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#1 Posted 2:12pm 20-01-10 nice one (but easy)Q1. If [im]http://codecogs.izyba.com/gif.latex?f%28x%29%20%3D%20x%5Cint_%7B0%7D%5E%7B1%7D%7Bf%28x%29%7Ddx%20+%20%5Cint_%7B0%7D%5E%7B2%7D%7Bf%28x%29%7Ddx-5[/im] , and the area of the region bounded by y= f(x) and y=(1-x) between x=0 and x=1 is A, then 2A equals _______ Q2. If [im]http://codecogs.izyba.com/gif.latex?f%28x%29%20%3D%20%5Cint%20x%5E%7Bx+1%7D%28logx+%28logx%29%5E2%29dx[/im] and f(1) = -1, then the value of [im]http://codecogs.izyba.com/gif.latex?%28%28e%5E%7B-e%7Df%28e%29+1%29e%5E%7B-1%7D%29[/im] is _______
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#2 Posted 2:27pm 20-01-10 Re: nice one (but easy)Ans 2) 1 |
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#3 Posted 2:29pm 20-01-10 Re: nice one (but easy)yes sir, could you just show how you solved the integral? I solved it by using hit n trial .. (time was short in hand)
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#4 Posted 2:36pm 20-01-10 Re: nice one (but easy)Q3. MULTI ANSWER CORRECT If a,b,c,d,c[ss]1[/ss],c[ss]2[/ss],c[ss]3[/ss]....,c[ss]n[/ss] are arbitrary constants, then the order of the differential equation whose solution is given by [im]http://codecogs.izyba.com/gif.latex?y%3D%20%28asin%28x+b%29%20+%20csin%28x+d%29%20+%20xtan%5E%7B-1%7D%28%5Cfrac%7Bc_%7B1%7D-c_%7B2%7D%7D%7B1+c_%7B1%7Dc_%7B2%7D%7D%29%20+%202xtan%5E%7B-1%7D%28%5Cfrac%7Bc_%7B2%7D-c_%7B3%7D%7D%7B1+c_%7B2%7Dc_%7B3%7D%7D%29%20+%20...%20+%20%28n-2%29xtan%5E%7B-1%7D%28%5Cfrac%7Bc_%7Bn-2%7D-c_%7Bn-1%7D%7D%7B1+c_%7Bn-1%7Dc_%7Bn-2%7D%7D%29%20+%20c_%7Bn%7De%5E%7Bx+c_%7Bn-1%7D%7D[/im] where n is a natural no. is (a) undefined (c) 3 (b) 2 (d) 4 Q4. MULTI ANSWER Let a[ss]1[/ss],a[ss]2[/ss],b[ss]1[/ss],b[ss]2[/ss],c[ss]1[/ss],c[ss]2[/ss] be selected from the set A= {1,2,3,.....,100}. If the roots of the equations a[ss]1[/ss]x[p]2[/p]+b[ss]1[/ss]x+c[ss]1[/ss] =0 and a[ss]2[/ss]x[p]2[/p]+b[ss]2[/ss]x+c[ss]2[/ss] =0 are x[ss]1[/ss], x[ss]2[/ss] and 2x[ss]1[/ss], 3x[ss]2[/ss] respectively, then the probability that (b[ss]1[/ss][p]2[/p]-4a[ss]1[/ss]c[ss]1[/ss])(b[ss]2[/ss][p]2[/p]-4a[ss]2[/ss]c[ss]2[/ss]) < 0 is always less than (a) 1/2 (b) 1/3 (c) 1/4 (d) 3/4
You dont walk to IIT, IIT walks 2 u!! Edited on 2:42pm 20-01-10 |
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#5 Posted 2:50pm 20-01-10 Re: nice one (but easy)hey in the first is it y=1-x or [b]y=f(1-x)[/b] ???
