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"Saarang is here" 21st - 26th January 2004 For five days in January, IIT-M is identified as the venue of India's biggest cultural festival. Saarang, which since its genesis in 1974 (as Mardi-Gras), has become a symbol of youth, a symbol of this country's heritage (which is why it insists on being held on the Republic day every year) and its multifarious culture. The best talent in the country has succeeded, time and again, in sending hoards of people to an ineffable state of euphoria.

P R O G R A M M E -----------------

21st -- Inaugural and Classical Music Show.
22nd -- Light Music Show by Udit Narayan and his 21 member dance troupe. 23rd -- The Professional Rock Show by Mother Jane and Pin Drop Violence. 24th -- Western Music and Light Music(group) Final followed by Professional fashion Show by Provouge (tentative).
25th -- Choreo - Nite followed by the Saarang Main Quiz.
26th -- The most hyped pro-show ... named as the 'Unity Concert' .. Featuring string from Pakistan and Euphoria from India (please note that it's on the Republic Day) .. wait to watch it happen. Well other than these there are almost 25 events .. events of the highest quality and huge participation... For latest details/updates visit http://www.saarang.org. For a preview/schedule read 'Hindu' - Metro plus of January 5th - 2004.

### $f(x)=x^6+2x^4+x^3+2x+3 $$\mathop {\lim }\limits_{x \to 1} \frac{{{x^n}f(1) - f(x)}}{{x - 1}} = 44$$n=?$

Let $f(x)=x^6+2x^4+x^3+2x+3,x \in R$. Then the natural number n for which $\mathop {\lim }\limits_{x \to 1} \frac{{{x^n}f(1) - f(x)}}{{x - 1}} = 44$ is _ _ _ _ . Solution Since the limit has $\left[ {\frac{0}{0}} \right]$ form, L.H. Rule is applicable. Thus, $\mathop {\lim }\limits_{x \to 1} n{x^{n - 1}}f(1) - f'(x) = 44$ $\therefore nf(1) - f'(1) = 44$ $\therefore n.9 - ({6.1^5} + {8.1^3} + {3.1^2} + 2.1) = 44$ $\Rightarrow 9n - 19 = 44$ $\Rightarrow n=7$