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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 _______
sadly life is not masti in IITK with MTH 101 making first yr hell fr all freshers (no exception)... even got seniors repeating the course |
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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)
sadly life is not masti in IITK with MTH 101 making first yr hell fr all freshers (no exception)... even got seniors repeating the course |
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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
sadly life is not masti in IITK with MTH 101 making first yr hell fr all freshers (no exception)... even got seniors repeating the course 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] ???
Dont Mess With Che~! |
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#6 Posted 2:52pm 20-01-10 Re: nice one (but easy)y=1-x
sadly life is not masti in IITK with MTH 101 making first yr hell fr all freshers (no exception)... even got seniors repeating the course |
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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 ______
sadly life is not masti in IITK with MTH 101 making first yr hell fr all freshers (no exception)... even got seniors repeating the course |
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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 |
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#11 Posted 2:22pm 21-01-10 Re: nice one (but easy)thx
sadly life is not masti in IITK with MTH 101 making first yr hell fr all freshers (no exception)... even got seniors repeating the course |
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#12 Posted 7:51pm 27-01-10 Re: nice one (but easy)Q3,4 unsolved [2]
sadly life is not masti in IITK with MTH 101 making first yr hell fr all freshers (no exception)... even got seniors repeating the course |
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