1) What do you understand from Curl and Div of a vector field F? Explain them with examples.  Is there any difference between Grad and Div of F? What are the applications of Grad, Div and Curl?
2) Find the area of a parallelogram spanned by the vectors  and  where .
3) State and Prove Cayley-Hamilton theorem. Using Caley-Hamilton theorem find the inverse of the matrix A = 
4) Define Contra positive, Converse, and Inverse of a statement. What are the contra positive, the converse, and the inverse of the conditional statement "The home team wins whenever it is raining?". Give an example of statement is a Tautology. Justify your example. 
5) Prove without contradiction, that if  is an integer and  is odd, then  is odd. Can this be proved using contradiction? If so, prove using contradiction also. 
6) Verify that the conditions of Rolle's Theorem are satisfied by the function  and determine a value of c in  for which   Is Rolles' theorem related Mean value theorem? If yes, how is it related? What is the significance of Mean Value theorem?
7) What do you understand by series being conditionally convergent and absolutely convergent? Determine whether the series  and  are absolutely convergent, conditionally convergent or divergent. 
8) Determine the radius of convergence of each of the following power series