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SSC CGL Tier 1 Quantitative Aptitude Questions and Answers Online Test 3

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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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