Nobel Prize, the most prestigious honor awarded to physicists in his life time for outstanding contribution to physics. In 2013, Nobel Prize in Physics has been awarded to physicist Peter Higgs along with F. Englert for their contribution of Higgs Boson, the particle which is supposed to give mass to other particles. Higgs boson is also known as the God particle named by Leo Lederman. And it deserves the name. The dilemma of how a particle gets mass was theorized by these scientists in back 60s which has been confirmed experimentally on March, 2013 in Large Hadron Collider, world’s most costly laboratory. Since Nobel Prize cannot be given to more than three people at a time, and also not to dead scientist, so these two scientist were awarded with the prize and other scientists were awarded another high honor with J.J. Sakurai Prize in theoretical physics in 2010.

John Forbes Nash, Jr. is an American mathematician who is known for his very revolutionary “Nash Equilibrium” and work in Game Theory. His works in Game Theory, Differential Geometry, and Partial Differential Equations have provided insight into the forces that govern chance and events inside complex systems in daily life. His theories are used in market economics, computing, evolutionary biology, artificial intelligence, accounting, politics and military theory. Serving as a Senior Research Mathematician at Princeton University during the latter part of his life, he shared the 1994 Nobel Memorial Prize in Economic Sciences with game theorists Reinhard Selten and John Harsanyi.

01 September 2013 (Class XI and XII)   Marks: 10 X 10 = 100 Time: 1.30 pm to 4.30 pm Answer the following ten questions 1. Prove that $$4(x_1^4+ x_2^4+dots + x_{14}^4)=7(x_1^3+ x_2^3+dots + x_{14}^3)$$ has no solution in positive integers. (Hint: Suppose on the contrary $$sum_{k=1}^{14}(x_k^4-frac{7}{4}x_k^3)=0.$$ Also use $$sum (x_k-1)^4.$$)   2. Find...

01 September 2013 (Class IX and X)   Marks: 10 X 10 = 100 Time: 1.30 pm to 4.30 pm Answer the following ten questions 1. Show that there does not exist a function $$f:Nrightarrow N$$ which satisfy (a) $$f(2)=3,$$ (b) $$f(mn)=f(m)f(n)$$ for all m,n in N; (c) $$f(m)<f(n)$$ whenever $$m<n.$$ (Hint: Suppose the contrary....

01 September 2013 (Class VII and VIII)   Marks: 5 X 20 = 100 Time: 1.30 pm to 4.30 pm Answer the following questions 1. If the radius of a circle is increased by 100%, determine the increase percent in the area of the circle. এটা বৃত্তৰ ব্যাসাৰ্দ্ধ 100% বৃদ্ধি হ’লে বৃত্তটোৰ...

01 September 2013 (Class V and VI)   Marks: 5 X 20 = 100 Time: 1.30 pm to 4.30 pm Answer the following questions 1. Show that 52563744 is divided by 24 without direct division. হৰণ প্ৰক্ৰিয়া প্ৰয়োগ নকৰাকৈ প্ৰমাণ কৰা যে 52563744 সংখ্যাটো 24 ৰে বিভাজ্য।   2. Find the remainder when $$7^{84}$$...

[caption id="attachment_5131" align="alignleft" width="191"]Dr. Eknath Prabhakar Ghate Dr. Eknath Prabhakar Ghate[/caption] Dr. Eknath Prabhakar Ghate, of the School of Mathematical Sciences, Tata Institute of Fundamental Research (TIFR) Mumbai has been selected for the prestigious Shanti Swarup Bhatnagar Prize for Science and Technology for the year 2013 in Mathematical Science category along with seven other scientists in various other disciplines. This year the other awardees include Dr Sathees Chukkurumbal Raghavan (Biological Sciences) from IISc Bangalore, Dr Yamuna Krishnan (Chemical Science) from Tata Institute of Fundamental Research (TIFR) Mumbai, Dr Bikramjit Basu from IISc and Dr Suman Chakraborty from IIT Kharagpur (both from Engineering Sciences), Dr Amol Dighe from TIFR and Dr Vijay Balakrishna Shenoy from IISc (Physical Science). There is no awardee this year in the Earth, Atmosphere, Ocean & Planetary Sciences category.