The math puzzle 18 collinear points and perpendicular lines.
1) A cylindrical pail having height 16 and radius of base 9 is filled with sand. This pail is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 18, what is the radius of its base?
A. 4√3 B. 9 C. 10 D. 12 E. 16
2) Among the following lines, which are perpendicular to each other?
I slope of lines are 3 and 3
II slope of lines are 3 and -3
III slope of lines are 3 and -1/3
IV slope of lines are 3 and 0
A. I only B. II only C. III only D. IV only E. None of these
3) If the points (2, - 5), (0, 3) and (-3, b) are collinear, what is b?
A. -15 B. -10 C. 5 D. 10 E. 15
4) 2 circles touch each other at one point. Diameter of the larger circle is 10 and smaller one is 6. What is the distance between the centers of the 2 circles?
A. 3 B. 5 C. 8 D. 16 E. None of these
5) A rectangle is turned 3600 about the long edge. What shape will get created?
A. Cone B. Pyramid C. Cylinder D. Triangular prism E. Hemisphere
6) One point moves about another point so that the distance between them remains constant. What geometric pattern gets created by this movement?
A. Square B. Equilateral Triangle C. Oval D. Rectangle E. Circle
7) If a paper cut in the shape of an isosceles right angle triangle is folded such that base angles and equal sides overlap, then the resulting triangle will be
A. Equilateral B. Isosceles C. Isosceles right angled D. Right angle E. Scalene
8) If eight equal cubes are stacked together such that they form shapes of regular solids, then the cubes could form the shapes of a
A. I only B. II only C. III only D. I and II only E. II and III only
9) Suppose births are equally likely on each of the seven days of the week. What is the probability that three persons selected at random are born on the same day of the week?
A. 1/4 B. 1/210 C. 1/343 D. 1/49 E. 1/7
10) Average of 5 numbers is 16. Sum of 3 numbers is 32. What are the possible values for the other 2 numbers?
I) 10, 14; II) 24, 24 III) 20, 28 IV) 30, 28 V) 29, 29
A. I only B. II and IV only C. III and V only D. II and III only
E. IV and V only