300+ Top Maths GK Questions and Answers MCQs Quiz

Maths General Knowledge Questions

1. Who invented the discovery of calculus and binomial theorem?

  1. Diophantus
  2. Ada Lovelace
  3. Archimedes
  4. Issac Newton

Answer: D Issac Newton

Explanation: In the late 17th century, the English Mathematician Isaac Newton discovered calculus. They also invented differential and integral calculus.

2. Which of the following English Mathematicians is considered to be the world’s first computer programmer?

  1. Gottfried Wilhelm Leibniz
  2. Issac Newton
  3. Ada Lovelace
  4. Archimedes

Answer: C Ada Lovelace

Explanation: Ada Lovelace, a Mathematician, and writer from England, is often considered the world’s first computer programmer. She worked on Charles Babbage’s planned mechanical general-purpose computer, the Analytical Engine, in the nineteenth century.

3. Who is the Father of Geometry?

  1. Euclid
  2. Pythagoras
  3. Archimedes
  4. Aristotle

Answer: A Euclid

Explanation: Euclid, an ancient Greek Mathematician is considered the Father of Geometry. He is well known for his book “Elements,” which was a thorough collection of geometric knowledge at the time.

4. Amongst which of the following is considered the origin of the calculator?

  1. Abacus
  2. Derivative
  3. Stepped Reckoner
  4. Curta Calculator

Answer: A Abacus

Explanation: The abacus is the first calculating device; dating back thousands of years. It was commonly used to execute fundamental Mathematical operations like addition, subtraction, multiplication, and division. The abacus is made up of beads or counters strung on rods, and its design allowed for quick and accurate calculations.

5. Amongst which of the following is the smallest perfect number?

  1. 5
  2. 10
  3. 1
  4. 6

Answer: D 6

Explanation: A perfect number is a positive integer whose total of appropriate divisors (excluding it) is equal to one. The proper divisors of the number 6 are 1, 2, and 3, and their sum is 1 + 2 + 3 = 6, making it a perfect number.

6. Who is the Founder of Trigonometry?

  1. Hipparchus
  2. Aryabhata
  3. Pythagoras
  4. Aristotle

Answer: A Hipparchus

Explanation: Hipparchus was recognized as the Founder of Trigonometry. He was an ancient Greek astronomer and Mathematician who flourished between 190 and 120 BCE. Hipparchus invented trigonometry to overcome problems of celestial navigation and the motion of celestial bodies. He constructed a chord table, which is considered one of the earliest trigonometric tables.

7. Who discovered the square root of numbers?

  1. Ptolemy
  2. Eratosthenes
  3. Hero of Alexandria
  4. Xenocrates

Answer: C Hero of Alexandria

Explanation: Hero of Alexandria, also known as Heron, was a Greek Mathematician who developed different Mathematical principles, notably the square root of numbers. He published “Metrica,” a treatise in which he elaborated methods to find the square roots of whole integers and fractions.

8. What is the formula to find out the diagonal of a square?

  1. A√4
  2. √A
  3. A√2
  4. 4√4

Answer: C A√2

Explanation: The diagonal of a square is equal to 2 times the length of its side (also known as its “A” side length), A√2.

As a result, the correct formula is A√2.

9. 0 is considered as ____number?

  1. Even number
  2. Odd number
  3. Both A and B
  4. None of the above

Answer: A Even number

Explanation:

The number 0 is considered an even number. Even numbers are integers that are exactly divisible by 2 and got 0 remainder. For example – 0 divided by 2 = 0, which fits the definition of an even number.

10. A palindromic number is a number that is the same when written ____.

  1. Forwards or backward
  2. 1 and 2
  3. 10 and 20
  4. None of these

Answer: A Forwards or backward

Explanation: A palindromic number is a number that is the same when written forwards or backward. Ex – 66, 101, 111, 121

11. What is Pythagoras’ constant?

  1. The square root of 3
  2. The square root of 2
  3. Cube root of 100
  4. None of the above

Answer: B The square root of 2

Explanation: The Pythagorean constant is defined as the square root of 2 (1.41421356237). The Pythagorean constant is used to calculate the length of a right triangle’s hypotenuse or one of its other sides.

12. Who was the first Mathematician to determine the circumference of the Earth?

  1. Luca Pacioli
  2. John Napier
  3. Omar Khayyam
  4. Eratosthenes

Answer: D Eratosthenes

Explanation:

Eratosthenes, an ancient Greek Mathematician, geographer, and astronomer, was the first to measure the Earth’s circumference with considerable accuracy. Based on his measurements and computations, Eratosthenes estimated the Earth’s diameter to be roughly 39,375 kilometers (24,662 miles), which is very close to the real amount.

13. Who is often considered as the ‘Father of Indian Statistics’?

  1. Ashutosh Mukherjee
  2. C.R. Rao
  3. Prasanta Chandra Mahalanobis
  4. Srinivasa Ramanujan

Answer: C Prasanta Chandra Mahalanobis

Explanation: P.C. Mahalanobis was known as the “Father of Indian Statistics.” Mahalanobis was best known for creating the Mahalanobis distance, a statistical measure commonly used in multivariate research.

