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रविवार, १४ एप्रिल, २०१३

Mathematics - Quiz

Mathematics - Quiz (15 Minutes)

1> A car travels to hill top at the speed of 20 km /hr from base and returns at the speed of 25 km /hr. If the distance of hill top from base is 100 km then what is the average speed during this entire journey?
2> Give two practical examples where 11 + 3 = 2 holds good.
3> How many numbers are there which are less than 100 and divisible by both 2,3?
4> What is the angle between Hr and Minute Hands at 1:45 P.M.?
5> Was yr 1900 a leap year?
6> What is sqaure of 75?
7> 27th Feb 2012 was Monday then what would be day on 27th Feb 2013 and 27th Feb 2014?
8> x = 17, a = 1, b = 2, ..., z = 26 then
( x - a ) * ( x - b ) * ...*(x - z) = ?
9> 101 * 101 = 10201

102 * 102 = 10404
103 * 103 = 10609
then 109 * 109 = ?10> A monley has to cross distance of 100 m. In his first leap he crosses 50 m and in each of his subsequent leaps he crosses half of the distance remaining. How many leaps he would take to cross finish line.



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Answers
1> Average speed = Total distance travelled / total time taken
Here Total distance travelled = 200 KM
Total time taken = 9 Hr
Hence average speed = 200 / 9 = 22.22 km /hr

Here you may get tempted to answer this as 22.5 in hurry.

2> 3 Hrs after 11 A.M. we have 2 P.M.
3 months after November we are in February the second month

3> Answer 16
The number divisible by both 2 and 3 is 6
There are 16 numbers less than 100 which are divisible by 6 and hence the answer.

4> The minute hand is at 9
The angle between 9 and 1 = 120
The Hr hand travels 30 degrees in 60 minutes
so in 45 minutes it will travel 22.5 degrees
Hence the total angle = 142.5 degrees

5> No.
The year which ends with 00, needs to be divisible by 400 to qualify as leap year

6> 5625.
To get square of any number ending with 5, first write 25 and then precede it with product of the number  (7) and the subsequent number (8)

7> Wednesday and Thursday respectively.
In leap year we have 366 days, which means 2 additional days to 52 weeks. So weekday shift by 2 days
In normal year we have 365 days, which means 1 additional day to 52 weeks and hence the weekday shift by 1 day

8> 0
One of the term in the series would be (x-x)

9> 11881

(a+b)*+(a+b) = a*a + 2*a*b+ b*b
Here a = 100, b = 9

10> Monkey won't reach the finish line.



शुक्रवार, १२ एप्रिल, २०१३

Abhimanyu and We!

Abhimanyu participated in the Mahabharata war when he was sixteen years old. During the Mahabharata war, Abhimanyu held at bay great warriors such as Drona, Karna, Duryodhana and Dushasana. Abhimanyu entered the war fighting the battle but then enemy had made such trap (Chakravyuh) that he couldn't break away from it and eventually got killed.

In today's world, we also get trapped in various temptations, responsibilities and then can't find real ourselves.
  1. Once a child is born, he/she is trapped in expectations of the parents.
  2. Then, in current world, it is technology which take control of mind of the kid.
  3. We form our firm opinions which take control of us for rest of the life. We never realize how much these opinions restrict our abilities to see the world with open eyes.
  4. We then fall in love with someone. People love a person for selfish reasons many times. They love someone else because by doing so the pleasure sensations in their brains are triggered. More intense these sensations are more addicted the person is to that love. Sometimes people make sacrifices for their love.  Because love makes them weaker. They can't stand the thought of loosing the person whom they love.
  5. Then comes professional life. Some people become successful in it, and then get entrapped in their own successful image. They have to continue to keep on trying to maintain this successful image
  6. Some people have to resort to not so legal ways of earning money. They become part of system / chain which don't let them break free from it. So they are also trapped.
  7. Then we get trapped with our loves for our kids.
In short we all are Abhimanyus. The only difference being, the real abhimanyu entered war at his own choice, we don't have that choice.

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