CAT Exam Logical Reasoning Cryptography

Rajat draws a 10 x 10 grid on the ground such that there are 100 identical squares numbered 1 to 100. If he has to place two identical stones on any two separate squares in the grid, how many distinct ways are possible?

Option
(1) 2475
(2) 4950
(3) 9900
(4) 10000

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CAT Other Question
All Analysts are Engineers. One-third of all Engineers are Analysts. Half of all Technicians are Engineers. Only one Technician is an Analyst. Eight Technicians are Engineers. If the number of Engineers is 90, how many Engineers are neither Analysts nor Technicians?

Option
(1) 65
(2) 79
(3) 82
(4) 53 Mohan is a carpenter who specialises in making chairs. For every assignment he undertakes, he charges his commission and cost. His commission is fixed and equals Rs.560 per assignment while the cost equals Rs.2n² where n is the total number of chairs he makes. If for a certain assignment the average cost per chair is not more than Rs.68 then the minimum and maximum possible number of chairs in the assignment are, respectively.

Option
(1) 13 and 19
(2) 13 and 20
(3) 14 and 19
(4) 14 and 20