Indian Institute of Technology Kanpur (IIT-K) 2006 JT - Question Paper


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Q.107 A filter paper of the form of a right circular cone of base radius 20 cm and altitude 40 cm is placed
with its axis vertical and the vertex downwards. Water flows out at the rate of 22.5 cc. The rate at
which the level of the water falls when the depth of the water is 30 cm is
(A)
10p
1 (B)
100p
1 (C)
p
10 (D)
p
100
Solution 107; ' >" 
 F 
3
1 p1% 1 F1
F"-1
-
"+ 
"

F 
3
1 p
4
h3

 2"1
dt
h dh
dt
dV
4
3
3
1 2
= p 

 2
4
dt h
dV
dt
dh
p
= ´ 


p 10p
1
30 30
22.5 four =
´ ´
= ´
dt
dh

 2" "+ +
G
 = 
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Q.108 An antenna stands in the middle of a square tower. A man on the ground, opposite the middle of the
face of the tower and at a distance of 100 m from its foot, just sees the top of the antenna; on receding
a different 100 m, the tangents of elevation of the top of the tower and the antenna are obtained to be one and -
respectively. The ground being horizontal, the height of the antenna (in meters) is (neglect the height
of the person for computations)
(A)
9
1000 (B) 25 (C) 50 (D)
9
550
Solution 108 : Cq 



 
f 




C
B
D
A
M N
P
Q
R
f
q
100
M
100
M
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5
= tanf =
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9
5
200
100 =
+
+
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Q.109 An aeroplane flying horizontally one km above the ground is observed by a person on his right side at an
elevation of 600. If after 10 seconds the elevation is observed to be, from the identical point and in the
identical direction, 30°, the uniform speed per hour (in km) of the aeroplane is (neglect the height of the

Earning:   Approval pending.