14. Amongst which of the following symbol is known as the product symbol?

  1. E

Answer: A

Explanation: In Mathematics, the sign “∏” is referred to as the product symbol. It is the sum of a series of numbers or phrases. For example, if we have a sequence of numbers s1, s2, s3, n, the product of these numbers can be expressed as ∏ (si).

15. ∵ represents ____ in Mathematics?

  1. Therefore
  2. Since
  3. Because
  4. Implies

Answer: C Because

Explanation: In Mathematical reasoning, the sign “∵” is used to denote “because.” It is frequently used to indicate the explanation or reasons for a particular statement or conclusion. When you encounter the symbol “∵” in a Mathematical argument or proof, it signifies that the assertion that comes after it is a result or consequence of the information that came before it.

16. Amongst which of the following is the typical sign used to indicate the end of a proof?

  1. □ (a small square)
  2. ⊓ (double up tack)
  3. ► (right-pointing triangle)
  4. All of the above

Answer: D All of the above

Explanation: All of the following symbols are routinely used to signal the end of a proof:

  • □ (a small square): This is a conventional and well-known symbol for indicating the end of a proof.
  • ⊓ (double up tack): Though less prevalent, it is yet employed as an “end of proof” symbol by some authors.
  • ► (right-pointing triangle): This sign is used to indicate the end of a proof on occasion.

Different authors or Mathematical communities may prefer different symbols to mark the end of a Mathematical proof, but all of the options given are viable choices.

17. 2 + 5 + 8 + 11 + 14 … is an example of which of the following series?

  1. Harmonic series
  2. Arithmetic series
  3. Convergent series
  4. Geometric series

Answer: B Arithmetic series

Explanation: An example of an arithmetic series is 2 + 5 + 8 + 11 + 14… Each term in an arithmetic series is created by adding a constant value (common difference) to the preceding term. The common difference between consecutive phrases in this situation is 3 because each term is created by adding 3 to the previous term.

18. In which of the following type of series sum grows indefinitely as the number of terms rises?

  1. Geometric series
  2. Alternating series
  3. Divergent series
  4. Convergent series

Answer: C Divergent series

Explanation: The sum of a divergent series expands indefinitely as the number of terms increases. In other words, as more terms are added to a divergent series, the total of the terms does not approach a finite number; instead, it becomes indefinitely huge.

The harmonic series is an example of a divergent series:

1 + 1/2 + 1/3 + 1/4 + 1/5 +

19. 1 + 2 + 4 + 8 + 16 + is an example of which of the following types of series?

  1. Harmonic series
  2. Convergent series
  3. Arithmetic series
  4. Geometric series

Answer: D Geometric series

Explanation: A geometric series is represented by the series 1 + 2 + 4 + 8 + 16 + … Each term in a geometric series is obtained by multiplying the previous term by a constant value known as the common ratio. The common ratio between consecutive phrases in this situation is 2 because each term is created by multiplying the previous term by 2.

1 × 2 = 2
2 × 2 = 4
4 × 2 = 8
8 × 2 = 16 and so on.

20. What will be the sum of the following series?

  1. -1
  2. 1
  3. 0
  4. Infinity

Answer: B 1

Explanation: The given series is a geometric series, and the sum of the terms can be calculated using the formula:

Sum = a / (1 – r), where ‘a’ is the first term, and ‘r’ is the common ratio.

In the series, a=1/2, r =1/2 < 1 and sum =

[Image: math gk q image 2]

Therefore, sum = 1.

21. The series is called as ____ if the common exponent is a positive real constant number.

  1. Alternating series
  2. P series
  3. Convergent series
  4. All of the above

Answer: B P series

Explanation: A “P series” is one in which the common exponent is a positive real constant number. The terms in a P series take the form: 1/np, where “n” is a positive integer and “p” is a positive real constant number.

The series 1/1p + 1/2p + 1/3p + 1/4p +… is an example of a P series.

22. Is 1 a prime number?

  1. True
  2. False
  3. Can’t say
  4. No option

Answer: B False

Explanation: The number 1 is not considered as a prime number.

23. Amongst which of the following types of series appears in nature?

  1. Fibonacci series
  2. Palindromic series
  3. Harmonic series
  4. Divergent series

Answer: A Fibonacci series

Explanation: The Fibonacci sequence can be found in nature. It is a number sequence in which each number is the sum of the two preceding numbers. The series begins with 0 and 1 and proceeds by adding the previous two numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,
The Fibonacci sequence can be found in many areas of nature, such as the arrangement of leaves on a stem, the distribution of seeds in a sunflower, rabbit breeding patterns, and so on.

24. Amongst which of the following is the smallest composite number?

  1. 1
  2. 2
  3. 4
  4. -4

Answer: C 4

Explanation: A composite number is a positive integer bigger than one with more than two positive divisors (that is, it is divided by more than simply 1 and itself). In the case of 4, the divisors are 1, 2, and 4, resulting in a composite number.

25. Between 90 and 100, which number is considered as a prime?

  1. 91
  2. 93
  3. 97
  4. All of the above

Answer: C 97

Explanation: Only 97 are considered as a prime number. A prime number is a natural number that is divisible by 1 and itself. 97 is only divisible by 1 and 97, which indicates that it is a prime number.

