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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. ...

A bit easy QOD.... *Image* ...

*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 ...

A pirate has buried his treasure on an island with five trees located at the following points: A(30.0 m,20.0 m), B(60.0 m, 80.0 m), C (10.0 m, 10.0 m), D(40.0 m, 30.0 m), and E(70.0 m, 60.0 m). All points are measured relativ ...

really a good one *Image* ...

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 ...

Find ALL Polynomials satisfying [P(x)]2=1+xP(x+1) For beginners ; ...

Q. In a beaker with water a thin capillary tube of radius r is dipped. and a rod of radius r/2 is inserted symmetrically in between. Find the height of water that rises in the tube. *Image* ...

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 ...

*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 ...

we are given 201 different numbers such that sum of any 100 numbers is less than the sum of remaining 101 numbers. prove that all the numbers are positive . ...

a,b,c are positive reals with abc=1 Prove that (a+(1/b)-1)(b+(1/c)-1)(c+(1/a)-1)≤1 ...

There exists a sequence such that i)a1=a ii)a2=b and an+2=(an+1+an)/2 n≥0 ; Find limn->∞ an ...

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 ...

Let x be a real number, and let e > 0. Then there exist integers p and q > 0 such that |x-p/q| < e This might seem obvious! but try to prove this.. It is not very difficult either. ...

This is a googley from resnick and halliday.. Those who can will do it in a flash otherwise keep thinking for the whole day and you wont get it ;) Find the maximum heap (Height) that sand can make in a circle of radius of R. ...

You must have all seen the SHM case when we dig a tunnel accross the earth. Now the question is slightly different.. The earth is not fully solid.. There is a hole inside it Will it be a SHM. If yes what is the time period. T ...

Near Mid-Night question of the day [6] A wire shpaed as a semi circle of radius a rotates about axis OO' with an angular velocity ω in a uniform magnetic field of induction B. The rotation axis is perpendicular to the fi ...

Not the kind of convergence that appears in undergrad courses. So please dont be scared away. In fact if you apply your mind to this one, you may be rewarded. For every integer n \ge 0 , let S(n) = n - m^2 where m is the grea ...

*Image* a bob suspended ina trolley is displaced 45* and is released. what is the tension in the strind just after the bob is released?? what is the acceleration of the trolley just after the bob is released?? Asish has been ...

This one is a simple one for those who have appeared in IIT Already But for those thta havent, Try proving this one.. DOnt refer any text .. It is an easy but important concept. Must know. (Work done by all external forces is ...

Prove that the surface area of the sphere is indeed what we read in our childhood as 4Ï€R2 ...

This is a bit dirty but "standard" question if I could call it so You must have seen it many times find the sum of all 6 digit numbers that can be formed using 1,1, 3, 4, 6, 9 ...

A Sphere of mass M and radius R is compressed to a disc.. The radius of the disc remains the same as R.. Mass also falls down to the same level. .(means there is no sideways movement of mass during compression) What is the Mo ...

Two conducting spheres of radii r and 3r initially have charges 3q and q respectively. their separation is much larger than their radii. if they are joined by a conductor of high resistance, the force btween them at time T=t ...

Explain Searle's Method in detail I am pretty sure that a Question on this one is possible! ...

The other day we solved to find the no. of ways in wich a given no. can be expressed as a product of two nos!!! I wanted to know if v can hav such a generalization for expressing a no. as product of 3integers Note** It may be ...

Q1) Rate of Physisorbtion increases with A) Decrease in Temperature B) Inc in Temp C) Dec in pressure D) Dec in surface area Q2 Lyophilic sols are A) Irreversible sols B) Prepared from inorganic compounds C) coagulated by add ...

Question 1) p(x)= 51x101 - 2323 x100 - 45x +1035 Prove that atleast one root lies between (451/100, 46) Question 2) for -1≤p≤1, show that 4x3-3x-p=0 has a unique root in the interval [1/2, 1] and identify it. Question 3) ...

You might say why the QOD has become 5 questions a day! but its JEE season and we have to change ourselves in a similar way ;) Solve these: (Again a few of these are tough!) 1) for x>0, let f(x)=\int_{1}^{x}{\frac{ln t}{1+ ...