Matrices And Determinants - Algebra - Mathematics Previous Year Questions

1

2016 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2016

Let A be a 3 \(\times\) 3 matrix and B be its adjoint matrix. If | B | = 64, then | A | is equal to

A

\(\pm\)2

B

\(\pm\)4

C

\(\pm\)8

D

\(\pm\)12

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2

2016 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2016

If x, y and z are greater than 1, then the value of \(\left| {\matrix{ 1 & {{{\log }_x}y} & {{{\log }_x}z} \cr {{{\log }_y}x} & 1 & {{{\log }_y}z} \cr {{{\log }_z}x} & {{{\log }_z}y} & 1 \cr } } \right|\) is

A

log x . log y . log z

B

log x + log y + log z

C

0

D

1 \(-\) {(log x) . (log y) . (log z)}

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3

2017 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2017

The value of det A, where \(A\, = \left( {\matrix{ 1 & {\cos \theta } & 0 \cr \[{ - \cos \theta } & 1 & {\cos \theta } \cr\] \[{ - 1} & { - \cos \theta } & 1 \cr\] } } \right)\), lies

A

in the closed interval [1, 2]

B

in the closed interval [0, 1]

C

in the open interval (0, 1)

D

in the open interval (1, 2)

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4

2017 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2017

The linear system of equations

\(\left. \matrix{ 8x - 3y - 5z = 0 \hfill \cr 5x - 8y + 3z = 0 \hfill \cr 3x + 5y - 8z = 0 \hfill \cr} \right\}\) has

A

only zero solution

B

only finite number of non-zero solutions

C

no non-zero solution

D

infinitely many non-zero solutions.

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5

2017 · Mathematics · Algebra · Matrices And Determinants

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 over R. Then,

A

P is proper subset of Q

B

Q is proper subset of P

C

Neither P is proper subset of Q nor Q is proper subset of P

D

P \(\cap\) Q = \(\phi\), the void set

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6

2017 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2017

Let \(A = \left( {\matrix{ 1 & 1 & 1 \cr 0 & 1 & 1 \cr 0 & 0 & 1 \cr } } \right)\). Then, for positive integer n, Aⁿ is

A

\(\left( {\matrix{ 1 & n & {{n^2}} \cr 0 & {{n^2}} & n \cr 0 & 0 & n \cr } } \right)\)

B

\(\left( {\matrix{ 1 & 1 & {n\left( {{{n + 1} \over 2}} \right)} \cr 0 & 1 & n \cr 0 & 0 & 1 \cr } } \right)\)

C

\(\left( {\matrix{ 1 & {{n^2}} & n \cr 0 & n & {{n^2}} \cr 0 & 0 & {{n^2}} \cr } } \right)\)

D

\(\left( {\matrix{ 1 & n & {2n - 1} \cr 0 & {{{n + 1} \over 2}} & {{n^2}} \cr 0 & 0 & {{{n + 1} \over 2}} \cr } } \right)\)

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7

2017 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2017

Let a, b, c be such that b(a + c) \(\ne\) 0. If \(\left| {\matrix{ a & {a + 1} & {a - 1} \cr { - b} & {b + 1} & {b - 1} \cr c & {c - 1} & {c + 1} \cr } } \right| + \left| {\matrix{ {a + 1} & {b + 1} & {c - 1} \cr {a - 1} & {b - 1} & {c + 1} \cr {{{( - 1)}^{n + 2}}a} & {{{( - 1)}^{n + 1}}b} & {{{( - 1)}^n}c} \cr } } \right| = 0\), then the value of n is

A

any integer

B

zero

C

any even integer

D

any odd integer

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8

2017 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2017

Let \(A = \left( {\matrix{ {x + 2} & {3x} \cr 3 & {x + 2} \cr } } \right),\,B = \left( {\matrix{ x & 0 \cr 5 & {x + 2} \cr } } \right)\). Then all solutions of the equation det (AB) = 0 is

