@raman_sharma
BC =1 , CA =2 so AB =rt5using similarity in triangle ABC and ADCwe get CD= 2/rt5 and diameter of circle as 4/rt5
now using tangent secant theoremCD^2 = CE * AC4/5 = CE *2CE =0.4so AE=1.6hence 1.6/0.4 = 4

Q30) There are 10 consecutive positive integers written on a blackboard. One number is erased. The sum of remaining nine integers is 2011. Which number was erased?

for any weight we have 3 possibilities:-
Place it on the weight panPlace it on other pan, along with something whose weight we need to findWe don't use itSo, it is similar to base 3, hence by taking weight of form 3^n, we can ensure that we are using least number of weights and when we just have two possibilities. so 3^n >=300 so n=6