Explore popular questions from Matrices and Determinants for JEE Advanced. This collection covers Matrices and Determinants previous year JEE Advanced questions hand picked by experienced teachers.

## Chemistry

Matrices and Determinants

Correct Marks 4

Incorrectly Marks -1

Q 1. Consider the set {tex}A{/tex} of all determinants of order 3 with entries {tex}\mathrm 0 \quad or \quad1{/tex} only. Let {tex}B{/tex} be the subset of {tex}A{/tex} consisting of all determinants With value {tex}1{/tex}.Let {tex} C{/tex} the subset Of {tex}A{/tex} consisting of all determinants with value {tex}-1{/tex}.Then

A

{tex}C{/tex} is empty

{tex}B{/tex} has as many elements as {tex}C{/tex}

C

{tex} A = B \cup C {/tex}

D

{tex} B {/tex} has twice as many elements as elements as {tex} C {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 2. Let {tex} a , b , c {/tex} be the real numbers. Then following system of equations in {tex} x , y {/tex} and {tex} z {/tex}
{tex} \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } - \frac { z ^ { 2 } } { c ^ { 2 } } = 1 , \frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } + \frac { z ^ { 2 } } { c ^ { 2 } } = 1 {/tex},
{tex} - \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } + \frac { z ^ { 2 } } { c ^ { 2 } } = 1 {/tex} has

A

no solution

B

unique solution

C

infinitely many solutions

finitely many solutions

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 3. The parameter, on which the value of the determinant
{tex} \left| \begin{array} { c c c } { 1 } & { a } & { a ^ { 2 } } \\ { \cos ( p - d ) x } & { \cos p x } & { \cos ( p + d ) x } \\ { \sin ( p - d ) x } & { \sin p x } & { \sin ( p + d ) x } \end{array} \right| {/tex} does not depend
upon is

A

{tex} a {/tex}

{tex} p {/tex}

C

{tex} d {/tex}

D

{tex} x {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 4. If the system of equations {tex} x - k y - z = 0 , k x - y - z = 0 , x + y - z = 0 {/tex} has a non-zero solution, then the possible values of {tex} k {/tex} are

A

{tex} - 1,2 {/tex}

B

{tex} 1,2 {/tex}

C

{tex} 0,1 {/tex}

{tex} - 1,1 {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 5. If {tex} A = \left[ \begin{array} { l l } { \alpha } & { 0 } \\ { 1 } & { 1 } \end{array} \right] {/tex} and {tex} B = \left[ \begin{array} { l l } { 1 } & { 0 } \\ { 5 } & { 1 } \end{array} \right] , {/tex} then value of {tex} \alpha {/tex} for which
{tex} A ^ { 2 } = B , {/tex} is

A

1

B

- 1

C

4

no real values

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 6. For the values of the value of
is

{tex}0{/tex}

B

C

D

##### Explanation

The determinants can be rewritten as 8 determinants and the value of each of these 8 determinants is zero.

Similarly, other determinants can be shown zero.

Correct Marks 4

Incorrectly Marks -1

Q 7. If are in AP, then the value of the det is, where

0

B

1

C

2

D

None of these

##### Explanation

We have,

[Applying ]
[Applying ]

Correct Marks 4

Incorrectly Marks -1

Q 8. is equal to

A

{tex}0{/tex}

C

D

None of the above

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 9. If and then the value of is

A

B

D

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 10. If and are the given determinants, then

A

C

D

##### Explanation

We have,

Correct Marks 4

Incorrectly Marks -1

Q 11. The value of is equal to

A

C

D

##### Explanation

We have,

Correct Marks 4

Incorrectly Marks -1

Q 12. If are non-zero real numbers, then vanishes, when

B

C

D

##### Explanation

Given,

Correct Marks 4

Incorrectly Marks -1

Q 13. =0, then

is one of the cube roots of unity

B

is one of the cube roots of unity

C

is one of the cube roots of unity

D

is one of the cube roots of unity

##### Explanation

is one of the cube roots of unity.

Correct Marks 4

Incorrectly Marks -1

Q 14. The repeated factor of the determinant
is

B

C

D

None of these

##### Explanation

We have,

Hence, the repeating factor is

Correct Marks 4

Incorrectly Marks -1

Q 15. The value of is equal to

0

B

1

C

D

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 16. The value of the determinant, is

A

C

D

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 17. The value of the determinant
is

Independent of

B

Independent of

C

Independent of and

D

None of these

##### Explanation

Applying

which is independent of

Correct Marks 4

Incorrectly Marks -1

Q 18. In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then, it can be decomposed into determinant, where has the value

A

1

B

9

C

16

24

##### Explanation

Since, the first column consists of sum of two terms, second column consists of sum of three terms and third column consists of sum four terms.

Correct Marks 4

Incorrectly Marks -1

Q 19. If then is equal to

A

1

B

3

4

D

2

##### Explanation

On comparing with , we get

Correct Marks 4

Incorrectly Marks -1

Q 20. If (where is a real valued function of then the value of

A

Depends upon the function

B

is 4

C

is

is zero

##### Explanation

So, is an odd function.
is an odd function

Correct Marks 4

Incorrectly Marks -1

Q 21. A root of the equation is

A

B

D

1

##### Explanation

On expanding the given determinant, we obtain

Correct Marks 4

Incorrectly Marks -1

Q 22. If then the value of

0

B

1

C

D

None of these

##### Explanation

[ two columns are identical]

Correct Marks 4

Incorrectly Marks -1

Q 23. The value of is equal to

A

C

D

##### Explanation

Applying we obtain

[Expanding along ]

Correct Marks 4

Incorrectly Marks -1

Q 24. The value of the determinant is

A

B

D

##### Explanation

Let

Correct Marks 4

Incorrectly Marks -1

Q 25. If to terms, to terms and to terms, then equals

A

B

0

D

##### Explanation

We have, upto terms

upto terms=
and upto terms=

two rows are identical]