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Question

The curve passes through (1,1) satisfies the differential equation
dydx+(11x2)(11y2)=0
If it passes through (2,k) then the possible value(s) of [k] is/are
(where [.] denote the greatest integer function)

A
1
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B
1
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C
2
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D
2
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Solution

The correct option is D 2
dydx+(11x2)(11y2)=0
dy(11y2)=(11x2)dx

Let y=secθ and x=secϕ
dy=secθtanθ dθ, dx=secϕtanϕ dϕ

sec2θ dθ=(sec2ϕ1)dϕ
Integrating both the sides
tanθ=tanϕ+ϕ+Cy21=x21+sec1x+C
It passes through (1,1) so,
C=0

Putting (2,k)
k21=1+π4k2=(π41)2+11<k2<2 [0<(π41)2<1][k]=1,2

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