Elementary Mathematics Quiz - Competitive Exams CDS

Free practice quiz: Elementary Mathematics (Competitive Exams CDS). 66 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This Competitive Exams CDS practice quiz has 66 multiple-choice questions on Elementary Mathematics. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. What is the value of the determinant of the matrix [[2, 3], [4, 5]]?

   1. 10
   2. -2
   3. 2
   4. -10
   Show answer

   Answer: B. -2

2. If log₁₀ 2 = 0.3010, then the number of digits in 2^64 is:

   1. 21
   2. 19
   3. 20
   4. 22
   Show answer

   Answer: C. 20

3. What is the remainder when 7^100 is divided by 5?

   1. 3
   2. 1
   3. 4
   4. 2
   Show answer

   Answer: B. 1

4. If A can complete a task in 9 days and B in 18 days, and they work together, in how many days will the task be completed?

   1. 4.5 days
   2. 7 days
   3. 6 days
   4. 5 days
   Show answer

   Answer: C. 6 days

5. What is the value of the derivative of x³ at x = 5?

   1. 75
   2. 15
   3. 25
   4. 125
   Show answer

   Answer: A. 75

More questions in this quiz

Answers and explanations are in the full quiz.

1. If a sum of money doubles itself in 8 years at simple interest, what is the annual rate of interest?
2. A train running at the speed of 72 km/h crosses a pole in 15 seconds. What is the length of the train?
3. The average of first 20 natural numbers is:
4. What is the value of sin 30° + cos 60°?
5. A shopkeeper marks an item at 40% above cost price and gives a discount of 25%. What is his profit percentage?
6. If x + 1/x = 5, find the value of x^3 + 1/x^3.
7. Two pipes can fill a tank in 12 and 15 hours respectively. If both are opened together, how long will it take to fill the tank?
8. The compound interest on Rs. 8000 at 10% per annum for 2 years, compounded annually, is:
9. If the diagonal of a square is 10√2 cm, what is its area?
10. In how many ways can the letters of the word 'LEADER' be arranged?
11. A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in 6.5 hours. What is the speed of the current?
12. The sum of the squares of two positive integers is 100, and the difference of their squares is 28. What is the product of the two integers?
13. A cone, a hemisphere, and a cylinder have equal bases and equal heights. What is the ratio of their volumes?
14. The number of real roots of the equation x^3 - 3x + 1 = 0 is:
15. What is the probability of getting a sum of 9 from two throws of a dice?
16. The angle of elevation of the top of a tower from a point on the ground is 30°. On walking 40 m towards the tower, the angle of elevation becomes 60°. What is the height of the tower?
17. What is the value of (1 + cot²θ)(1 - cos²θ)?
18. The roots of the quadratic equation x² - 5x + 6 = 0 are:
19. If the sum of an infinite geometric series is 12 and the first term is 8, what is the common ratio?
20. The area of a triangle with sides 7 cm, 8 cm, and 9 cm is:
21. If a : b = 2 : 3 and b : c = 4 : 5, what is a : c?
22. Find the coordinates of the point which divides the line segment joining A(1, 2) and B(4, 5) internally in the ratio 2:1.
23. If sinθ + cosθ = √2, what is the value of tanθ + cotθ?
24. If 2^(x-3) = 32, what is the value of x?
25. The value of (256)^(0.16) × (256)^(0.09) is:
26. What is the smallest number that must be subtracted from 2000 so that the resulting number is exactly divisible by 17?
27. The LCM of two numbers is 48 and their HCF is 4. If one number is 12, what is the other number?
28. If a sum of money at compound interest amounts to Rs. 2420 in 2 years and Rs. 2662 in 3 years, what is the rate of interest per annum?
29. The present ages of A and B are in the ratio 4:5. After 6 years, the ratio becomes 11:13. What is A's present age?
30. If the price of sugar increases by 25%, by what percentage should a family reduce its consumption so that the expenditure remains the same?
31. The difference between the simple interest and compound interest on a sum for 2 years at 10% per annum is Rs. 20. What is the principal?
32. What is the value of 1² + 2² + 3² + ... + 20²?
33. If the sum of the first n natural numbers is 210, what is the value of n?
34. How many numbers between 100 and 500 are exactly divisible by 11?
35. If the simple interest on a certain sum for 3 years at 8% per annum is Rs. 1440, what is the principal?
36. What is the value of (0.08 × 0.08 × 0.08) - (0.02 × 0.02 × 0.02)?
37. A clock shows 3:00. What is the angle between the hour hand and the minute hand?
38. If the equations 2x + 3y = 7 and kx + 9y = 21 have infinitely many solutions, what is the value of k?
39. The median of the observations 8, 12, 15, 7, 10, 20 is:
40. What is the 7th term of the arithmetic progression 3, 7, 11, ...?
41. If the polynomial x³ - 6x² + 11x - 6 is divided by (x - 1), what is the quotient?
42. What is the value of i^2025 + i^2025, where i = √(-1)?
43. If A = {1,2,3} and B = {3,4}, what is the number of elements in the power set of A ∩ B?
44. In a right triangle, one acute angle is 36°. What is the measure of the other acute angle in radians?
45. The length of the tangent from a point 10 cm away from the centre of a circle of radius 6 cm is:
46. If the volume of a sphere is numerically equal to its surface area, what is its radius?
47. What is the perpendicular distance from the point (3, 4) to the line 3x + 4y - 10 = 0?
48. If the slope of a line passing through (2, 3) and (k, 7) is 2, what is the value of k?
49. If ∫ from 0 to 2 of (3x²) dx equals K, what is K?
50. What is the value of 8! / (6! × 2!)?
51. A bag contains 4 red and 6 blue balls. Two balls are drawn without replacement. What is the probability both are red?
52. If the standard deviation of a data set is 5, what is the variance?
53. The mean of five numbers is 18. If one number is excluded, the mean becomes 16. What is the excluded number?
54. What is the value of the sum: 1/2 + 1/6 + 1/12 + 1/20 + 1/30?
55. If a number is increased by 20% and then decreased by 20%, what is the net change?
56. A man rows downstream at 10 km/h and upstream at 6 km/h. What is the speed of the stream?
57. If log₂ x + log₂ (x - 2) = 3, what is the value of x?
58. What is the value of cos 0° × sec 0° × tan 0°?
59. The value of (1 + tan²θ) / (1 + cot²θ) is equal to:
60. In how many ways can 3 boys and 2 girls be seated in a row so that the girls occupy the end positions?

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