1 .
Two houses are collinear with the base of a tower and are at distance 3 m and 12 m from the base of the tower. The angles of elevation from these two houses of the top of the tower are complementary. What is the height of the tower?
A.  4 m
B.  6 m
C.  7.5 m
D.  36 m
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2 .
A round balloon of unit radius subtends an angle of 90° at the eye of an observer standing at a point, say A. What is the distance of the centre of the balloon from the point A?
A.  $1\over \sqrt 2$
B.  $\sqrt 2$
C.  2
D.  $1 \over 2$
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3 .
If the area of a circle, inscribed in an equilateral triangle is 4$\pi$$cm^ 2$ , then what is the area of the triangle?
A.  12$\sqrt$$cm^2$
B.  9$\sqrt$$cm^2$
C.  8$\sqrt$$cm^2$
D.  18$cm^2$
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4 .
The difference between the area of a square and that of an equilateral triangle on the same base is $1/over4$ $cm^ 2$ . What is the length of side of triangle?
A.  $(4 - \sqrt 3)^{1 \over 2}$ cm
B.  $(4 + \sqrt 3)^{1 \over 2}$ cm
C.  $(4 - \sqrt 3)^{- 1 \over 2}$ cm
D.  $(4 + \sqrt 3)^{- 1 \over 2}$ cm
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5 .
If the diameter of a wire is decreased by 10%, by how much per cent (approximately) will the length be increased to keep the volume constant?
A.  5%
B.  17%
C.  20%
D.  23%
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6 .
A cone is inscribed in a hemisphere such that their bases are common. If C is the volume of the cone and H that of the hemisphere, then what is the value of C : H?
A.  1 : 2
B.  2 : 3
C.  3 : 4
D.  4 : 5
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7 .
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In the given triangle, AB is parallel to PQ. AP = c, PC= b,PQ = a, AB= x. What is the value of x?
A.  a + $ab \over c$
B.  a + $bc \over a$
C.  b + $ca \over b$
D.  a + $ac \over b$
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8 .
What is the number of points in the plane of a $\Delta$ABC which are at equal distance from the vertices of the triangle?
A.  0
B.  1
C.  2
D.  3
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9 .
An obtuse angle made by a side of a parallelogram PQRS with other pair of parallel sides is 150. If the perpendicular distance between these parallel sides (PQand SR) is 20 cm, what is the length of the side RQ?
A.  40 cm
B.  50 cm
C.  60 cm
D.  70 cm
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10 .
42 men take 25 days to dig a pond. If the pond would have to be dug in 14 days, then what is the number of men to be employed?
A.  67
B.  75
C.  81
D.  84
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