1 .If 2x 2 cos 60º – 4 cot 2 45º – 2 tan 60º = 0, then what is the value of x?
A.2, B.3 , C.$\sqrt{3}$-1 , D.$\sqrt{3}$+1
A.  a
B.  b
C.  c
D.  d
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2 .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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3 .A round balloon of unit radius subtends an angle of 90º 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.$^1\over2$
A.  a
B.  b
C.  c
D.  d
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4 .If the area of a circle, inscribed in an equilateral triangle is 4pcm 2 , then what is the area of the triangle?
A.$12\sqrt{3}$ $cm^2$ , B. $9\sqrt{3}$ $cm^2$ , C. $8\sqrt{3}$ $cm^2$ , D. $18cm^2$
A.  a
B.  b
C.  c
D.  d
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5 .The difference between the area of a square and that of an equilateral triangle on the same base is 1/4 cm 2 . What is the length of side of triangle?
a.$\left(4-\sqrt{3}\right)$$^{1/2}$cm , b.$\left(4+\sqrt{3}\right)$$^{1/2}$cm
c.$\left(4-\sqrt{3}\right)$$^{-1/2}$cm , d.$\left(4+\sqrt{3}\right)$$^{+1/2}$cm
A.  a
B.  b
C.  c
D.  d
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6 .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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7 .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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8 .
A.  30º
B.  35º
C.  45º
D.  55º
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9 .
A.  a
B.  b
C.  c
D.  d
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10 .What is the number of points in the plane of a DABCwhich are at equal distance from the vertices of the triangle?
A.  0
B.  1
C.  2
D.  3
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