Matrices

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SET-A

1. If A=1 -2

3 0

, B=1 4

,2 0

0 1C=

-1 0

then 5A-3B+2C is equal to

5A-3B+2C is equal to

a.8 7

-20 -9

b. 8 -20

7 -9

c.8 20

7 9

d. 8 20

7 9

2. If A=1 1 1

,3 3 3

-2 3

B= 1 -5 ,

4 1

then AB is equal to

a. -3 -1

9 -3

b. 3 -1

9 -3

c. -3 1

9 3

d. 3 1

-9 3

3. If A=1 2 1 0

,B=3 0 2 3

then which of the following is correct?

a. 2A A b.

2B B

c. AB=BA d. None of these

4. If A=

1 2 3

2 1 2 , then A is

3 2 1

a. A symmetric matrix b. A skew

c.A singular matrix d. Non singular matrix

5. If A=0 1

0 0

and I is the unit matrix of order 2, then 2

a I+bA , where ‘a’ and ‘b’ are

given constants, is equal to

a. 2 2a b A b.

2 2a abA

c. 2a abA d.

2 2a b A

Matrices

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6. If 0 2 1 2 5 3 4

,1 3 4 4 3 01

x

y

then ordered pair (x,y) is

a. 1, 2 b. 1,2

c. 1,2 d. 1, 2

7. If A= cos sin 1 0

and A adj A-sin cos 0 1

then is equal to

a.1 b. 2

c. 3 d.1/2

8. If A=1 12

1 1

and A , thena ba b

b a b a

a. 2 2 2 2

1 1,a a b b a b b.

2 2

1 12 ,a ab b a b

c. 2 2

1 1,a a b b ab d.

2 2

1 1, 2a a b b ab

9. If 1 2 5

,2 1 4

x

y

then the value of

2 2x y

xy

is equal to

a.5

2 b.

3

2

c.13

6 d.

13

6

10. If A=2 1

1 2

and A2-4A-nl=0, where I is the unit matrix of order 2, then

a.1

3n b.

1

3n

c. 3n d. 3n

11. If for the matrices A and B, AB=4 and BA=B, then A2 is equal to

a. I b. A

c. B d. None of these

12. The matrix

1 2

1 2 5

2 1 1

a

will be non-singular if

Matrices

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a.a=1 b. 1a

c. 9a d. 9a

13. If

1 0 1 1

1 1 0 1 ,

0 1 1 2

x

y

z

then ordered triplet (y, x, z) is

a. 0, 1, 2 b. 1, 0, 2

c. 1, 2,0 d. 0,2, 1

14. If A 1 2 4 1

,3 1 7 7

then A equals to

a.1 1

2 3

b.1 1

2 3

c.1 1

2 3

d. 1 1

2 3

15. If T

cos sinA= , then A.A

-sin cos

is equal to

a. 0 0

0 0

b. 1 1

1 1

c. 1 0

0 1

d. 0 1

1 0

16. If A=n

1 1, then A , , is equal to

0 1n N

a.n n

0 n

b. 1 n

0 1

c.n 1

0 1

d. 1 1

0 n

17. If ‘A’ is a matrix of order m x n, and Im, In represent the unit matrices of order ‘m’ and

‘n’ respectively, then

a.m n

I A=A=AI b. m n

AI A=I A

c.m n

AI =A=AI A d. m n

I A=A=I A

Matrices

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18. Every square matrix can be expressed as the sum of

a. Two symmetric

b. Two skew symmetric matrices

c. a symmetric and a skew symmetric matrix

d. A singular matrix and nonsingular matrix

19. If A is symmetric matrix and B is a skew symmetric matrix, then for any nN, which of

the followings is not correct?

a. An b. An is symmetric if n is odd

c. Bn is skew symmetric if n is odd d. Bn is symmetric if n is even

20. If a2+b2+c2+d2=1, and -1

a+ib c+idA= , then A

c+id a-ib

is equal to

a.a+ib id c

c id a ib

b.a-ib id c

c id a ib

c. a-ib id c

c id a ib

d. a+ib id c

c id a ib

Matrices

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SET-B

1. Which of the following statements is correct?

a. A skew-symmetric matrix of odd order is always invertible

b. Askew-symmetric matrix of odd order is always non-invertible

c. A skew-symmetric matrix of even order is always non-invertible

d. None of these

2. If A=

2

n

2

0 0 and A ,

0 0

ab b

a ab

then minimum value of ‘n’ is equal to

a. 2 b. 4

c.6 d. 3

3. If A and B are square matrices such that AB=B and BA=A, then A2+B2 is always equal

to

a. 2AB

b. 2BA

c. A+B

d. AB

4. If A=3 4

n n

, then An is equal to (nN)

a.3 4n n

n n

b.

3 4

1 1

nn

n

c. 2 5n n

n n

d. None of these

5. If A+B=1 0

1 1

and A-2B=1 1

,0 1

then A is equal to

a. 1 1

2 1

b.

2 1

3 3

1 2

3 3

c.

