DSE last year papers problems

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DSE last year papers problems

riddhima
2012

Question 40, ( i get an infinite AP with difference as 1/2 and a= -1/2)
Question 57, I am getting a as my answer, anybody can give me the working so that I may know where the minus sign is getting wrong
question 36

2011
Q 36

2010

q 19 and q 20, q 27, q 38, q 42, q 51, q 54

2009

Option b q 15, q 17, q 27, q 39

Thanks guys! I know these are lots of queries!