CBSE Guess > Papers > Important Questions > Class XII > 2009 > Maths > Mathematics By Mr. Aravind
CBSE CLASS XII
Q. 1. 
Determine value without expansion
Q. 2. A = 
Prove that (aI + bA)
= anI + nan-1bA for all n values 
N
Q. 3. A = 
satisfies 
and hence solve
2x – 3y = -1
3x+ 4y = 7
Q. 4. Prove that A = 
is invertible
Q. 5. Prove that
3x + 2y + z =6
4x + 3y + 2z = 9 Has a solution
8x + 16y + y = 25
Q. 6. (a). 
= 
xyz(x - y) (y - z) (x - z)
b) A = 
Find A 
using ET
Q. 7. Does 
exist within R 
? Justify your answer
= 
Q. 8. (a). An amount of Rs.5000/- is invested in 3 different rates of interests 6%,7%,8% respectively. The total annual income is Rs.358/- and the combined income of the 1st two investments is Rs.70/- more than the 3rd. Find each investment using Matrix Method
(b). Show using properties of determinants
= 2 
Q. 9. (a). 
Show using properties
(b). A = 
; B 
= 
Find (AB)
and 
Q. 10. Prove A = 
is invertible AA-1 is I3
Q. 11. (a). Find A adjA in the following
= A ;- A=
Q. 12. A and B are symmetric prove that :
- AB+BA is symmetric
- B’AB is symmetric
- (A+B)’ is symmetric
Q. 13. Solve using Matrix equations:
3x + y + z = 2
2x - 4y = 3z =-1
4x + y - 3z =-11
Q. 14.Suppose A is a square matrix of order 4. We multiply the matrix by a scalar .Express the determinant of that matrix in terms of the scalar
Q. 15. A = 
and A+A’ = I find the value of 
Q. 16. Inverse of a Matrix using Elementary transformations:
Q. 17. Show using properties of determinants that:
Q. 18. 
Show that this determinant is independent of 0.
Paper By Mr. Aravind
