I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2016. Subjective Problem no.1.
7 out of 10[/et_pb_accordion_item][et_pb_accordion_item title="Suggested Book" _builder_version="3.23.3" open="off"][/et_pb_accordion_item][/et_pb_accordion][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" custom_margin="48px||48px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]
we define a sequence \(p_1\)>\(p_2\)>\(p_3\)...........>\(p_n\) .such that \(p_i>p_{i+1}\) implies \(p_i\) has beaten \(p_{i+1}\)
[/et_pb_tab][et_pb_tab title="Hint 2" _builder_version="3.22.4"]let assume that the statement is true for n=k i.e \(p_1> p_2>p_3.........p_k\)now look into the case of \(p_{k+1}\)
[/et_pb_tab][et_pb_tab title="Hint 3" _builder_version="3.23.3"]if \(p_{k+1}\) > \(p_1\) or \(p_k\)>\(p_{k+1}\) we are done (why?)[/et_pb_tab][et_pb_tab title="Hint 4" _builder_version="3.22.4"] if \(p_k\)<\(p_{k+1}\) or \(p_{k+1}\)<\(p_1\) then we can find out at least one pair \(p_i\) >\(p_{i+1}\) such that \(p_i\)> \(p_{k+1}\) >\(p_{i+1}\) , we can just find it by shifting \(p_{k+1}\) term by term [ you can make some small experiment ].other wise it contradict our initial assumption that \(p_k\)<\(p_{k+1}\) or \(p_{k+1}\)<\(p_1\) [ why?] hence we are done
[/et_pb_tab][/et_pb_tabs][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" min_height="12px" custom_margin="50px||50px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.
The entrances to these programs are far more challenging than usual engineering entrances. Cheenta offers an intense, problem-driven program for these two entrances.
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Fakesolve. There is no guarantee that there is an i such that in the arrangement p_1>p_2>p_3>...>p_k such that p_i>p_k+1>p_i+1