26. Between 70 and 90 which of the following numbers are considered as prime?

  1. 71, 73, 72, 79, 83, 87, 89
  2. 71, 73, 79, 87, 89
  3. 71, 73, 79, 89
  4. 71, 73, 79, 83, 89

Answer: D 71, 73, 79, 83, 89

Explanation: The prime numbers between 70 and 90 are as follows: 71, 73, 79, 83, and 89.

27. Which of the following is considered a composite number from the given numbers: 17, 47, 49, 27, 79, 80, 71, 83, 89, and 79?

  1. 49, 27, 80
  2. 83, 27, 49, 80
  3. 49, 27, 83, 80, 79
  4. None of the above

Answer: A 49, 27, 80

Explanation: The composite numbers from the given numbers are: 49, 27, and 80.

28. What is the 11th prime number?

  1. 23
  2. 29
  3. 31
  4. 37

Answer: C 31

Explanation: The initial prime numbers are as follows: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31 is the eleventh prime number.

29. Fill in the blank: Prime numbers are always ____.

  1. Positive
  2. Negative
  3. Both
  4. None

Answer: A Positive

Explanation: Prime numbers are natural numbers higher than one that have no positive divisors other than one and themselves. They are always positive integers. Negative integers are not considered prime numbers.

30. A number divided by zero is referred as ____ number.

  1. Negative
  2. Irrational
  3. Undefined
  4. Real

Answer: C Undefined

Explanation: A number divided by zero is referred as an “undefined” number. In Mathematics, division by zero is not defined, and attempting to do so yields an indeterminate result. For example, “5 divided by 0” is undefined and cannot be represented by any real integer.

31. Which of the following is a correct formula to calculate simple interest?

  1. Simple Interest = (Principal x Rate x Time) / 100
  2. Simple Interest= (Profit / Cost price) x 100
  3. Simple Interest= Principal + Interest
  4. Simple Interest = (Principal x Rate x Time) + 100

Answer: A Simple Interest = (Principal x Rate x Time) / 100

Explanation: The correct formula is: Simple Interest = (Principal x Rate x Time) / 100,

Where,

  • The principal is the original amount borrowed or invested.
  • The annual interest rate (expressed as a percentage) is known as the rate.
  • Time is the duration (in years) for which money is borrowed or invested.

32. What is the formula to find the volume of a cone?

  1. (1 / 3 )πr2h
  2. (1 / 3 )πrh
  3. (1 / 3 )πr1/2h
  4. (1 / 3 )π2r2h

Answer: A (1 / 3 )πr2h

Explanation: Volume = (1/3)πr2h is the formula for calculating the volume of a cone.

Where,

  • r is the radius of the cone’s circular base.
  • The height of the cone is given by h.
  • A cone’s volume is one-third that of a cylinder with the same base and height.

33. The most often occurring value in a data set is known as ____.

  1. Mean
  2. Median
  3. Mode
  4. None of the above

Answer: C Mode

Explanation: The most often occurring value in a data set is referred to as the “Mode.” The mode in statistics is a value that appears the most frequently in a particular set of data. Depending on the frequency of occurrence of values, a data set can have one mode (unimodal), two modes (bimodal), or more (multimodal).

34. tan(90 Degrees – A) is equal to ____ ?

  1. Cosec A
  2. Cot A
  3. Tan A
  4. Sec A

Answer: B Cot A

Explanation: tan(90° – A) = cot(A).

The tangent of the complementary angle (90° – A) equals the cotangent of angle A.

35. What is the value of sin² θ + cos² θ?

  1. 1
  2. 1-cos² θ
  3. Sin θ * cosec θ
  4. Infinity

Answer: A 1

Explanation: The sum of sin2 θ and cos2 θ is equal to one. This identity is true for all trigonometric angles. It demonstrates the basic link between the sine and cosine functions in a right triangle.

36. Rahul’s net sales in the preceding quarter were Rs 100,000, and he spent a total of Rs 75,000 on various expenses. What will be Rahul’s total profit margin?

  1. 20%
  2. 10%
  3. 25%
  4. 50%

Answer: C 25%

Explanation: We can use the following calculation to get Rahul’s overall profit margin:

Profit Margin = (Net Profit / Net Sales) * 100

And, Net Profit = Net Sales – Total Expenses

Net Profit = 100,000 – 75,000 = 25,000

Now, we can calculate the profit margin:

Profit Margin = (25,000 / 100,000) * 100 = 25%

Rahul’s entire profit margin is thus 25%.

37. What is the derivative of f(x) = 100?

  1. 1
  2. Infinity
  3. -Infinity
  4. 0

Answer: D 0

Explanation: A constant function’s derivative, such as f(x) = 100, is always zero.

If f(x) is a constant (a fixed value that does not change with regard to x), then its derivative with respect to x is: f'(x) = 0

As a result, when f(x) = 100, the derivative f'(x) is 0.

38. In a ____ triangle, the sides are all measured differently?

  1. Isosceles Triangle
  2. Equilateral Triangle
  3. Scalene Triangle
  4. Obtuse Triangle

Answer: C Scalene Triangle

Explanation:

All three sides of a scalene triangle are in different lengths. It is a triangle with no sides of equal length and no angles of equal measure. An isosceles triangle has two equal-length sides, an equilateral triangle has three equal-length sides, and an obtuse triangle has one angle greater than 90 degrees.

