CAT4MBA

Q1. A spherical glass ornament of radius 10 cm has a cube manufactured inside it. What is the volume of the largest cube that can fit inside the ornament?
a. (8000  - √ 3)/9
b. (8000 + √ 3)/9
c. (6000 √ 3)/9
d. (8000 √ 3)/9

Q2. A square is inscribed inside of a circle. The area of the square is what percent of the area of the circle (to the nearest tenth of a percent)?
a. 63.7%
b, 31.8%
c. 15.9%
d. 40.6%
e. 50%

Q3. If altitude PS meets the circumcircle of triangle PQR at T and H is the orthocenter, then what is the length of the line segment HT? (Given that angle RUP is same as angle PSQ is 90 degree)

a. 4cm
b. 5cm
c. 6cm
d. 8cm

Q4. The end points of a diameter of a circle are (3, 9) and (11, 3). A triangle inscribed in this circle has two of its vertices at the given points. Find the coordinates of all points at which the third vertex of the triangle can be located for this triangle to have its
maximum possible area.
a. (4, 2) , (10, 10)
b. (5, 3), (8, 8)
c. (5, 5), (8, 8)
d. (5, 5), (8, 10)

Q5. How many circular pipes with inside diameter of 1 inch will carry the same
amount of water as a pipe with an inside diameter of 6 inches?
a. 3
b. 6
c. 12
d. 36
e. 48

Q6. A regular polygon has sum of its interior angles less than 1800 degree. Each of its exterior angles is less than 36 degree. The number of sides in the polygon equals
a. 11
b. 12
c. 13
d. Cannot be determined

Q7. Circle O is circumscribed about ΔABC , where the length of AB is 5 cm, the length of BC is 5 cm, and the length of AC is 6 cm. Find the length of the radius of circle O.

a. 3.225
b. 3.125
c. 4.33
d. 2.875