समय: तीन घंटा दिसम्बर 01, 2013 निर्देश: · किसी भी तरह कैलकुलेतर तथा चांदा (protractor) के उपयीग की अनुमति नहीं है। · पैमाना (ruler) तथा परकार (compass) उपयीग किये जा सकते हैं। · सभी प्रश्नों का उत्तर दीजिये। · सभी प्रश्नों के अंक समान हैं। अधिकतम अंक: 102 · प्रत्येक प्रश्न के...

[caption id="attachment_7349" align="alignleft" width="320"] Image Source : Shutterstock[/caption] The 2012 exam question papers of Mathematical Sciences, Assamese, English, Economics, Education, History, Philosophy, Political Science, Geography, Manipuri, Bodo, Bengali, Hindi, Anthropology, Sanskrit, Sociology, Commerce, Chemical Science, Life Science and Physical Science for SET conducted by SLET Commission, Assam...

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....