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JEE Advanced Model Paper 1 with solutions for online practice
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© examsnet.com
Question : 60
Total: 60
Column - I
Column - II
A) The eccentricity of the ellipse which meets the straight line 2x -3 y = 6 on the X-axis and the straight 1 line 4x + 5y= 20 on the Y-axis and whose principal axes lie along the coordinate axes, is
p) 1/2
B) A bar of length 20 units moves with its ends on two fixed straight lines at right angles. A point P marked on the bar at a distance of 8 units from one end describes a conic whose eccentricity is
q) 1/
√
2
C) If one extremity of the minor axis of the ellipse
x
2
a
2
+
y
2
b
2
= 1and the foci form an equilateral triangle , then its eccentricity is
r)
√
5
/3
D) There are exactly two points on the ellipse
x
2
a
2
+
y
2
b
2
= 1 whose distance from the centre of the ellipse are greatest and equals to
√
a
2
+
2
b
2
2
Eccentricity of this ellipse is equal to
s)
√
7
/4
a - q ; b - r ; c - p ; d - s
a - r ; b - s ; c - p ; d - q
a - p ; b - r ; c - s ; d - q
a - s ; b - r ; c - p ; d - q
Validate
Solution:
(A)-S;(B)-R;(C)-P;(D)-Q
(A)
e
2
= 1 -
9
16
=
7
16
ellipse meets the x-axis at (3,0) and y -axis at (0,4)
(B) Locus is a ellipse (C) We have
b
a
e
=
√
3
⇒
a
2
(
1
−
e
2
)
= 3
a
2
e
2
(As
b
2
=
a
2
(
1
−
e
2
)
(D) The given distance is clearly the length for semi major axis
Thus ,
√
a
2
+
2
b
2
2
= a ⇒
2
b
2
=
a
2
⇒
2
a
2
(
1
−
e
2
)
=
a
2
⇒
e
2
=
1
2
⇒ e =
1
√
2
© examsnet.com
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