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let f:R\rightarrow R and f(x+y)=f(x)+f(y) for all x,y\epsilon R f(x) is continuous at x=0 find f(x)........[JEE 1981] ...
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If (1+x)^{n}=C_{0}+C_{1}x+C_{2}x^{2}+.......C_{n}x^{n} then prove that \sum_{0\leq i}^{}{\sum_{<j\leq n }^{}{}}C_{i}C_{j}(i+j)=n(2^{2n-1}-\frac{1}{2}. ^{2n}C_{n}) ...
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my aieee AIR is 6504 and state rank is 124. can i get Mech. in NIT-surathkal? ...
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does IIST allow its students to pursue higher studies (M.Tech and Ph.D) immidiately after B.Tech?? ...
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all surfaces are frictionless. three cylinders are placed as shown in the diagram. find the least angle θ that prevents the arrangement from collapsing 1. tan-11/2 2.tan-11/2√3 3.tan-11/3√3 4.tan-11/4√3 *Image* this is ...
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i have got 3410 rank. cud someone tell me the branches available to me. ...
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a strip of metal of resistance R, length l and width d, is kept in a uniform magnetic field B. it is connected to an external source of potential and a current i flows through it. find the potential difference between A and B ...
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solve the equation 1 - x + x(x-1)/1.2 - x(x-1)(x-2)/1.2.3 + ...... +(-1)nx(x-1)(x-2)....(x-n+1)/n! = 0 putting x=n in the equation, it becomes nC0-nC1+nC2.........+ (-1)n nCn = 0 so x=n is a solution. how can we say that no o ...
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(12x-1)(6x-1)(4x-1)(3x-1)=5 SOLVE ...
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1! + 2! + 3! ............. + n! = k! where kεI+ find all solutions ...
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Two cylinders one heavy and the other light of diameters D and d respectively rest on a horizontal plane. the larger cylinder has a string wound around it to which a horizontal force F is applied. the co-eff. of friction is Î ...
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can anyone suggest me which text book i should for organic. i am very weak in it. ...
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A square of n units by n units is divided into n2 squares of 1 sq. unit each. find the number of ways in which 4 points ( out of (n+1)2 points) be selected so that they form the vertices of a square. i was able to count the n ...
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*Image* if all surfaces are frictionless, and the edge of the floor has sufficient friction for the rod to rotate about it, find the minimum distance d for the rod to topple. (length of the rod is l) i am getting d≥(l/2) pl ...
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a particle moves in the xy plane with velocity v= ai + bxj a and b being constants. at t=0 particle was at (0,0).. find (a) the equation of the particles trajectory (b) the curvature radius as a function of x ...
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two point charges are kept in space. they exert force on each other the magnitude and direction given by coulomb's law. now, if an infinitely large metallic plate of considerable thickness is placed between the charges, do th ...
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can anyone suggest me which test series to take. ...
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*Image* the direction of current induced in the circular loop if an electron moves in the indicated direction is 1. clockwise 2. antticlockwise 3. no current is induced 4. direction of current varies with time ...
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could somebody explain the effect of addition of inert gas to a system in equilibrium under different conditions???? ...
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if n positive terms are multiplied together the probabilities that the last digit are *Image* ...
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