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Metal strip of width „x‟ cm. 2 metal strips are placed one over the other, then the combine length of 2 strips is „y‟. If „z‟ strips are placed in that manner. What is the final width of that arrangement?

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45 people (a1, a2…….a45) meet and shake hands in a circular fashion. In other words there totally 45 handshakes involving the pairs (a1, a2), (a2, a3)……(a44, a45), (a45, a1). Then the size of the smallest set of people such that the rest have shaken hands with atleast one person in the set is. 20. In 1911 a French Physicist Paul devised a thought experiment based on Einstien’s Special Relativity. In the experiment, a person makes a journey into space at nearly speed of light and comes back to earth. He finds that he has aged five times less than his twin who stays back on earth for 40 years. This is popularly known as the twins paradox. Now consider the case of Hansel and Gretel, who are not twins five years ago. Hansel was twice as old as was Gretel. If they journey in to space, and automatic clock assists in logging the start time of their journey accurately. If the do not journey in to space, 5 years hence Hansel age will be 4/3 times the age of Gretel. Find Hansel’s age today in binary numbers.