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Determinants Test - 8 Class 12 Notes | EduRev

Class 12 : Determinants Test - 8 Class 12 Notes | EduRev

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CBSE TEST PAPER-08 
CLASS - XII MATHEMATICS (Algebra) 
Topic:- Determinants
1. Find value of x, if
2 4 2 4
5 1 6
x
x
= [1] 
2. Find adj A for
2  3
1  4
A
? ?
=
? ?
? ?
[1] 
3. Without expanding, prove that
x+y     y+z      z+x
  z         x          y 0
  1        1          1
? = = [1] 
4. If matrix
1      -2      3
1       2      1
x      2      -3
A
? ?
? ?
=
? ?
? ?
? ?
is singular, find x. [1] 
5. Show that, using properties if det.
( )
2
2
2 3
2
1        x       x
x      1       x 1
x       x      1
x = - [1] 
6. If a, b, c is in A.P, and then finds the value of
x+2       x+3      x+2a
x+3       x+4      x+2b
x+4       x+5      x+2c
[4] 
7. 
3  2
,
1  1
A
? ?
=
? ?
? ?
Find the no. a and b such that A
2
 + aA + bI = 0 Hence find A
-1
[4] 
8. Find the area of ? whose vertices are (3, 8) (-4, 2) and (5, 1) [4] 
9. Evaluate
0           sin       -cos
-sin       0           sin
cos    -sin          0
a a
a ß
a ß
? ?
? ?
? =
? ?
? ?
? ?
[4] 
10. Solve by matrix method [4] 
x – y + z = 4
2x + y – 3 z = 0
x + y + z = 2

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