39. What is the sum of the interior angles of a triangle?

  1. 360 Degrees
  2. 180 Degrees
  3. 90 Degrees
  4. 0 Degree

Answer: B 180 Degrees

Explanation: The sum of a triangle’s interior angles is always 180 degrees.
This trait applies to all triangles, regardless of size or shape. The sum of the triangle’s three internal angles is always 180 degrees, whether the triangle is equilateral, isosceles, scalene, acute, right-angled, or obtuse.

40. In a triangle, the sum of the interior and exterior angles is ____?

  1. Supplementary
  2. Complimentary
  3. Vertical
  4. None of the above

Answer: A Supplementary

Explanation: The sum of the interior angles and the sum of the exterior angles of a triangle are additional to each other. This means that the sum of the interior angles plus the sum of the exterior angles equals 180 degrees.

41. What is the area of an isosceles triangle?

  1. Area= Base* height2
  2. Area= Base* √3*height
  3. Area= (Base * height )/2
  4. Area= √3/4 height

Answer: C Area= (Base * height )/2

Explanation: To compute the area of an isosceles triangle, use the formula: Area = (base * height) / 2

Where,

  • The base is the length of the base of the isosceles triangle.
  • The height is the perpendicular distance from the base to the opposite vertex.

42. Amongst which of the following statement is True about the Transitivity property of a triangle?

  1. The transitivity property states that A triangle () is similar to itself.
  2. Transitivity property states that: If △ ABC ∼ △ DEF, Then △ DEF ∼ △ ABC
  3. Transitivity property states that: If△ ABC ∼△ DEF and△ DEF ∼△ XYZ, then △ ABC ∼△ XYZ
  4. All of the above

Answer: C Transitivity property states that: If△ ABC ∼△ DEF and△ DEF ∼△ XYZ, then △ ABC ∼△ XYZ

Explanation: According to the Transitivity property of triangle similarity, if two triangles are similar to one another and one of them is similar to a third triangle, then the first triangle is also similar to the third triangle.

43. How many types of Triangles are there?

  1. 4
  2. 5
  3. 6
  4. 7

Answer: D 7

Explanation: There are seven types of triangles, based on different criteria and properties: equilateral, right isosceles, obtuse isosceles, obtuse scalene, acute isosceles, right scalene, and acute scalene.

44. How do you calculate the sum of the measure of the interior angles of a triangle?

  1. (n+2)/180
  2. (n-2)*180
  3. (n+2)*180
  4. (n*2)*180

Answer: B (n-2)*180

Explanation: The correct formula for calculating the sum of the internal angles of a triangle is:

Interior Angle Sum = (n – 2) * 180 degrees

Where “n” is the number of sides (or vertices) of the polygon, and “n” is 3 for a triangle.

45. Who developed the infinity symbol?

  1. John Wallis
  2. Issac Newton
  3. Aryabhata
  4. Aristotle

Answer: A John Wallis

Explanation: English Mathematician John Wallis is credited with popularizing the infinity symbol () in its contemporary form in the 17th century. In his work “Arithmetica Infinitorum” published in 1655, he utilized the sign to depict the concept of infinity.

46. What is the square root of 256?

  1. 17
  2. 16
  3. 26
  4. 15

Answer: B 16

Explanation: 256’s square root is 16.

A number’s square root is a value that, when multiplied by itself, yields the original number. Because 16 * 16 = 256 in this situation, the square roots of 256 are 16.

47. ____ is the distance calculated across the center between any two places on the circumference.

  1. Radius
  2. Circumference
  3. Area
  4. Diameter

Answer: D Diameter

Explanation: The diameter of a circle is the distance measured across its center between two points on its perimeter. It is the circle’s longest chord, passing through the center and dividing it into two equal halves. The radius is twice as long as the diameter.

48. The ellipse has ____ axis?

  1. 5
  2. 4
  3. 3
  4. 2

Answer: D 2

Explanation: There are two axes in an ellipse:

  • Major Axis: The ellipse’s longest diameter, which runs through the center and has, ends on the ellipse’s farthest points.
  • Minor Axis: The ellipse’s shortest diameter, which runs through the center, and its ends are located on the ellipse’s narrowest points.

49. What is the area of the ellipse?

  1. πr1r2
  2. πr1+r2
  3. πr1-r2
  4. πr1/r2

Answer: A πr1r2

Explanation: The formula for calculating the area of an ellipse is: Area = π * r1 * r2

Where:

  • The length of the semi-major axis (half of the major axis) is denoted by r1.
  • The length of the semi-minor axis (half of the minor axis) is given by r2.
  • (pi) is a Mathematical constant that is roughly equivalent to 3.14159.

50. How do you calculate the percentage change?

  1. PercentChange = (NewValue) OldValue x 100
  2. PercentChange = (OldValue + NewValue) OldValue x 100
  3. PercentChange = ((NewValue – OldValue) / OldValue) x 100
  4. PercentChange = (OldValue – NewValue) NewValue x 100

Answer: C PercentChange = ((NewValue – OldValue) / OldValue) x 100

Explanation:

To compute the percentage difference between an old and new value use the following formula: ((NewValue – OldValue) / OldValue) 100

Where:

  • OldValue represents the initial or “before” value.
  • The ultimate value, or “after” value, is NewValue.
  • This formula computes the percentage difference between the old and new values. The outcome specifies whether the change is positive or negative, and by how much.

