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Consider two sets of distinct real numbers A and B such that A={A1,A2,...A100) B={B1,B2,....B50) Consider all kinds of onto mappings from set A to set B such that f(A1)≤f(A2)≤....f(A100) Find the number of such mappings. ...
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*Image* The figure shows a rope looped over two pipes A and B.If the coefficient of static friction is 0.25 in both the surfaces , determine smallest and largest values of m for which equillibrium is possible ...
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Let x,y>0 be real numbers and let s be the smallest of the numbers x,y+(1/x),1/y Find the greatest possible value of s . For which x,y is this value assumed? Again for beginners .. but experienced ones can answer if they w ...
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Find ALL Polynomials satisfying [P(x)]2=1+xP(x+1) For beginners ; ...
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*Image* Identical wires, each with resistance R, are connected so as to form the edges of the platonic solid Icosahedron.(The figure is given , additionally note that it is a polyhedron with 20 faces, each face an equilateral ...
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a,b,c are positive reals with abc=1 Prove that (a+(1/b)-1)(b+(1/c)-1)(c+(1/a)-1)≤1 ...
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Given a,b,c, are positive reals with abc=1 Prove that 1/a^3(b+c) + 1/b^3(a+c) + 1/c^3(a+b) \geq 3/2 ...
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1st - easy a,b,c All are real numbers such that a+b+c >0 ab+bc+ca >0 abc >0 Prove a,b,c are all >0 2nd - medium Find all functions f which follows the following equation - f(x)+f(1/(1-x))=x ...
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There exists a sequence such that i)a1=a ii)a2=b and an+2=(an+1+an)/2 n≥0 ; Find limn->∞ an ...
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A particle is initially situated at origin . It starts moving with a velocity v towards right .During motion a force F always acts on the body towards left . given coefficient of friction μ , find the time taken by particle ...
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Take a system of two conductors of any shape and size with charges Q1 and Q2 and potentials V1 and V2.Let q be the charge that would flow from the conductor when they are shorted.Prove that the quantity q/(V1-V2) is a constan ...
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let f be continuous for any x>1 and [] denoting the greatest integer function prove that \int_{1}^{x}(+1)f(u)du =2\sum_{i=1}^{[x]}{i\int_{i}^{x}{f(u)du}} ...
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*Image* given AB=L1 AO=L2 E is mid point of arc BAEC EO perpendicular to AC find OC .. a starter .. ...
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*Image* A charged particle (mass m) is hanging from a point and is just abocve the ground initially. Let the position of the charged particle now be G .. A man brings another charged particle from infinity to G along a straig ...
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a particle of mass m is give a certain velocity along a plane which is at angle θ to the horizontal. the velocit given is at a angle of β to the horizontal and the coefficitnet of friction is μ>tanθ hence as the partic ...
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what is the product formed in this reaction?? Na , Et2O 2 C2H5CN --------------------> product????? ...
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Let S be the set of all vertices of a unit cube.Let T be the set of the triangles having vertices in S then the number of equilateral , scalene, and isoceles triangles are ? PLz answer quickly i want to check my answers.. ...
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A quadratic equation with integral coefficients has two prime numbers as its roots. If the sum of the coefficients of the equation is prime then the sum of the roots is - ? Post the method also ...
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Prove rigorously that for an isoceles prism a ray of light falling on one side will suffer minimum deviation when angle of incidence= angle of emergence .. ...
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Prove that for any integer n n7+7 is not a perfect square i have proved it for all cases except for n of the form - 7k+1 plz help . ...
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*Image* An infinitely stretchable rubber band has one end nailed to a wall, while the other end is pulled away from the wall at the rate of 1 m/s; initially the band is 1 meter long. A bug on the rubber band, initially near t ...
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please dont get afraid by the size of the question beleive me it is easy (give it a thought cmon)!! *Image* ABOVE THE background neede to solve this one is given the two questions are given below *Image* i will tell the sourc ...
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a particle is approaching with a velocity of 5i^+3j^ and it returns after colliding with a velocity of -3i^+4j^ find the coefficient of restitution ...
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In triangle ABC, D is a point on AB and E is a point on AC such that BE and CD are bisectors of ∠B and ∠C respectively. Let Q,M and N be the feet of perpendiculars from the midpoint P of DE onto BC, AB and AC, respectivel ...
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One end of a spring of unstretched length L and force constant k is fixed to a pivot, and a body of mass m is attached to its other end The spring is released from an unstretched, horizontal position, as shown in figure What ...
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*Image* threads of lengths h1 ,h2 and h3 are fastened to the vertices of a homogenous triangular plate of weight W The other ends are fastened to a common point,as shown in the figure What is the tension in each thread, expre ...
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*Image* This is a really easy question if you can grasp the concept within A small hamster is put into a circular wheel-cage which has a frictionless central pivot,A horizontal platform is fixed to the wheel below the pivot.I ...
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find all functions f:R->R such that for all x,y belonging to - R f(f(x)+y)=f(x2-y) + 4yf(x) this has a two line answer!! ...
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Let p,q,r,be three prime numbers such that 5<=p<q<r and 2p2-r2>=49 2q2-r2<=193 find p, q ,r ...
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i have created a test paper but some of its answers need to be changed how can it be done? please answer quickly!! ...
