CAT4MBA

Q1. How many small squares are crossed by the diagonal in a rectangular table formed by 16 x 17 small squares?
a. 32                      b. 33                 c. 34                     d. None of these

Q2. A right circular cone is cut(parallel to its base) into 5 slices, all of equal height. What is the ratio of the volume of the middle slice to that of the biggest slice?
a. 27: 125                b. 19: 61                 c. 37 : 91                   d. 4 : 25

Q3. A number N has 3 prime factors and 27 factors which are perfect cubes. If 125 of the factors of N are perfect squares, how many factors does N have?
a. 648                  b. 729                  c. 900                        d. 1000

Q4. In a cyclic quadrilateral ABCD, if AB = 2, BC = 3, CD = 4 and DA = 5, what is the ratio of the lengths of the diagonals?
a. 7 : 11                b. 11 : 13                  c. 10 : 11                  d. 13 : 15

Q5. What is the length of the side of a square inscribed in a regular hexagon of side 2?
a. √3 + 1            b. 6 - 2√3            c. √2 + √3                  d. 4 - √3

Q6. Find the maximum possible perimeter (in cm) of a rectangle of area 8√3 sq cm drawn inside an equilateral triangle of side 10 cm, where the vertices of the triangle lie on the triangle?
a. 8√3 + 4               b. 8√3 + 8            c. 16 + 2√3                  d. 12 + 4√3

Q7. A and B run a 10km race. In the first heat, A gives B a head start of 500 mts and beats him by 50 seconds. In the second heat, A gives B a head start of 80 seconds and is beaten by 100 mts. What is the ratio of speeds of A and B?
a. 24 : 36                    b. 35 : 24                c. 25 : 26               d. 34 : 22