51. What is the LCM of 12 and 20?

  1. 120
  2. 80
  3. 60
  4. 100

Answer: C 60

Explanation: The explanation is:

  • The prime factors of 12 are 22 and 3 (since 12 = 2 * 2 * 3).
  • The prime factors of 20 are 22 and 5(since 20 = 2 * 2 * 5).
  • Now, taking the greatest possible power of each prime factor from both numbers, in this case, 22,31,51
  • Multiply all the highest powers together to get the LCM.
  • LCM = 22 * 31 * 51 = 4 * 3 * 5 = 60
  • Therefore, the LCM of 12 and 20 is 60.

52. What is the HCF of 18 and 28?

  1. 8
  2. 10
  3. 2
  4. 6

Answer: D 6

Explanation: The explanation is:

  • 18 has two prime factors: 21 and 32 (since 18 = 2 * 3 * 3).
    28 have two prime factors: 22 and 71 (since 28 = 2 * 2 * 7).
  • Now, from both numbers, take the least power of each prime factor.
    The smallest power of 2 is 21.
    The smallest power of 3 is 31.
    There is no common prime factor of 7 in both numbers.
  • To calculate the HCF, multiply all of the common prime factors together.
    HCF = 2^1 * 3^1 = 2 * 3 = 6

Therefore, the HCF of 18 and 28 is 6.

53. HCF of 25 and 5 is 5, find their LCM?

  1. 25
  2. 5
  3. 10
  4. 15

Answer: A 25

Explanation: LCM = (Number 1 * Number 2) / HCF

If the HCF of 25 and 5 is 5, then their LCM can be found as follows:

LCM (25, 5) = (25 * 5) / 5 = 125 / 5 = 25

Therefore, the LCM of 25 and 5 is 25.

54. Which of the following formulas will be used to compute the downstream speed if the boat’s speed in still water is u km/hr and the speed of the stream is v km/hr?

  1. (u- v) Km/hr
  2. (u+v) Km/hr
  3. u/v Km/hr
  4. u*v Km/hr

Answer: B (u+v) Km/hr

Explanation: The downstream speed of a boat is calculated by adding the boat’s speed in still water (u km/hr) and the speed of the stream (v km/hr). The stream contributes to the boat’s speed as it proceeds downstream (in the same direction as the stream), resulting in a quicker downstream speed. As a result, the right formula for calculating downstream speed is (u + v) km/hr.

55. What is the formula to find the sum of an arithmetic progression’s first n terms?

  1. (Sn) = (n/2) * [2a + (n+1)d]
  2. (Sn) = (n/2) +[2a + (n-1)d]
  3. (Sn) = (n*2) * [2a + (n-1)d]
  4. (Sn) = (n/2) * [2a + (n-1)d]

Answer: D (Sn) = (n/2) * [2a + (n-1)d]

Explanation: The following formula can be used to calculate the sum of the first n terms of an arithmetic progression (AP):

Sum of first n terms (Sn) = (n/2) * [2a + (n-1)d]

Where:

  • Sn is the sum of the arithmetic progression’s first n terms.
  • n is the number of terms in the progression.
  • a is the first term of the progression.
  • d is the common difference between consecutive terms.

56. If two triangles are similar, their side ratios are equal. True or False?

  1. True
  2. False
  3. N/A
  4. N/A

Answer: A True

Explanation: When two triangles are comparable, their respective sides have the same ratio. This signifies that the lengths of the corresponding sides of the two triangles have the same ratio. If triangles ABC and DEF seem alike, then: BC/EF = AC/DF = AB/DE.

57. What is the sum of the opposite angles of a cyclic quadrilateral?

  1. 360 Degrees
  2. 180 Degrees
  3. 260 Degrees
  4. 120 Degrees

Answer: B 180 Degrees

Explanation: The sum of the opposite angles in a cyclic quadrilateral is always equal to 180 degrees. Each opposite-angle pair in a cyclic quadrilateral is supplementary, which means they sum up to 180 degrees.

58. Complete the sentence. All right angles are ____.

  1. Incongruent
  2. Congruent
  3. Lateral
  4. None of the above

Answer: B Congruent

Explanation: “All right angles are congruent.”

A right angle is one that is exactly 90 degrees in length. All right angles in geometry are congruent, which means they have the same measure of 90 degrees.

59. Complete the sentence. A ____ is a straight line that intersects only one point on a circle.

  1. Arc
  2. Segment
  3. Chord
  4. Tangent

Answer: D Tangent

Explanation: A tangent is defined as “a straight line that intersects only one point on a circle.” A tangent is a line that intersects a circle at exactly one point without crossing it. At the point of tangency, the tangent line is perpendicular to the radius of the circle.

60. Which of the following shapes will have the shortest perimeter if their areas are the same?

  1. Triangle
  2. Polygon
  3. Circle
  4. Square

Answer: C Circle

Explanation: If the areas of the various forms are the same, the circle has the shortest perimeter of the options given.

