Their reciprocals are in arithmetic progression when:











AM-GM gives



Thus ,

_________________

"Those things that hurt, instruct."

-- Ben Franklin

thanks sir

if a ,b ,c are in HP   then minimum value of (a+b)/(2a-b) +(c+b)/( 2c-b) is-------------

 

a,b,c are +ve numbers

thanks

99^50+100^50

or 101^50 which is greater

if two cards are drawn one

by one from apack of 52 cards find the no of ways in which cards

drawn if cards are drawn in definite order whats the significance of

definite order here

 

  6 person 1,2,3,4,5,6 are  to be seated at a circular table . the number of ways in which this can be done if 1 must       have either 2 or 3 on his right  & 2 must have 3 or 4 on his right ??

2) number of 4 digit numbeers that can be made with digits 1,2,3,4,5 in which atleast two digits are identical is

3)reg ular polygon of 10 sides is made. no of ways in which 3 verices r selcted such that 2 vertices  areconsecutive

thanks sir

Q2.The sides of a triangle are Ur=xcosAr+ysinAr -Pr=0 (r=1,2,3)

Show that orthocenter is given by U1cos (A2-A3)=U2COS(A3-A1)=U3 COS(A1-A2)

1,2 ,3 r all are subscripts

bansal notes question in my recent questions solve it

P is the point (-1,2). A variable line through P cuts the X and Y axis at A and B respectively.Q  is the point on AB such that PA ,PQ ,PB are in HP.show that locus of Q is line y=2x

 if a ,b ,c are in HP   then minimum value of (a+b)/(2a-b) +(c+b)/( 2c-b) is-------------

a,b,c are +ve numbers

The sides of a triangle are Ur=xcosA_r+ysinA_r -P_r=0  (r=1,2,3)















Show that orthocenter is given by U1cos (A₂-A₃)=U₂COS(A₃-A1)=U₃ COS(A₁-A₂₎

The third question has 3 answers:

Replacing x+y with a and xy with b.

Now, by eliminating b we get:

Now, by trial and error, we get a=2.

By using factor theorem we have (a-2) divides the previous equation. Solving it we get a quyadratic euation:

By applying quadratic formula we get 3 answers, namely

2,1+root6 and 1-root 6

How can we distribute 7 identical necklace in 5 women  such that each women gets atleast one necklace each .pl explain the solution

Q 1  .A music academy  has to send 10 members to 5 shows ,two in each show. two of the shows are in city and the 3 are outside .two of the five members prefer to work in city while  3 prefer to work  outside  city..the number of ways in which five shows can be held if preference are to be satisfied . 

options are 5200, 5400,5472,5250