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#1 Posted 8:25pm 03-02-10 algebraQ1. The value of [im]http://codecogs.izyba.com/gif.latex?%5E%7B100%7DC_%7B0%7D%5C%3B%20%5E%7B200%7DC_%7B100%7D%20-%20%5E%7B100%7DC_%7B1%7D%5C%3B%20%5E%7B199%7DC_%7B100%7D%20+%20%5E%7B100%7DC_%7B2%7D%5C%3B%20%5E%7B198%7DC_%7B100%7D-%5E%7B100%7DC_%7B3%7D%5C%3B%20%5E%7B197%7DC_%7B100%7D+.......+%5E%7B100%7DC_%7B100%7D%5C%3B%20%5E%7B100%7DC_%7B100%7D[/im] Q2. If [im]http://codecogs.izyba.com/gif.latex?%5Cleft%7Caz+b%5Cbar%7Bz%7D+c%20%5Cright%7C%20%3D%20%5Calpha%20%5Cleft%7Ca%20%5Cright%7C%5Cleft%7Cz-z_%7B1%7D%20%5Cright%7C[/im] a≠0, a=[o]b[/o],c ε R, where z[ss]1[/ss] is a given non-zero complex number and α ε R[p]+[/p], then locus of z may be (a) Parabola (b) Ellipse (c) Hyperbola (d) Circle Q3. If z lies on the unit circle with centre at origin then the maximum value of [im]http://codecogs.izyba.com/gif.latex?I_%7Bm%7D%281-%5Cbar%7Bz%7D+z%5E2%29[/im] is
You dont walk to IIT, IIT walks 2 u!! Edited on 09:39am 04-02-10 |
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#2 Posted 10:34am 04-02-10 Re: algebra2) parabola ellipse hyperbola ?? since here a=[o]b[/o] so [im]http://codecogs.izyba.com/gif.latex?%5Cleft%7Ca%20%5Cright%7C%3D%5Cleft%7Cb%20%5Cright%7C%3D%5Cleft%7C%5Cbar%7Bb%7D%20%5Cright%7C%3D%5Cleft%7C%5Cbar%7Ba%7D%20%5Cright%7C[/im] and since the given eq is [im]http://codecogs.izyba.com/gif.latex?2%5Cleft%28%5Cfrac%7B%5Cleft%7C%5Cbar%7Bb%7Dz+b%5Cbar%7Bz%7D%20+c%5Cright%7C%7D%7B2%5Cleft%7Cb%20%5Cright%7C%7D%20%5Cright%29%3D%5Calpha%20%5Cleft%7Cz-z_%7B1%7D%20%5Cright%7C[/im] [im]http://codecogs.izyba.com/gif.latex?%5Cleft%28%5Cfrac%7B%5Cleft%7C%5Cbar%7Bb%7Dz+b%5Cbar%7Bz%7D%20+c%5Cright%7C%7D%7B2%5Cleft%7Cb%20%5Cright%7C%7D%20%5Cright%29[/im]=distance of z from line [im]http://codecogs.izyba.com/gif.latex?%5Cbar%7Bb%7Dz+b%5Cbar%7Bz%7D%20+c[/im] and [im]http://codecogs.izyba.com/gif.latex?%5Cleft%7Cz-z_%7B1%7D%20%5Cright%7C[/im] is distance of point z from z[ss]1[/ss] hence we can clearly see here [im]http://codecogs.izyba.com/gif.latex?%5Cfrac%7B2%7D%7B%5Calpha%20%7D[/im] is the eccentricity of conic and z[ss]1[/ss] is teh focus and [im]http://codecogs.izyba.com/gif.latex?\bar{b}z+b\bar{z}+c=0[/im] is the directrix now [im]http://codecogs.izyba.com/gif.latex?e%3D%5Cfrac%7B2%7D%7B%5Calpha%20%7D[/im] wen [im]http://codecogs.izyba.com/gif.latex?%5Calpha%20%3D2[/im] it is a parabola wen [im]http://codecogs.izyba.com/gif.latex?%5Calpha%20%3E2[/im] it is an ellipse wen [im]http://codecogs.izyba.com/gif.latex?%5Calpha%20%3C2[/im] it is a hyperbola
i m a guy who rules ma life according to my own wishes and i dun care a damm abt those nerdy insane creatures who hate me....A GPL to them from ma side....Goodbye. Edited on 11:07am 04-02-10 |
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#3 Posted 10:46am 04-02-10 Re: algebra3) put z=cosθ+isinθ then u hav to find max value of 2sin(3θ/2)cos(θ/2) i guess i m getting 1.76 something
i m a guy who rules ma life according to my own wishes and i dun care a damm abt those nerdy insane creatures who hate me....A GPL to them from ma side....Goodbye. Edited on 11:09am 04-02-10 |
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#4 Posted 11:01am 04-02-10 Re: algebraWhere are these qns from? BTW, I've just seen a beautiful soln to #1 on Mathlinks - http://www.mathlinks.ro/viewtopic.php?t=329319 Do read it. Someone's posted Q3 is disguised form asking what is max of sin θ + sin 2θ |
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#5 Posted 11:39am 04-02-10 Re: algebrayup i saw u posted der :P
i m a guy who rules ma life according to my own wishes and i dun care a damm abt those nerdy insane creatures who hate me....A GPL to them from ma side....Goodbye. |
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#6 Posted 1:13pm 04-02-10 Re: algebracheck this for another way for 1st q http://www.mathlinks.ro/viewtopic.php?p=1762870#1762870 it turns out to be Vandermonde's Convulution identity got to know abt it today only [3] [hide]btw this aint related to jee by miles[/hide]
i m a guy who rules ma life according to my own wishes and i dun care a damm abt those nerdy insane creatures who hate me....A GPL to them from ma side....Goodbye. |
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#7 Posted 4:46pm 04-02-10 Re: algebrathanks a lot prophet sir and che.. these were the unit test questions at aakash for another batch....(1 yr course)
You dont walk to IIT, IIT walks 2 u!! |
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#8 Posted 11:24am 05-02-10 Re: algebra[b]can someone solve [im]http://codecogs.izyba.com/gif.latex?sin%5Ctheta%20+sin2%5Ctheta[/im] with the help of Trigonometry[/b] |