61. Euler’s formulas work on which of the following shapes?

  1. Polyhedron
  2. Sphere
  3. Cylinder
  4. Cone

Answer: A Polyhedron

Explanation: Euler’s formula is a fundamental concept in geometry that relates the number of vertices (V), edges (E), and faces (F) of a polyhedron (a three-dimensional geometric structure with flat faces). According to Euler’s formula, V – E + F = 2.

62. What is the surface area of a cube?

  1. Surface_area=6*A
  2. Surface_area=6*A2
  3. Surface_area=6*A3
  4. Surface_area=3*A2

Answer: B Surface_area=6*A2

Explanation: All six faces of a cube are equal squares, and each face has an area of A * A = A2. Because a cube has six faces, its total surface area (SA) equals the sum of the areas of all six faces, as given by: Surface_area = 6 * A2

63. What is the value of the following mathematical expression?

  1. 1
  2. 0
  3. e^x
  4. Infinity

Answer: C e^x

Explanation: The exponential function’s derivative with respect to x is simply the exponential function itself, which is ex. As a result,

[Image: math gk q image 3(a)]

64. What will be the area of a parallelogram, if base = 17 and height = 13?

  1. 30
  2. 14
  3. 1.30
  4. 221

Answer: D 221

Explanation: A parallelogram’s area can be computed using the formula: Area = Base * Height. The base of a parallelogram is either of its sides, and the height is the perpendicular distance between the base and the opposite side. Area = 17 * 13 = 221 square units

65. What is the largest two-digit prime number?

  1. 89
  2. 99
  3. 97
  4. 93

Answer: C 97

Explanation: 97 is the greatest two-digit prime number. The Prime numbers are those that are greater than one and have no divisors other than one and themselves. The greatest prime number among the provided alternatives is 97.

66. What is the smallest co-prime number?

  1. 0
  2. 1
  3. 2
  4. 3

Answer: B 1

Explanation: If two integers have the same greatest common divisor (GCD), they are said to be co-prime (or substantially prime). The number 1 is co-prime with any other positive integer because its only positive divisor is 1, and it has no other common divisors with other positive integers.

67. What is a Central Angle Formula?

  1. Central Angle Measure = (Arc Length / Radius) * 180°
  2. Central Angle Measure = (Arc Length + Radius) * 180°
  3. Central Angle Measure = (Arc Length – Radius) / 180°
  4. Central Angle Measure = (Arc Length * Radius) * 180°

Answer: A Central Angle Measure = (Arc Length / Radius) * 180°

Explanation: The central angle formula is used to compute the size of a circle’s central angle. A central angle is an angle whose vertex is at the middle of a circle and whose sides are two circle radii.

The formula for calculating the size of a central angle is: Central Angle Measure = (Arc Length / Radius) * 180°

68. In the Venn diagram, what does a rectangle is used to represent?

  1. Universal set
  2. Subset
  3. Minor Set
  4. None of the above

Answer: A Universal set

Explanation: The rectangle represents the universal set in a Venn diagram. The universal set is the set that includes all of the elements in a given context or problem.

69. How do you represent the null set?

  1. []
  2. ()
  3. All of the above

Answer: C

Explanation: The symbol (∅) represents the null set, also known as the empty set. This sign, which differs from the symbols used to represent other sets, indicates that the set has no elements.

70. A set that contains only one element is called a ____ set.

  1. Monoset
  2. Independent set
  3. Unidirectional set
  4. Singleton set

Answer: D Singleton set

Explanation: A singleton set is a set that has only one element. The term “singleton” refers to a set that has only one member or element. There is just one unique element in a singleton set, and no other elements are present.

71. How do you write 90 in a Roman number?

  1. C
  2. CX
  3. XC
  4. XXC

Answer: C XC

Explanation: 90 is written as XC in Roman numerals. The Roman numeral system represents different numbers by combining letters from the Latin alphabet. In this system, X symbolizes ten and C represents one hundred. To express 90, we use a subtractive notation using X (10) and C (100), with X (10) positioned before C (100) to signify 100 – 10 = 90. As a result, the Roman numeral for 90 is XC.

72. How do you write 500 in Roman numbers?

  1. CCC
  2. K
  3. CCCC
  4. D

Answer: D D

Explanation: 500 is written as D in Roman numerals. The Roman numeral system represents distinct numbers by using letters from the Latin alphabet. D symbolizes 500 in this system. So D is the Roman numeral for 500.

73. If U= {1, 2,8, 9}, A = {1, 2, 3, 4} and B = {2, 4, 6, 8} then find A complement?

  1. {1,2}
  2. {2}
  3. {8,9}
  4. {3,4}

Answer: C {8,9}

Explanation: The complement of a set A, denoted by A’ in set theory, it is the set of all items in the universal set U that are not in A. To discover A’, we must first determine which items in the universal set U are not in A. A’ = {8, 9}

74. Which of the following is the correct representation of an idempotent theorem in sets?

  1. A ∩ A = A
  2. A ∩ U = A
  3. A ∩ B = B ∩ A
  4. A ∩ ϕ = ϕ

Answer: A A ∩ A = A

Explanation: Set theory’s idempotent theorem asserts that the intersection of a set with itself is the set itself. It is written as follows in Mathematical notation: A ∩ A = A

That is, any element that appears in both A and A is simply an element of A.

