Gate Exam

using the transformation x=r cosθ and y=r sinθ,find the singular solutionof the differential equation x+py=(x-y)(p2+1)½ where p=dy/dx

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Gate Other Question

(a-5)2+(b-c)2+(c-d)2+(b+c+d-9)2=0

then the value of (a+b+c)(b+c+d) is ?

a)0

b)11

c)33

d)99 A drawer holds 4 red hats & 4 blue hats.what is the probability of getting exactly three red hats or exactly three lue hats when taking out 4 hats randomly out of the drqwer & immediately returning every hat to the drawer before taking out the next?