1 1

3 3

2 1

3 3

d. 2

13

11

3

Matrices

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6. If a is skew-symmetric matrix of order ‘n’ then the maximum number of non-zero

elements in ‘a’ is

a. 1

2

n n b.

2 1 1

6

n n n

c. 1n n d.

21

2

n n

7. If ‘A’ is a symmetric matrix of order ‘n’ , then maximum number of non-zero elements

in ‘A’ is

a. n2 b. n (n-1)

c. 1

2

n n d.

1

2

n n

8. The minimum number of zero elements in an upper triangular matrix of order nn is

a. 1

2

n n

b. 1

2

n n

c. 2 1

2

n

d. 2 1

2

n

9. If A=1 2 1 4 4 8

,B= and A.B.C=3 0 2 3 3 7

then C equals to

a.

59

3111 1

22 6

b.

59

3111 1

22 6

c.

59

3111 1

22 6

d. None of these

10. If -1

1 2 3

A= 0 1 2 , then A

0 0 1

is equal to

Matrices

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a.

1 2 1

0 1 2

0 0 1

b.

1 0 0

2 1 0

1 -2 1

c.

1 2 1

0 1 2

0 0 1

d. None of these

11. If A-B=1 2

2 4

and A+B=3 2

,2 0

Then AB equals to

a.2 4

-4 -4

b. 2 4

-4 -4

c.2 -4

4 4

d. 2 -4

4 -4

12. If A=

1 2 21

2 1 23

2x y

is a orthogonal matrix, then the value of x +y is equal to

a. 3 b.-3

c.0 d. 1

13. The total number of matrices that can be formed using 5 different letters such that no

letter is repeated in any matrix, is equal to

a. (5!) b. 2 (5!)

c. 2. 56 d. 56

14. 2 2ijA= aij and a ,

n ni j

then ‘A’ is necessarily

a. A unit matrix b. A zero matrix

c. A symmetric matrix d. A skew symmetric matrix

15. If 1 1 2 2

1 1 1 2

2 2

cos sin 0 cos 0 sinx

A x sinx cos 0 andA x = 0 1 0

sin 0 cos0 0 1

x x x

x

x x

then 1

1 2A x .A x

is equal

to

a. 1 2A x .A x b. 1 2

A -x .A -x

c. 2 1A x .A x d. 2 1

A -x .A x

Matrices

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16. If A=2

1 1 1

21 1 1

cos sin cos,

sin cos sin

x x x

x x x

then 1 2x x is equal to

a.0 b. , 1n n

c. 2 1 , 12

n n

d. 2 , 1n n

17. If A=

1 tan 1 tan2 2

,B=x

tan 1 tan 12 2

x x

x

then A. B-1 is equal to

a. cos sin

sin cos

x x

x x

b.cos sin

sin cos

x x

x x

c. cos sin

sin cos

x x

x x

d. cos sin

sin cos

x x

x x

18. If A= -1

2 2

,, then A

,

i j i jaij whereaij

i j i j

is equal to

a.

10

3

10

3

b.

2 1

9 3

10

3

c.

10

3

1 2

3 9

d. None of these

19. If 1 2

1,0 0 1 cos sinI ,I and A=

0,1 1 0 -sin cos

and ‘A’ can be written as

a. 1 2

I cos I sin b. 1 2I cos I sin

c. 1 2

I sin I cos d. 1 2

I cos I sin

20. If

1 2 1 0

0 1 0 2 ,

3 1 1 1

x

y

z

then ordered triplet (x,y,z) is

a. 9 7

,2,4 4

b. 7 9

,2,4 4

c. 9 7

, 2,4 4

d.

7 9, 2,

4 4

Matrices

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Answers Exercise-1 Matrices

1. b 2. b 3. d 4. a 5. d 6. a 7. a 8. d 9. a 10. c

11. b 12. b 13. b 14.a 15. c 16.b 17. a 18. c 19. b 20. c

Answers Exercise-2 Matrices

1. d 2. a 3. c 4. d 5. c 6. c 7. a 8. a 9. b 10. c

11. a 12. b 13. b 14.d 15. d 16.c 17. c 18. a 19. a 20. b

Matrices

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Matrices

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Matrices

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Matrices

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Answers Exercise-1 Quadratic Equation and Expressions

1. a 2. a 3. b 4. a 5. b 6. d 7. d 8. b 9. a 10. b

11. b 12. c 13. b 14.d 15. d 16.b 17. d 18. b 19. d 20. a

21. c 22. a 23. c 24. b 25. c

Answers Exercise-2 Quadratic Equation and Expressions

1. d 2. a 3. d 4. b 5. c 6. b 7. a 8. a 9. b 10. b

11. d 12. c 13. c 14.b 15. c 16.b 17. b 18. d 19. b 20. a

21. a 22. a 23. d 24. c 25. c

Answers Exercise-3 Quadratic Equation and Expressions

Matrices

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1. d 2. b 3. a 4. b 5. c 6. a 7. c 8. d 9. a 10. b

11. c 12. a 13. a 14.a 15. c 16. a 17. b 18. c 19. a 20. d

21. d 22. a 23. b 24. b 25. a