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

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Exercise

 "Success has many fathers, while failure is an orphan." - (Proverb)
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 b c d
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?
 4 m 6 m 7.5 m 36 m
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 b c d
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 b c d
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 b c d
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?
 5% 17% 20% 23%
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?
 1 : 2 2 : 3 3 : 4 4 : 5