75. Amongst which of the following is the largest two-digit perfect square number?

  1. 99
  2. 90
  3. 88
  4. 81

Answer: D 81

Explanation: The largest two-digit perfect square number is 81, which is the square of 9.

76. Who is the father of Indian Mathematics?

  1. Srinivasa Ramanujan
  2. Aryabhata
  3. Brahmagupta
  4. C.R. Rao

Answer: B Aryabhata

Explanation: Aryabhata was a Mathematician and astronomer from ancient India. He is known as the “Father of Indian Mathematics” due to his tremendous contributions to the area.

77. Evaluate 4 + 5 * 2 – 3?

  1. 10
  2. 3
  3. 6
  4. 11

Answer: D 11

Explanation: We will use BODMAS to conduct the following operations in the following order:

5 * 2 = 10 in division and multiplication.

Subtraction and addition: 4 + 10 – 3 = 11.

As a result, the expression’s unique sum is 11.

78. Find the midpoint of a line whose endpoints are (10, 15) and (9, 8)?

  1. 5.5
  2. 8.5
  3. 9.5
  4. 10.5

Answer: C 9.5

Explanation: The midpoint formula can be used to locate the midpoint of a line segment with provided endpoints (x1, y1) and (x2, y2).

((x1 + x2) / 2, (y1 + y2) / 2) is the midpoint.

The provided endpoints are (10, 15) and (9, 8).

((10 + 9) / 2, (15 + 8) / 2) is the midpoint.

(19 / 2, 23 / 2) = midpoint

The midpoint is (9.5, 11.5).

79. What is a diagonal formula of a rectangle?

  1. D²= √(L²+W²)
  2. D²=L²*W²
  3. D²=L²+W²
  4. D²=L²/W²

Answer: A D²= √(L²+W²)

Explanation: The diagonal formula of a rectangle can be determined using the Pythagorean theorem, which connects the sides of a right triangle to the length and width of the rectangle as “L” and “W”, respectively. The Pythagorean theorem can be used to compute the diagonal “D” as follows:

D² = L² + W²

To calculate the length of the diagonal “D,” multiply both sides of the equation by the square root:

D = √(L² + W²)

80. What is the length of a diagonal of a cube?

  1. 3√A
  2. 2√3A
  3. √3A
  4. √6A

Answer: C √3A

Explanation: All sides of a cube are the same length. Let “a” represent the length of one side of the cube. A cube’s diagonal runs through its center and joins two opposite corners. Within the cube, this diagonal creates the hypotenuse of a right triangle.

The diagonal “D” can be determined using the Pythagorean theorem as follows:

D² = a² + a² + a²

D² = 3a²

Taking both sides square roots:

D = √(3a²) D = √3a

81. An Euler’s number ‘e’ is approximately equal to?

  1. 3.4182
  2. 3.114
  3. 2.718
  4. 3.418

Answer: C 2.718

Explanation: The number “e,” often known as Euler’s number, is a significant Mathematical constant with an estimated value of 2.71828. It is the natural logarithm’s base and has numerous uses in Mathematics, science, and engineering.

82. What is the square root of 144?

  1. 12
  2. 13
  3. 14
  4. 9

Answer: A 12

Explanation: When you square a number, you get the original number when you multiply it by itself. Finding the square root of 144 in this context implies finding a number that, when multiplied by it, equals 144. Because 12 * 12 = 144, that number is 12. As a result, the square root of 144 is 12.

83. What is the formula to find the area of a circle?

  1. Area = π * r
  2. Area = π + r3
  3. Area = r²
  4. Area = π * r²

Answer: D Area = π * r²

Explanation: The formula for calculating the area of a circle is: Area = π * r²

Where “Area” is the circle’s area.

  • (pi) is a Mathematical constant with an approximate value of 3.14159.
  • r is the radius of the circle, which is the distance squared (raised to the power of 2) from the circle’s center to any point on its edge.

So, to find the area of a circle, square the radius and multiply by pi.

84. What is the sum of the angles in a triangle?

  1. 360 degrees
  2. 180 degrees
  3. 280 degrees
  4. 90 degrees

Answer: B 180 degrees

Explanation: The sum of a triangle’s angles is always 180 degrees. This is a fundamental geometric feature shared by all triangles, whether equilateral (all sides and angles are equal), isosceles (two sides and angles are equal), or scalene (no sides or angles are equal). The total of a triangle’s three internal angles will always equal 180 degrees, regardless of its shape.

85. Which of the following is a Fibonacci series formula?

  1. Fn = Fn+1 – Fn+2
  2. Fn = Fn-1 * Fn-2
  3. Fn = Fn+1 + Fn-2
  4. Fn = Fn-1 + Fn-2

Answer: D Fn = Fn-1 + Fn-2

Explanation: The Fibonacci sequence can be stated Mathematically using the following recurrence relation: F(n) = F(n-1) + F(n-2)

Where:

  • F(n) is the nth Fibonacci number.
  • F(n-1) is the (n-1)th Fibonacci number.
  • F(n-2) is the (n-2)th Fibonacci number

86. Who introduced the Arabic numeral system to the Western world?

  1. Euclid
  2. Pythagoras and samos
  3. Leonardo Fibonacci
  4. Archimedes

Answer: C Leonardo Fibonacci

Explanation: Leonardo of Pisa, often known as Fibonacci, introduced the Arabic numerical system to the Western world. Fibonacci introduced the Hindu-Arabic numeral system, which contains the digits 0 to 9, and the place value system in his work “Liber Abaci” (1202).

