Zoravar, Yatish, Xandra, Waheeda, Varun, Umesh, Tarun and Satish are 8 friends who are sitting in a circular dining table and all of them are facing the centre. Tarun is the immediate neighbor of Umesh. Yatish and Umesh are not immediate neighbours. Varun is 2nd to the left of Zoravar and his immediate neighbours are Tarun and Xandra. Zoravar and Waheeda are not immediate neighbours. Yatish is not seated between Satish and Waheeda. Satish is not seated between Waheeda and Umesh.
Who is opposite to Varun?
Answers
Given : Zoravar, Yatish, Xandra, Waheeda, Varun, Umesh, Tarun and Satish are 8 friends who are sitting in a circular dining table and all of them are facing the centre.
To Find : Who is opposite to Varun
Solution:
Tarun is the immediate neighbor of Umesh
two cases
Tarun Right of Umesh or Tarun Left of Umesh
Lets take case 1:
Tarun Left of Umesh
Varun is 2nd to the left of Zoravar and his immediate neighbours are Tarun and Xandra
Varun can be in Left of Tarun only as in right of Tarun is Umesh already
Hence Varun in 2nd to the left of Umesh
But Varun is 2nd to the left of Zoravar
Hence this case not possible
Lets take case 1:
Tarun Right of Umesh
Varun is 2nd to the left of Zoravar and his immediate neighbours are Tarun and Xandra
Hence Varun is also Right of Tarun as left of Tarun is already occupied
and Xandra if right of Varun
and Zoraver is right of Xandra
Now 3 Spaces left between Left of Umesh and Right of Zoraver
Yatish and Umesh are not immediate neighbours
Hence Yatish can be 1 or 2 right of Zorvaer or 2 or 3 left of Umesh
Zoravar and Waheeda are not immediate neighbours.
Hence Waheeda can be 2 or 3 right of Zorvaer or 1 or 2 left of Umesh
Yatish is not seated between Satish and Waheeda
Hene Yatish can not be 2 right of Zoraver or 2 left of Umesh.
Hence Yatish can be 1 right of Zorvaer
Satish is not seated between Waheeda and Umesh.
Hence Satish would be right of Yatish and and Waheeda will be right of Satish
X
Z V
Y T
S U
W
Hence Satish is opposite to Varun
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Answer:
Let us assume that 5 -√3 is rational.
Let ,
5 - √3 = r , where "r" is rational
5 - r = √3
Here,
LHS is purely rational.
But on the other hand ,RHS is irrational.
This leads to a contradiction.
Hence,5-√3 is irrational