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Which is the smallest integer-sided square that is Inscribed in a integer-sided right triangle so that one side of the Square lies on the hypotenuse?
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There is A one-way road one km long with two lanes, each lane five meters broad. Cars Cruise at 60 kmph on each lane. Distance between front bumpers of any two Successive cars is 10 meters which includes length of one car plus the clear Between the two cars. question (a): how many cars exit the road in one hour (your brilliant readers will find this childs play). then one morning mtnl digs a trench across one Lane at location half km of road length. The trench is 5m x 5m which makes a Single lane road for 10 meters (2.5 meters on either side of the trench for Maneuvering). As the driving discipline and etiquette of indian rivers is World famous they allow five cars from one lane and then five cars from The other lane to enter the single lane portion of the road. This Involves deceleration, stoppage and acceleration of cars. Assume optimum Points of stoppage and from the cruising speed. Question (b): how many cars Exit the road in one hour?
There are some bulbs,which are numbered from 1 to 100.all the bulbs are in on conditions. The following operations are performed:-
1. Those bulbs number which are divisible by 2 are switched OFF.
2. Those bulbs numbered which are divisible by 3 are switched ON (which are already OFF) and OFF bulbs are switched ON.
3. Similarly bulbs numbers divisible by 4 are either switched ON or OFF depending upon there previous condition
4. This procedure is adopted till 100th bulb.
At the end there were how many bulbs which were in ON condition?