JEE 2021
If the vectors $$\alpha = \widehat i + a\widehat j + {a^2}\widehat k,\,\beta = \widehat i + b\widehat j + {b^2}\wideha... WB JEE 2020 If f : S$$ \to $$R, where S is the set of all non-singular matrices of order 2 over R and$$f\left[ {\left( {\matrix{ ...
WB JEE 2020
If $$\left| {\matrix{ {{a^2}} &amp; {bc} &amp; {{c^2} + ac} \cr {{a^2} + ab} &amp; {{b^2}} &amp; {ca} \cr {... WB JEE 2020 Let$$A = \left( {\matrix{ a &amp; b \cr c &amp; d \cr } } \right)$$be a 2$$ \times $$2 real matrix with ... WB JEE 2020 Let$$A = \left[ {\matrix{ {12} &amp; {24} &amp; 5 \cr x &amp; 6 &amp; 2 \cr { - 1} &amp; { - 2} &amp; 3 \...
WB JEE 2020
Let A = $$\left( {\matrix{ {3 - t} \cr { - 1} \cr 0 \cr } \matrix{ {} \cr {} \cr {} \cr ... WB JEE 2020 The system of equations$$\eqalign{ &amp; \lambda x + y + 3z = 0 \cr &amp; 2x + \mu y - z = 0 \cr &amp; 5x + 7y...
WB JEE 2019
Let A and B be two square matrices of order 3 and AB = O3, where O3 denotes the null matrix of order 3. Then,...
WB JEE 2019
If $$A = \left( {\matrix{ 5 &amp; {5x} &amp; x \cr 0 &amp; x &amp; {5x} \cr 0 &amp; 0 &amp; 5 \cr } } \... WB JEE 2019 If M is any square matrix of order 3 over R and if M' be the transpose of M, then adj(M')$$-$$(adj M)' is equal to WB JEE 2019 Let A be a square matrix of order 3 whose all entries are 1 and let I3 be the identity matrix of order 3. Then, the matr... WB JEE 2019 The least positive integer n such that$${\left( {\matrix{ {\cos \pi /4} &amp; {\sin \pi /4} \cr { - \sin {\pi ...
WB JEE 2018
If the following three linear equations have a non-trivial solution, thenx + 4ay + az = 0x + 3by + bz = 0x + 2cy + cz = ...
WB JEE 2018
If $${S_r} = \left| {\matrix{ {2r} &amp; x &amp; {n(n + 1)} \cr {6{r^2} - 1} &amp; y &amp; {{n^2}(2n + 3)} \cr ... WB JEE 2018 If$$\left| {\matrix{ { - 1} &amp; 7 &amp; 0 \cr 2 &amp; 1 &amp; { - 3} \cr 3 &amp; 4 &amp; 1 \cr } } \...
WB JEE 2018
Let a, b, c be such that b(a + c) $$\ne$$ 0. If $$\left| {\matrix{ a &amp; {a + 1} &amp; {a - 1} \cr { - b} &a... WB JEE 2017 Let$$A = \left( {\matrix{ 1 &amp; 1 &amp; 1 \cr 0 &amp; 1 &amp; 1 \cr 0 &amp; 0 &amp; 1 \cr } } \right...
WB JEE 2017
The value of det A, where $$A\, = \left( {\matrix{ 1 &amp; {\cos \theta } &amp; 0 \cr { - \cos \theta } &amp; 1 ... WB JEE 2017 Let$$A = \left( {\matrix{ {x + 2} &amp; {3x} \cr 3 &amp; {x + 2} \cr } } \right),\,B = \left( {\matrix{ ...
WB JEE 2017
Let P be the set of all non-singular matrices of order 3 over R and Q be the set of all orthogonal matrices of order 3 o...
WB JEE 2017
The linear system of equations$$\left. \matrix{ 8x - 3y - 5z = 0 \hfill \cr 5x - 8y + 3z = 0 \hfill \cr 3x + 5y ... WB JEE 2017$$\left| {\matrix{ {a - b} & {b - c} & {c - a} \cr {b - c} & {c - a} & {a - b} \cr {c - a} & {a - b} & {b -...
WB JEE 2011
If one of the cube roots of 1 be $$\omega$$, then $$\left| {\matrix{ 1 & {1 + {\omega ^2}} & {{\omega ^2}} \cr {... WB JEE 2011 If$$z = \left| {\matrix{ 1 & {1 + 2i} & { - 5i} \cr {1 - 2i} & { - 3} & {5 + 3i} \cr {5i} & {5 - 3i} & 7 ...
WB JEE 2011
If $$A = \left( {\matrix{ 3 & {x - 1} \cr {2x + 3} & {x + 2} \cr } } \right)$$ is a symmetric matrix, then t...
WB JEE 2011
If A and B are two matrices such that A + B and AB are both defined, then
WB JEE 2011
If $$A = \left[ {\matrix{ 1 & 2 \cr { - 4} & { - 1} \cr } } \right]$$ then A$$-$$1 is
WB JEE 2010
If $$\omega$$ is an imaginary cube root of unity and $$\left| {\matrix{ {x + {\omega ^2}} & \omega & 1 \cr \ome... WB JEE 2010 If the matrices$$A = \left[ {\matrix{ 2 & 1 & 3 \cr 4 & 1 & 0 \cr } } \right]$$and$$B = \left[ {\matrix{ ...
WB JEE 2010
If A and B are square matrices of the same order and AB = 3I, then A$$-$$1 is equal to
WB JEE 2009
If A2 $$-$$ A + I = 0, then the inverse of the matrix A is
WB JEE 2009
If A is a square matrix. Then
WB JEE 2009
If the matrix $$\left[ {\matrix{ a & b \cr c & d \cr } } \right]$$ is commutative with the matrix $$\left[ {... WB JEE 2008 The values of x for which the given matrix$$\left[ {\matrix{ { - x} & x & 2 \cr 2 & x & { - x} \cr x & { -...
WB JEE 2008

## Subjective

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If A, B are two square matrices such that AB = A and BA = B, then prove that B2 = B.
WB JEE 2010

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