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.

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.

Invisible Power and Parenting

In a relationship which involves two individuals, societies or nations, there always exists a battle to gain control of the relationship between two parties involved. In the most premature state this battle is open and stronger party uses power to gain control of relationship and forces the other entity to behave as per its wish. But this model of controlling the relationship can not be sustained for longer duration since there will be always unhappiness prevailing in minds of weaker entity. It will try to become more powerful in course of time and take control of relationship.
In more matured model of relationship, the stronger entity controls the behaviour of the weaker entity by putting it in controlled environment. The environment is organized in such a way that weaker party is brainwashed into behaving in a pattern desirable to the stronger one. This needs a lot of thought processing and self discipline on behalf of stronger one.
The similar principle can be applied to parenting in which parents can thoughtfully create an environment at home in which kids are driven into behaviour as desired by parents. In modern age it is desirable philosophy of parenting. Here is word of caution though, considering the intelligence of new generation, it is highly likely that this philosophy may not be long sustaining unless parents always keep on evolving their techniques.
Same principle applies to other relationships in professional and personal life. The complexity of the equation varies according to relation.

State of Indian Cricket

Here are some important points

1. There is change in nature of Indian Fan. We now have more fans for whom Cricket is just another means of spending time at weekend or at work. The passion for real cricketing skills in Indian fans is diminishing.
2. Any team goes through the cycle of peaks and lows. After retirements of legends, Indian team is also going through similar phase.
3. Indian team could never give a great performance outside sub-continent. The advantage which we had in our conditions is slowly diminishing due to IPL where foreign players get constant exposure to Indian conditions.
4. We spend a lot of time in analyzing the game. This is gross misuse of national resources. Every person who is scrutinizing the performance of Indian team, how comfortable he / she would be if their own professional performance is scrutinized on public forum.

LIFE OF PIE च्या निमित्ताने

 
गेल्या आठवड्यात लाईफ ऑफ पाय हा चित्रपट बघितला. चित्रपटाच्या आरंभीच येणारे नितांत सुंदर गाण, पोंडेचरीतील वसाहतकालीन शांत जीवन, सुंदर तब्बू सारे काही मस्त. त्यानंतरचे छायाचित्रणातील अद्भुत करामती. माणसाची कल्पनाशक्ती आणि संगणकाची तंत्रे वापरून विविध सुंदर देखावे निर्माण केले गेले आहेत. मानवाच्या मर्त्य जीवनापलीकडे काही असल्यास ते कसे असेल ह्याची विविध लोक वेगवेगळी चित्रे रंगवतात. ह्या चित्रपटातील छायाचित्रणातील अद्भुत करामती पाहून आपणही ह्या वेगळ्या विश्वाची आपल्या परीने चित्र रेखाटू शकतो.
चित्रपटाच्या शेवटी नायक कथेला थोडी रूपकात्मक जोड देण्याचा प्रयत्न करतो. परंतु हा चित्रपट कथानकाच्या पातळीवर भयंकर मार खातो. तंत्रज्ञानाची खूप उंची गाठलेल्या ह्या चित्रपटाने कथेच्या बाबतीत इतका मार खाल्ल्याचे पाहून वाईट वाटते. मग आठवला तो जब तक हैं जान हा चित्रपट. तो ही तसाच. कथानकाच्या पातळीवर सगळी बोंब. मग आठवले ते ह्या वर्षी सुद्धा विकत घेतलेला दिवाळी अंकांचा संग्रह. पूर्वी वाचलेल्या दिवाळी अंकातील दीर्घ कथेच्या आठवणीने मी दर वर्षी दिवाळी अंकाचा संच विकत घेतो आणि दर वर्षी निराशाच पदरी पडते. केबल टीवी वर वर्ल्ड मूवी नावाची एक वाहिनी येते. त्यातील तंत्रज्ञानाच्या प्राथमिक पातळीवर असणारे पण कथानकाच्या आणि कथेतील व्यक्तिमत्वाच्या रंगछटा रंगविण्याच्या बाबतीत विलक्षण पातळी गाठलेले चित्रपट आठवतात. एकंदरीत काय तंत्रज्ञान आणि सर्जनशीलता विरुद्ध दिशेने जात असाव्यात असा मी घाईघाईने निष्कर्ष काढतो.