annoying precision |
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#6 Posted 2:52pm 20-01-10 Re: nice one (but easy)y=1-x
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#7 Posted 3:33pm 20-01-10 Re: nice one (but easy)Q1. Let [im]http://codecogs.izyba.com/gif.latex?%5Cint_0%5E1f%28x%29%5C%20%5Cmathrm%20dx%20%3Da[/im] and [im]http://codecogs.izyba.com/gif.latex?%5Cint_0%5E2f%28x%29%5C%20%5Cmathrm%20dx%20%3Db[/im] Then [im]http://codecogs.izyba.com/gif.latex?f%28x%29%3Dax+b-5[/im] Hence [im]http://codecogs.izyba.com/gif.latex?a%3D%5Cint_0%5E1f%28x%29%5C%20%5Cmathrm%20dx%20%3D%5Cint_0%5E1%28ax+b-5%29%5C%20%5Cmathrm%20dx%3D%5Cdfrac%7Ba%7D%7B2%7D+b-5[/im] which gives 2b - a = 10 --- (1) Again [im]http://codecogs.izyba.com/gif.latex?b%3D%5Cint_0%5E2f%28x%29%5C%20%5Cmathrm%20dx%20%3D%5Cint_0%5E2%28ax+b-5%29%5C%20%5Cmathrm%20dx%3D2a+2b-10[/im] which gives 2a +b =10 ---- (2) Solving for a and b gives a=2, b=6 Hence [im]http://codecogs.izyba.com/gif.latex?f%28x%29%3D2x+1[/im] Hence A = 3/2 and so 2A = 3 |
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#8 Posted 4:15pm 20-01-10 Re: nice one (but easy)Let [im]http://codecogs.izyba.com/gif.latex?g%28x%29%20%3D%20x%5Ex[/im] Then [im]http://codecogs.izyba.com/gif.latex?g%27%28x%29%20%3D%20x%5Ex%281+%5Clog%20x%29[/im] and [im]http://codecogs.izyba.com/gif.latex?%5Clog%20g%28x%29%20%3D%20x%20%5Clog%20x[/im] The integrand is [im]http://codecogs.izyba.com/gif.latex?x%5Ex%281+%5Clog%20x%29%20x%20%5Clog%20x%20%3D%20g%27%28x%29%20%5Clog%20g%28x%29[/im] Hence [im]http://codecogs.izyba.com/gif.latex?%5Cint%20x%5Ex%281+%5Clog%20x%29%20x%20%5Clog%20x%20%5C%20dx%20%3D%20%5Cint%20g%27%28x%29%20%5Clog%20g%28x%29%20%5Cdx%20%3D%20%5Cint%20%5Clog%20y%20%5C%20dy[/im] where [im]http://codecogs.izyba.com/gif.latex?y%20%3D%20%5Clog%20g%28x%29[/im] Hence the integral evaluates to [im]http://codecogs.izyba.com/gif.latex?g%28x%29%20%28%5Clog%20g%28x%29%20-1%29+C[/im] Then evaluate at x =e
Edited on 4:15pm 20-01-10 |
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#9 Posted 2:05pm 21-01-10 Re: nice one (but easy)thanks anant sir, and bhatt sir Q3,4 --> #4 Q5. Let [im]http://codecogs.izyba.com/gif.latex?%5Calpha%20%5E%7B2010%7D+%5Cbeta%20%5E%7B2010%7D[/im] can be expressed as a polynomial in [im]http://codecogs.izyba.com/gif.latex?%5Calpha%20+%5Cbeta[/im] and [im]http://codecogs.izyba.com/gif.latex?%5Calpha%20%5Cbeta[/im]. The sum of coefficients of the polynomial is ______
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#10 Posted 2:19pm 21-01-10 Re: nice one (but easy)http://targetiit.com/iit-jee-forum/posts/sum-of-coefficients-13190.html
bye~ |
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#11 Posted 2:22pm 21-01-10 Re: nice one (but easy)thx
You dont walk to IIT, IIT walks 2 u!! |
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#12 Posted 7:51pm 27-01-10 Re: nice one (but easy)Q3,4 unsolved [2]
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