CAREER POINT
PRACTICE WORKJEE (Mains)SUB : MATH
HEIGHT & DISTANCES
1.Two towns A and B are 60 km apart. A school is to be built to
serve 150 students in town A and 50 students in town B. If the
total distance to be traveled by all 200 students is to be as small
as possible, then the school should be built at [IIT- 1982]
(a) town B
(b) 45 km form town A
(c) town A
(d) 45 km from town B
2.From the top of light-house 60m high with its base at
sea-level, the angle of depression of a boat is 150. The distance
of the boat from the foot of the light-house is
[IIT- 1983]
(a)
(b)
(c)
(d) None of these
3.A pole stands vertically inside a triangular park ABC. If the
angle of elevation of the top of the pole from each corner of the
park is same, then in (ABC the foot of the pole is at the
[IIT- 2000]
(a) centroid
(b) circumcentre
(c) incentre
(d) orthocenter
4.A man from the top of a 100 m high tower sees a car moving
towards the tower at an angle of depression of 300. After some
time, the angle of depression becomes 600. The distance (in metres)
traveled by the car during this time is
[IIT- 2001]
(a) 100
(b) 200/3
(c) 100/3
(d) 200
5.The upper (3/4)th portion of a vertical pole subtends an angle
(3/5) at a point in the horizontal plane through its foot and at a
distance 40 m from the foot. A possible height of the vertical pole
is [AIEEE- 2001]
(a) 20 m (b) 40 m (c) 60 m (d) 80 m6.A person standing on the
bank of a river, observes that the angle of elevation of the top of
a tree on the opposite bank of the river is 600 and when he retires
40 m away from the tree the angle of elevation becomes 300. The
breadth of the river is
[AIEEE- 2004]
(a) 20 m (b) 30 m (c) 40 m (d) 60 m
7.A tower stands at a centre of a circular park. A and B are two
points on the boundary of the park such that AB(=a) subtends and
angle of 600 at the foot of the tower and the angle of elevation of
the top of the tower from A or B is 300. The height of the tower
is
[AIEEE- 2004]
(a) 2a/
(b) 2a
(c) a/
(d)
8.AB is a vertical pole with B at the ground level and A at the
top. A man finds that the angle of elevation of the point A from a
certain point C on the ground is 600. He moves away from the pole
along the line BC to a point D such that CD = 7 m. From D the angle
of elevation of the point A is 450. Then the height of the pole
is
[AIEEE- 2004]
(a) (b)
(c)
(d)
9. A bird is sitting on the top of a vertical pole 20 m high and
its elevation from a point O on the ground is 45. It flies off
horizontally straight away from the point O. After one second, the
elevation of the bird from O is reduced to 30. Then the speed (in
m/s) of the bird is [JEE MAINS-2014] (a)
(b)
(c)
(d)
Mahaveer Classes , Chaitanya Nagar, Ganesh Colony, Jalgaon (MH)
Phone - 0257-2254545
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