TCS Company Numerical Ability Time Distance and Speed

A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says ' At least n of the statements on this sheet are false. ' Which statements are true and which are false?

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TCS Other Question

Paul the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous accuracy has now been invited to predict ICC world cup matches in 2011. We will assume that the world cup contenders have been divided into 2 groups of 9 teams each. Each team in a group plays the other teams in the group. The top two teams from each group enter the semi finals (after which the winner is decided by knockout). However, Paul has a soft spot for India and when India plays any team, Paul always backs India. Alas, his predictions on matches involving India are right only 2 out of 3 times. In order to qualify for the semi finals, it is sufficient for India to win 7 of its group matches. What is the probability that India will win the ICC world cup? A lady has fine gloves and hats in her closet- 18 blue 32 red and 25 yellow. The lights are out and it is totally dark. inspite of darkness she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that it is a glove. How many gloves must she take out to make sure that she has a pair of each colour?