A

1, \(-\)1, 0, 2

B

1, 4, 0, \(-\)2

C

1, \(-\)1, 4, 3

D

\(-\)1, 4, 0, 3

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9

2018 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2018

The least positive integer n such that \({\left( {\matrix{ \[{\cos \pi /4} & {\sin \pi /4} \cr\] \[{ - \sin {\pi \over 4}} & {\cos {\pi \over 4}} \cr\] } } \right)^n}\) is an identity matrix of order 2 is

A

4

B

8

C

12

D

16

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10

2018 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2018

If \(\left| {\matrix{ { - 1} & 7 & 0 \cr 2 & 1 & { - 3} \cr 3 & 4 & 1 \cr } } \right| = A\), then \(\left| {\matrix{ {13} & { - 11} & 5 \cr { - 7} & { - 1} & {25} \cr { - 21} & { - 3} & { - 15} \cr } } \right|\) is

A

\({A^2}\)

B

\({A^2} - A + {I_3}\)

C

\({A^2} - 3A + {I_3}\)

D

\(3{A^2} + 5A - 4{I_3}\)

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11

2018 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2018

If \({S_r} = \left| {\matrix{ {2r} & x & {n(n + 1)} \cr {6{r^2} - 1} & y & {{n^2}(2n + 3)} \cr {4{r^3} - 2nr} & z & {{n^3}(n + 1)} \cr } } \right|\), then the value of

\(\sum\limits_{r = 1}^n {{S_r}}\) is independent of

A

only x

B

only y

C

only n

D

x, y, z and n

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12

2018 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2018

If the following three linear equations have a non-trivial solution, then

x + 4ay + az = 0

x + 3by + bz = 0

x + 2cy + cz = 0

A

a, b, c are in AP

B

a, b, c are in GP

C

a, b, c, are in HP

D

a + b + c = 0

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13

2018 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2018

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

A

skew symmetric

B

symmetric

C

not invertible

D

non-singular

Check answer

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14

2018 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2018

If the polynomial \(f(x) = \left| {\matrix{ {{{(1 + x)}^a}} & {{{(2 + x)}^b}} & 1 \cr 1 & {{{(1 + x)}^a}} & {{{(2 + x)}^b}} \cr {{{(2 + x)}^b}} & 1 & {{{(1 + x)}^a}} \cr } } \right|\), then the constant term of f(x) is

A

\(2 - {3.2^b} + {2^{3b}}\)

B

\(2 + {3.2^b} + {2^{3b}}\)

C

\(2 + {3.2^b} - {2^{3b}}\)

D

\(2 - {3.2^b} - {2^{3b}}\)

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15

2019 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2019

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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16

2019 · Mathematics · Algebra · Matrices And Determinants

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 matrix \(A - 3{I_3}\) is

A

invertible

B

orthogonal

C

non-invertible

D

real Skew Symmetric matrix

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17

2019 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2019

If \(A = \left( {\matrix{ 5 & {5x} & x \cr 0 & x & {5x} \cr 0 & 0 & 5 \cr } } \right)\) and \(|A{|^2} = 25\), then | x | is equal to

A

\({1 \over 5}\)

B

5

C

5²

D

1

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18

2019 · Mathematics · Algebra · Matrices And Determinants

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

A

M

B

M'

C

null matrix

D

identity matrix

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19

2019 · Mathematics · Algebra · Matrices And Determinants

WB JEE 2019

The system of equations

$$\eqalign{ & \lambda x + y + 3z = 0 \cr & 2x + \mu y - z = 0 \cr & 5x + 7y + z = 0 \cr}$$

has infinitely many solutions in R. Then,

A

\(\lambda\) = 2, \(\mu\) = 3

B

\(\lambda\) = 1, \(\mu\) = 2

C

\(\lambda\) = 1, \(\mu\) = 3

D

\(\lambda\) = 3, \(\mu\) = 1

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20

2019 · Mathematics · Algebra · Matrices And Determinants

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,

A

must be A = O₃ , B = O₃

B

if A \(\ne\) O₃, must be B \(\ne\) O₃

C

if A = O₃, must be B \(\ne\) O₃

D

may be A \(\ne\) O₃, B \(\ne\) O₃

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