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Applications of Matrices and Determinants - Choose the Correct Answers | 12th Mathematics : UNIT 1 : Applications of Matrices and Determinants

Chapter: 12th Mathematics : UNIT 1 : Applications of Matrices and Determinants

Choose the Correct Answers

Choose the Correct or the most suitable answer from the given four alternatives, Multiple choice questions with Answers, Solution and Explanation - Maths Book back 1 mark questions and answers with solution for Exercise Problems

Choose the Correct or the most suitable answer from the given four alternatives: 

1. If | adj(adj A) |=|, then the order of the square matrix is

(1) 3

(2) 4

(3) 2

(4) 5


 

2. If is a 3× 3 non-singular matrix such that AA= Aand = AA, then BB=

(1) A

(2) B

(3) I3

(4) BT


 

3. If A =  , B = adj A and C = 3, then | adj B | / |C| =

(1) 1/3

(2) 1/9

(3) 1/4

(4) 1


 

4. if , then A = 


Ans: (3)


 

5. if  , then 9I2 – A =

(1) A-1

(2) A-1/2

(3) 3A-1

(4) 2A-1

 


6. if  then | adj ( AB) |=

(1) -40

(2) -80

(3) -60

(4) -20


 

7. If P=  is the adjoint of 3× 3 matrix and | |= 4 , then is

(1) 15

(2) 12

(3) 14

(4) 11


 

8.If Aand A then the value of a23 is

(1) 0

(2) -2

(3) -3

(4) -1


 

9. If Aand are invertible matrices of some order, then which one of the following is not true?

(1) adj A =| A | A-1

(2) adj( AB) = (adj A)(adj B)

(3) det A-1 = (det A)-1

(4) ( ABC)-1 = C-1B-1A-1


 

10. If ( AB), and A-1 = then B= 


Ans: (1)


 

11. If AAis symmetric, then A=

(1) A-1

(2) (AT)2

(3) AT

(4) ( A-1 )2


 

12. If is a non-singular matrix such that A1  , then ( A)=


Ans: (4)


 

13.if A=  and A= A, then the value of is

(1) -4/5

(2) -3/5

(3) 3/5

(4) 4/5

Ans: (1)


 

14.if A= , and AB = I, then B=


Ans: (2)


 

15. if A= and A(adj A, then k=

(1) 0

(2) sinθ

(3) cosθ

(4) 1

Ans: (4)


 

16. If A= be such that λ A−1 , then λ is

(1) 17

(2) 14

(3) 19

(4) 21


 

17.If adj A= , adj B= , then adj ( AB) is


Ans: (2)


 

18. The rank of the matrix  is

(1) 1

(2) 2

(3) 4

(4) 3

Ans: (1)


 

19. If xy= exy= e  then the values of and y are respectively,

(1) e(Δ2 / Δ1 ) , e(Δ3 / Δ1 )

(2) log(Δ1/ Δ3 ), log(Δ23)

(3) log(Δ2/ Δ1 ), log(Δ31)

(4) ) e(Δ1 / Δ3 ) ,e(Δ2/Δ3 )


 

20. Which of the following is/are correct?

(i) Adjoint of a symmetric matrix is also a symmetric matrix.

(ii) Adjoint of a diagonal matrix is also a diagonal matrix.

(iii) If A is a square matrix of order n and λ is a scalar, then adj( λ A) =  λn adj( A) .

(iv) A(adjA) = (adjA) A =| A | I

(1) Only (i) 

(2) (ii) and (iii) 

(3) (iii) and (iv) 

(4) (i), (ii) and (iv) 


 

21. If ρ A= ρ ([ B]) , then the system AX = of linear equations is

(1) consistent and has a unique solution

(2) consistent

(3) consistent and has infinitely many solution

(4) inconsistent


 

22. If 0 ≤ θ ≤ π and the system of equations + (sinθ − (cosθ )= 0, (cosθ )− = 0, (sinθ )− = 0 has a non-trivial solution then θ is

(1) 2π/3

(2) 3π/4

(3) 5π/6

(4) π/4


 

23. The augmented matrix of a system of linear equations is  . The system has infinitely many solutions if

(1) λ = 7, μ ≠ -5

(2) λ = -7, μ = 5

(3) λ ≠ 7, μ ≠ -5

(4) λ = 7, μ = -5


 

