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# Determinants Test - 8 Class 12 Notes | EduRev

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

``` Page 1

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
= 
2  3
1  4
A
? ?
=
? ?
? ?

3. Without expanding, prove that
x+y     y+z      z+x
z         x          y 0
1        1          1
? = = 
4. If matrix
1      -2      3
1       2      1
x      2      -3
A
? ?
? ?
=
? ?
? ?
? ?
is singular, find x. 
5. Show that, using properties if det.
( )
2
2
2 3
2
1        x       x
x      1       x 1
x       x      1
x = - 
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

7.
3  2
,
1  1
A
? ?
=
? ?
? ?
Find the no. a and b such that A
2
+ aA + bI = 0 Hence find A
-1

8. Find the area of ? whose vertices are (3, 8) (-4, 2) and (5, 1) 
9. Evaluate
0           sin       -cos
-sin       0           sin
cos    -sin          0
a a
a ß
a ß
? ?
? ?
? =
? ?
? ?
? ?

10. Solve by matrix method 
x – y + z = 4
2x + y – 3 z = 0
x + y + z = 2
```
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