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Test- Matrices and Determinant

1. For non zero, cba ,, if 0111

111

111

c

b

a

, then the value of cba

111

(a) abc (b)abc

1

(c) )( cba (d) None of these

2. The value ofxobtained from the equation 0

x

x

x

will be

(a) 0 and )( (b) 0 and )(

(c) 1 and )( (d) 0 and )( 222

3. If 5 is one root of the equation 087

22

73

x

x

x

, then other two roots of the equation are

(a) 2 and 7 (b) 2 and 7

(c) 2 and 7 (d) 2 and

7

4. If kn 3 and 1, 2, are the cube roots of unity, then1

1

1

2

2

2

nn

nn

nn

has the value

(a) 0 (b)

(c) 2 (d) 1

5. If 00

0

0

ab

ba

ba

, then

(a) ais one of the cube roots of unity(b) b is one of the cube roots of unity

(c)

ba is one of the cube roots of unity

(d)

b

ais one of the cube roots of1

6. For positive numbers yx, and zthe numerical value of the determinant1loglog

log1log

loglog1

yx

zx

zy

zz

yy

xx

is

(a) 0 (b) 1

(c) xyzelog (d) None of these

7. nml ,, are the thth qp , and thr term of a G.P., all positive, then1log

1log

1log

rn

qm

pl

equals

(a) 1 (b) 2

(c) 1 (d) 0

8. If aybxzcxazybzcyx ,, (where x,y, zare not all zero) have a solution other than 0x , 0y , 0z then a, band careconnected by the relation

(a) 03222 abccba

(b) 02222 abccba

(c) 12222 abccba

(d) 1222 abcabccba 9. If |A| denotes the value of the determinant of the square matrix A of order 3, then | 2A|=(a) ||8 A (b) ||8 A

(c) ||2 A (d) None of these

10. IfA is a matrix of order 3 and |A| = 8, then || Aadj

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Test- Matrices and Determinant[

(a) 1 (b) 2

(c) 32 (d)6

2

11. If

cossin

sincosA , then 2A

(a)

2cos2sin

2sin2cos(b)

2cos2sin

2sin2cos

(c)

2cos2sin

2sin2cos(d)

2cos2sin

2sin2cos

12. If

213

132

321

A and Iis a unit matrix ofrd

3 order, then )9(2 IA equals

(a) 2A (b) 4A(c) 6A (d) None of these

13. If

12/tan

2/tan1

A and IAB , then B

(a) A.2

cos2

(b)T

A.2

cos2

(c) I.2

cos2

(d) None of these

14. If

11

24A and Iis the identity matrix of order 2, then )3)(2( IAIA

(a) I (b) O

(c)

00

01(d)

10

00

15. If IYX 23 and OYX 2 , where Iand O are unit and null matrices of order 3 respectively, then(a) )7/2(),7/1( YX (b) )7/1(),7/2( YX (c) IYIX )7/2(,)7/1( (d) IYIX )7/1(,)7/2(

16. If ,3

2

1

A then AA

(a) 14 (b)

3

4

1

(c)

963

642

321

(d) None of these

17. If

c

b

a

A

00

00

00

, then nA

(a)

nc

nb

na

00

00

00

(b)

c

b

a

00

00

00

(c)

n

n

n

c

b

a

00

00

00

(d) None of these

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Test- Matrices and Determinant

18. The inverse of

211

132

753

is

(a)

025

1113

2637

(b)

125

1113

2637

(c)

125

2637

1113

(d) None of these

19. If matrix

760

543

101

A and its inverse is denoted by

333231

232221

131211

1

aaa

aaa

aaa

A , then the value of 23a =

(a)20

21(b)

5

1

(c)

5

2 (d)

5

2

20. Let

100

0cossin

0sincos

)(

F , where .R

Then1)]([

F is equal to

(a) )( F (b) )( 1F

(c) )2( F (d) None of these

21. Out of the following a skew- symmetric matrix is

(a)

065

604

540

(b)

165

614

541

(c)

365

624

541

(d)

i

i

i

65

64

541

22. 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 ofthree terms and each element of the third column consists of sum of four terms. Then it can be decomposed into ndeterminants, where nhas thevalue

(a) 1 (b) 9

(c) 16 (d) 24