Q1. Define Cartesian product and symmetric difference of two sets.
Let A  1, 2 and B  a, b, c . Find  A  B    B  A  ,  A  B    B  A  and A  B .
Q2. Let A  1, 2,3, 4,5 and B  3, 4,5, 7,9,11 . Find  A  B    A  B  and  A  B    B  A .
Q3. Let A  1, 2,3, 4,5, 6, 7,8 . Let R be a relation on A defined as R   a, b  : a  b is odd . Find
R . Determine whether R is reflective, symmetric, and transitive.
 1 4 12 


Q4. Find the rank of the matrix  2 1 9  .
 1 2 10 


5 7 
 5 2 
Q5. If A  
 and B  
 , find AB and BA.
 1 10 
  1 5 
Q6. There are 15 students in a group. Of these, 8 students are selected for only sports and 4 students
are selected for both sports and NCC. Find the number of students selected for only NCC.
 2 1 5 


Q7. Find the inverse of the matrix A   4 1 7  .
1 1 3 



Q8. Show that the set of all positive rational numbers Q forms a group with respect to the
ab
,  a, b  Q  .
2
Q9. Determine whether the vectors v1  1,1,  2,  2  , v2   2,  3, 0, 2  , v3   2, 0, 2, 2  are
operation  defined as a  b 
linearly dependent or independent.
Q10. State Cayley-Hamilton theorem. Verify Cayley-Hamilton theorem for the matrix
 1 2 2 


1
 1 3 0  and hence find A .
 0 2 1 


Q11. Check whether the function f :

defined by f  x   9 x  5 is one-one and
onto.
 5 7
Q12. Find the eigen values and eigen vectors of the matrix 
.
 2 9 
1 2 3 


Q13. Find the value of k such that the rank of the matrix  2 k 7  is 2.
 3 6 10 


Q14. Prove that the set G  1,  1, i,  i forms a group under multiplication
Q15. Check whether the function f :

defined by f  x   12 x  5 is one-one and
onto.
*******