24. let A = , and 4B = , If is the inverse of , then the value of is

(1) 2

(2) 4

(3) 3

(4) 1


 

25.If A= , then adj(adj A) is


Ans: (1)



Choose the Correct or the most suitable answer from the given four alternatives: 

1. If | adj(adj A) |=|, then the order of the square matrix is

(1) 3

(2) 4

(3) 2

(4) 5

 

2. If is a 3× 3 non-singular matrix such that AA= Aand = AA, then BB=

(1) A

(2) B

(3) I3

(4) BT

 

3. If A =  , B = adj A and C = 3, then | adj B | / |C| =

(1) 1/3

(2) 1/9

(3) 1/4

(4) 1

 

4. if , then A = 


Ans: (3)

 

5. if  , then 9I2 – A =

(1) A-1

(2) A-1/2

(3) 3A-1

(4) 2A-1

 

6. if  then | adj ( AB) |=

(1) -40

(2) -80

(3) -60

(4) -20

 

7. If P=  is the adjoint of 3× 3 matrix and | |= 4 , then is

(1) 15

(2) 12

(3) 14

(4) 11

 

8.If Aand A then the value of a23 is

(1) 0

(2) -2

(3) -3

(4) -1

 

9. If Aand are invertible matrices of some order, then which one of the following is not true?

(1) adj A =| A | A-1

(2) adj( AB) = (adj A)(adj B)

(3) det A-1 = (det A)-1

(4) ( ABC)-1 = C-1B-1A-1

 

10. If ( AB), and A-1 = then B= 


Ans: (1)

 

11. If AAis symmetric, then A=

(1) A-1

(2) (AT)2

(3) AT

(4) ( A-1 )2

 

12. If is a non-singular matrix such that A1  , then ( A)=


Ans: (4)

 

13.if A=  and A= A, then the value of is

(1) -4/5

(2) -3/5

(3) 3/5

(4) 4/5

Ans: (1)

 

14.if A= , and AB = I, then B=


Ans: (2)

 

15. if A= and A(adj A, then k=

(1) 0

(2) sinθ

(3) cosθ

(4) 1

Ans: (4)

 

16. If A= be such that λ A−1 , then λ is

(1) 17

(2) 14

(3) 19

(4) 21

 

17.If adj A= , adj B= , then adj ( AB) is


Ans: (2)

 

18. The rank of the matrix  is

(1) 1

(2) 2

(3) 4

(4) 3

Ans: (1)

 

19. If xy= exy= e  then the values of and y are respectively,

(1) e(Δ2 / Δ1 ) , e(Δ3 / Δ1 )

(2) log(Δ1/ Δ3 ), log(Δ23)

(3) log(Δ2/ Δ1 ), log(Δ31)

(4) ) e(Δ1 / Δ3 ) ,e(Δ2/Δ3 )

 

20. Which of the following is/are correct?

(i) Adjoint of a symmetric matrix is also a symmetric matrix.

(ii) Adjoint of a diagonal matrix is also a diagonal matrix.

(iii) If A is a square matrix of order n and λ is a scalar, then adj( λ A) =  λn adj( A) .

(iv) A(adjA) = (adjA) A =| A | I

(1) Only (i) 

(2) (ii) and (iii) 

(3) (iii) and (iv) 

(4) (i), (ii) and (iv) 

 

21. If ρ A= ρ ([ B]) , then the system AX = of linear equations is

(1) consistent and has a unique solution

(2) consistent

(3) consistent and has infinitely many solution

(4) inconsistent

 

22. If 0 ≤ θ ≤ π and the system of equations + (sinθ − (cosθ )= 0, (cosθ )− = 0, (sinθ )− = 0 has a non-trivial solution then θ is

(1) 2π/3

(2) 3π/4

(3) 5π/6

(4) π/4

 

23. The augmented matrix of a system of linear equations is  . The system has infinitely many solutions if

(1) λ = 7, μ ≠ -5

(2) λ = -7, μ = 5

(3) λ ≠ 7, μ ≠ -5

(4) λ = 7, μ = -5

 

24. let A = , and 4B = , If is the inverse of , then the value of is

(1) 2

(2) 4

(3) 3

(4) 1

 

25.If A= , then adj(adj A) is


Ans: (1)



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