objective tips for exams in maths:

HELLO EVERYBODY GETS DOUBTED HOW TO USE FACILITY OF COMPETITIVE EXAMS BEING OBJECTIVE.I AM GIVING FIRST TIP FIRST ON MATHS.SOME OF U MAY ALREADY KNOW ABT THEM BUT I WANT HELP OTHERS WHO DONT KNOW THEM.
ANY QUESTIONS RELATED TO SERIES FOR NTERMS SUMMATION WE CAN USE SUBSTITUTION METHOD.I WILL GIVE TWO QUESTIONS SOLVED IN EASY WAY.
1.TANGENTS ARE DRAWN FRM PT P(1,8) TO CIRCLE :
2 2
x +y -6x-4y-11=0
touch circle at points A and B.the equation of circumcircle of the triangle PAB is
2 2
A)x +y +4x-6y+19=0
2 2
B)x +y -4x-10y+19=0
2 2
c)x +y -2x+6y-29=0
2 2
D)x+ y -6x-4y+19=0
THINK HOW CAN ONE SOLVE THIS IN 20 SECONDS.?????????????????

EASY YAAR the equation of circumcircle passes through P,A,B. we know P coordinates.so just substitute and only 2nd option (B) satisfies it ..so easy AM I RIGHT OR NOT.

NOW ANOTHER PROBLEM
if the sum of first n terms of an A.P is cn2(square),then the sum of squares of these n terms is

1)n(4n2-1)c2/6 2)n(4n2+1)c2/3 3)n(4n2-1)c2/3 4)n(4n2+1)c2/6

let n be 1.then sum will be c. so sum of squares will be c2.as there is only one term. now substitute n=1 in all options to get c2.only 3rd option satisfy to get c2. so easy to solve.
I WANT TO TELL U A FACT THAT THESE QUESTIONS APPEARED IN IIT 2009 .CAN U BELIEVE IT