Bangladesh Civil Service Preliminary Examination · Mathematical Reasoning and Mental Ability

Geometry, Mensuration and Mental Ability

35 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 35 questions

  1. Two angles are complementary, and their degree measures are in the ratio 2 : 3. What is the degree measure of the larger angle?
  2. An angle measures such that its supplementary angle is four times its complementary angle. What is the measure of this angle in degrees?
  3. The three interior angles of a triangle are in the ratio 3 : 4 : 5. What is the degree measure of the largest interior angle?
  4. What is the degree measure of each exterior angle of a regular octagon (an 8-sided regular polygon)?
  5. What is the sum of all interior angles of a convex hexagon (a 6-sided polygon)?
  6. A right-angled triangle has perpendicular legs measuring 9 cm and 12 cm. What is the length of its hypotenuse?
  7. Calculate the area of an equilateral triangle whose side length measures 6 cm.
  8. Find the area of a circle with radius 7 cm. (Take pi = 22/7)
  9. A sector of a circle of radius 6 cm subtends a central angle of 60 degrees. What is the area of this sector in terms of pi?
  10. An arc of a circle of radius 14 cm subtends a central angle of 90 degrees. What is the length of this arc? (Take pi = 22/7)
  11. In a cyclic quadrilateral ABCD, angle A measures 85 degrees. What is the degree measure of the opposite angle C?
  12. A tangent line segment is drawn from an external point P to a circle of radius 5 cm. If point P is 13 cm away from the circle center O, what is the length of the tangent segment?
  13. An arc subtends a central angle of 110 degrees at the center of a circle. What is the angle subtended by the same arc at any point on the remaining circumference?
  14. The perimeter of a rectangle is 40 cm, and its length is three times its breadth. What is the area of the rectangle?
  15. The diagonals of a rhombus measure 16 cm and 12 cm. What is the area of the rhombus?
  16. The parallel sides of a trapezoid measure 10 cm and 16 cm, and the perpendicular height between them is 8 cm. What is the area of the trapezoid?
  17. A solid rectangular block of wood has dimensions 5 cm by 8 cm by 10 cm. What is the total volume of the block?
  18. What is the volume of a right circular cylinder with radius 7 cm and height 10 cm? (Take pi = 22/7)
  19. Calculate the volume of a right circular cone having base radius 6 cm and vertical height 7 cm. (Take pi = 22/7)
  20. What is the total surface area of a solid sphere of radius 3.5 cm? (Take pi = 22/7)
  21. In how many distinct ways can 5 candidates be seated in a row of 5 adjacent chairs?
  22. In how many distinct ways can 5 committee members sit around a circular conference table?
  23. How many distinct committees of 3 members can be selected from a pool of 7 qualified candidates?
  24. How many distinct word permutations can be formed using all the letters in the word BANANA?
  25. A standard fair six-sided die is rolled once. What is the probability of rolling a prime number?
  26. Two fair coins are flipped simultaneously. What is the probability of obtaining at least one Head?
  27. What is the probability of drawing an Ace from a thoroughly shuffled standard deck of 52 playing cards?
  28. An urn contains 4 red marbles and 6 blue marbles. If two marbles are drawn one after another with replacement, what is the probability that both marbles drawn are blue?
  29. Find the next number in the numerical sequence: 2, 5, 10, 17, 26, ...
  30. What is the next number in the geometric progression: 3, 6, 12, 24, 48, ...?
  31. What is the 8th term in the standard Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, ...?
  32. Complete the letter sequence by identifying the next letter: B, E, H, K, N, ...
  33. A surveyor walks 10 meters directly North, turns 90 degrees East, and walks 24 meters. What is the shortest straight-line distance from the starting position to the final point?
  34. What is the acute angle formed between the hour hand and the minute hand of an analog clock at exactly 4:20?
  35. If 'All cats are felines' and 'All felines are mammals', which logical conclusion is strictly valid by classical deductive syllogism?

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