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WB JEE

Matrices and Determinants

Mathematics

Previous Years Questions

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 & 0 & 3 \cr 0 & 3 & 0 \cr 3 & 0 & 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 > j= ...
WB JEE 2018

MCQ (Single Correct Answer)

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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}} & {bc} & {{c^2} + ac} \cr {{a^2} + ab} & {{b^2}} & {ca} \cr {...
WB JEE 2020
Let $$A = \left( {\matrix{ a & b \cr c & d \cr } } \right)$$ be a 2 $$ \times $$ 2 real matrix with ...
WB JEE 2020
Let $$A = \left[ {\matrix{ {12} & {24} & 5 \cr x & 6 & 2 \cr { - 1} & { - 2} & 3 \...
WB JEE 2020
Let A = $$\left( {\matrix{ {3 - t} \cr { - 1} \cr 0 \cr } \matrix{ {} \cr {} \cr {} \cr ...
WB JEE 2020
The system of equations$$\eqalign{ & \lambda x + y + 3z = 0 \cr & 2x + \mu y - z = 0 \cr & 5x + 7y...
WB JEE 2019
Let A and B be two square matrices of order 3 and AB = O3, where O3 denotes the null matrix of order 3. Then,...
WB JEE 2019
If $$A = \left( {\matrix{ 5 & {5x} & x \cr 0 & x & {5x} \cr 0 & 0 & 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 $${\left( {\matrix{ {\cos \pi /4} & {\sin \pi /4} \cr { - \sin {\pi ...
WB JEE 2018
If the following three linear equations have a non-trivial solution, thenx + 4ay + az = 0x + 3by + bz = 0x + 2cy + cz = ...
WB JEE 2018
If $${S_r} = \left| {\matrix{ {2r} & x & {n(n + 1)} \cr {6{r^2} - 1} & y & {{n^2}(2n + 3)} \cr ...
WB JEE 2018
If $$\left| {\matrix{ { - 1} & 7 & 0 \cr 2 & 1 & { - 3} \cr 3 & 4 & 1 \cr } } \...
WB JEE 2018
Let a, b, c be such that b(a + c) $$ \ne $$ 0. If $$\left| {\matrix{ a & {a + 1} & {a - 1} \cr { - b} &a...
WB JEE 2017
Let $$A = \left( {\matrix{ 1 & 1 & 1 \cr 0 & 1 & 1 \cr 0 & 0 & 1 \cr } } \right...
WB JEE 2017
The value of det A, where $$A\, = \left( {\matrix{ 1 & {\cos \theta } & 0 \cr { - \cos \theta } & 1 ...
WB JEE 2017
Let $$A = \left( {\matrix{ {x + 2} & {3x} \cr 3 & {x + 2} \cr } } \right),\,B = \left( {\matrix{ ...
WB JEE 2017
Let P be the set of all non-singular matrices of order 3 over R and Q be the set of all orthogonal matrices of order 3 o...
WB JEE 2017
The linear system of equations$$\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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