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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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PROVE THIS ENQUALITY..... 2n ≥ 1 + n 2(n-1)/2 ...
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In the plane there are n points such that of any 3 points always two points can be chosen such that their distance is less than 1. Prove that within these n points there are [n+1/2] which can be covered by a circular area wit ...
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try doing this if u ve free time 1) two mirrors are inclined at an angle θ find the no of images formed 2) a person enters a room with ceiling and 2 adjacent walls as mirrors . how many images can he see ? ...
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WHY THE MAGNETIC FIELD LINES IN A TOROID R CONFINED TO WITHIN IT's CORE...BUT NOT SO IN CASE OF SOLENOID.... ...
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suppose there are 997 points given in a plane. if every two points are joined by a line segment with its mid point coloured in red, show that there are atleast 1991 red points in the plane. can u find a special case with exac ...
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There are 2 players in this game. The first player starts, and only positive integers can be written down on a piece of paper. If the numbers a,b have been written on the piece of paper any number written after those two cann ...
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A town has several clubs. Given any two residents there is exactly one club that both belong to. Given any two clubs, there is exactly one resident who belongs to both. Each club has at least 3 members. At least one club has ...
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In the figure shown surface of massless pulley is smooth. The string is massless. The two blocks are placed on a smooth horizontal surface . A time varying force F=20t is applied. Considering the two blocks and the pulley and ...
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*Image* There is a water retaining wall with semi cylindrical gate(ABC) at its bottom of radius 'R' and length 'b'. If 'H' be the height of the structure and 'Ï' be the density of water.... Q1 :- The horizontal component of ...
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Find the moment of inertia of a cube of side a along its diagonal. ...
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Is there a sequence of positive integers in which every positive integer occurs exactly once and for every k = 1, 2, 3, . . . the sum of the first k terms is divisible by k? ...
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Let a and b be two positive integers such that for any positive integer n, an + n divides bn + n. Prove that a = b. ...
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Find all positive integral solutions (a,b,c) to the equation (a+1)(b+1)(c+1)=2(abc + 1) ...
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Twenty-one girls and twenty-one boys took part in a mathematics competition. It turned out that (i) each contestant solved at most six problems, and (ii) for each pair of a girl and a boy, there was at least one problem that ...
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In a society of n people, any two persons who do not know each other have exactly two common acquaintances, and any two persons who know each other don’t have other common acquaintances. Prove that in this society every per ...
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A device consists of 4n elements, any two of which are joined by either a red or a blue wire. The numbers of red and blue wires are the same. The device is disabled by removing two wires of the same color connecting four di e ...
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A rope of length L and mass M is being pulled on a rough horizontal floor by a constant horizantal force F=Mg.The force is acting at one nd of the rope in the same direction as the length of the rope .Te coefficient of kineti ...
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a pile of n pebbles is placed in a vertical coloumn. this configuration is modified according to the following rules. a pebble can be moved if it is at the top of the coloumn which contains atleast 2 more pebbles than the col ...
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sveral numbers are written in a row. in each move, john choses any 2 adjacent numbers in which one on the left is greater than one on the right, doubles each of them and switches around. prove that roberts cn make only a fini ...
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try to solve it in a elegant way..... A circular table is divided into five sectors. You can paint each sector with one of five colors. If more than one sector can be painted the same color, how many ways are there to paint t ...
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A spherical ball in hung in a string of length l and is kept in a car moving wid a velocity v. The car suddenly stops and the ball moves in a circular path. If T is the tension @ the highest pt. is twice the wt. of the ball, ...
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Let a,b,s be in A.P. and (b-c)x2+(c-a)x+(a-b)=0 and 2(a+c)x2+(b+c)x=0 have a common root then.... a) a2,b2,c2 are in G.P. b) a2,b2,c2 are in A.P. c) a2,c2,b2 are in A.P. d) a2,c2,b2 are in G.P. PLzzzzzz GIVE the FuLl SolUTiOn ...
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I am not posting for fun pls solve this .this is 2004 K-Cet exam question 0.573757375737........=??????? 1) 284/497 2)284/495 3)568/999 4)567/990 Please solve this and tell me any method behind this. ...
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Let a,b,c be three distinct positive numbers which are in G.P. If logca , logbc , logab are in A.P., then the common difference of the A.P. is.... REPLY SOON..... ...
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wat is iupac name of--- *Image* ...
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Find the coefficient of x49 in the polynomial (x - 1/1*3) (x - 2/1*3*5).....(x - 50/1*3*.....*101) a)1/2 - 1/1*3*....*101 b) -1/2(1 - 1/1*3*....*101) c) 49/1*3*....*101 d) 50/1*3*...*101 ANS :- (b) as per the book..... ...
