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1.
The vertices of a family of triangles have integer coordinates. If two of the vertices of all the triangles are (0, 0) and (6, 8), then the least value of areas of the triangles is
2.
In a 
is equal to
is equal to
3.
The intercepts on the straight line 
by the line 
and 
is less than 5, then 
belongs to
by the line and is less than 5, then belongs to
4.
In 
is equal to
is equal to
5.
The inradius of the triangle whose sides are 3, 5, 6 is
6.
In a 
, if the sides are 
and 
, then 
is equal to
, if the sides are and , then is equal to
7.
The elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be 
. After walking 120 m towards it on level ground the elevation is found to be 
. Then the height of the object (in metres) is
. After walking 120 m towards it on level ground the elevation is found to be . Then the height of the object (in metres) is
8.
If the area of the triangle with vertices 
and (0, 2) is 4 sq unit, then the value of 
is
and (0, 2) is 4 sq unit, then the value of is
9.
At a distance 12 metres from the foot 
of a tower 
of height 5 metres, a flagstaff 
on top of and the tower subtend the same angle. The, the height of flagstaff is
of a tower of height 5 metres, a flagstaff on top of and the tower subtend the same angle. The, the height of flagstaff is
10.
A tower 50 m high, stands on top of a mount, from a point on the ground the angles of elevation of the top and bottom of the tower are found to be 
and respectively. the height of the mount is
and respectively. the height of the mount is