NIMCET 2025 Paper

Section: Mathematics

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Question : 20 of 120

Marks: +1, -0

Let

F_1, F_2

be the foci of the hyperbola

\;{x^2}/{a^2}-\;{y^2}/{b^2}=1, \;\; a>0, b>0,

and let

O

be the origin. Let

M

be an arbitrary point on curve

C

and above the x -axis, and

H

be a point on

M F_1

such that

\M\F_2 \⟂ \F_1\F_2

,

M\F_1 \⟂ \OH_{\;\text ", "\;}

\|OH|=λ{|OF_2|}

with

λ ∈ (\;{2}/{5}, \;{3}/{5})

.
Then the range of the eccentricity

e

is:

$({√{3}}, 2)$
$({√{2}}, {√{3}})$
$(1, √{\;{7}/{3}})$
$(√{\;{7}/{3}}, 2)$

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