87. Which of the following is True about prime numbers?

  1. Twin primes are prime number pairs with a difference of two.
  2. 2 is not only the even prime number.
  3. Every positive integer can be expressed uniquely as a product of prime integers (including one).
  4. All of the above

Answer: A Twin primes are prime number pairs with a difference of two.

Explanation: Twin Prime Numbers:

  • Twin primes are prime number pairs with a difference of two.
  • 2 is the only even prime number.
  • Every positive integer can be expressed uniquely as a product of prime integers (greater than one).

88. Evaluate (2*5)^3?

  1. 133
  2. 1000
  3. 117
  4. 144

Answer: B 1000

Explanation: (x*y) a = xa * ya

According to the question given,

=(2*5) 3
=23*53
=8*125
=1000

89. Evaluate x2 * x9?

  1. x7
  2. x11
  3. x-7
  4. x18

Answer: B x11

Explanation: xa * xb = xa+b , so x2 * x9 = x2+9 = x11

90. How will you evaluate the following expression?

  1. Xa-b
  2. Xa – Xb
  3. Xa+b
  4. Xa*b

Answer: A Xa-b

91. Complete the sentence. The variance of the given dataset is always ____.

  1. 0
  2. Infinity
  3. Negative
  4. Positive

Answer: D Positive

Explanation: A dataset’s variance is always a positive number. It quantifies the dispersion of data points around the mean. Because it can never be negative or infinite, the proper response is “Positive.”

92. Amongst which of the following is the correct value of

  1. n√xm
  2. √xmn
  3. √xm+n
  4. x√mn

Answer: A n√xm

93. What is the absolute value of 0?

  1. 1
  2. 0
  3. Infinity
  4. -Infinity

Answer: B 0

Explanation: A number’s absolute value is its distance from zero on the number line. Because 0 is at a distance of 0 units from itself, its absolute value is 0.

94. What is the smallest integer number?

  1. 0
  2. -1
  3. Infinity
  4. -Infinity

Answer: D -Infinity

Explanation: There is no smallest integer in the set of integers. On the number line, integers extend indefinitely in both the positive and negative directions. As a result, there is no one integer that can be deemed the smallest. Option D, “- infinity,” reflects this idea, as it represents the idea that integers extend to the left on the number line endlessly.

95. What is the smallest rational number?

  1. 1/1
  2. -1/2
  3. Infinity to -infinity
  4. -infinity

Answer: C Infinity to -infinity

Explanation: There is no smallest rational number in the context of rational numbers. Positive and negative fractions, as well as zero, are included in the rational numbers. The rational numbers become smaller or larger without bound as you walk along the number line to the left (towards negative infinity) or the right (towards positive infinity).

96. What is the smallest negative number?

  1. 0
  2. -1
  3. Infinity
  4. -Infinity

Answer: D -Infinity

Explanation: The negative infinity (-∞) with no bound is considered the smallest integer number.

97. Who introduced the ‘laws of planetary motion’?

  1. Isaac Newton
  2. Tycho Brahe
  3. Johannes Kepler
  4. Galileo Galilei

Answer: C Johannes Kepler

Explanation: The “laws of planetary motion” were developed by Johannes Kepler, a German Mathematician, astronomer, and astrologer. Kepler’s laws, which govern the motion of planets around the Sun, made an important addition to astronomy in the early 17th century.

98. How many degrees are there in a circle?

  1. 360 degrees
  2. 180 degrees
  3. Greater than 360 degrees
  4. 0 degree

Answer: A 360 degrees

Explanation: A circle contains 360 degrees. This 360-degree partition of a circle is a popular convention in geometry and trigonometry. Each degree is further subdivided into 60 minutes, which are further subdivided into 60 seconds. This measurement technique enables for exact angular computations.

99. What is the factorial of 0?

  1. 0
  2. 1
  3. Undefined
  4. Infinity

Answer: B

Explanation: The factorial of zero, represented as 0! is 1. The product of all positive integers from 1 to “n” is the factorial of a non-negative integer “n.” 5! (read as “5 factorial”), for example, is calculated as 5 * 4 * 3 * 2 * 1 = 120.

100. Which of the following is not considered as a rational number?

  1. 7/1
  2. 0/3
  3. -2/9
  4. None of the above

Answer: D None of the above

Explanation: Rational numbers are those that can be written as a fraction of two integers where the denominator is not zero. So in the above options all are considered as rational numbers.

101. On which date the PI Day around the world is celebrated?

  1. 15 Feb
  2. 13 March
  3. 14 March
  4. 19 March

Answer: C 14 March

Explanation: Around the world, PI Day is celebrated on 14th March.

102. Who discovered the logarithms and decimal points?

  1. John Napier
  2. Helen Napier
  3. Katherine Drummond
  4. Elizabeth Stirling

Answer: A John Napier

Explanation: The logarithms and decimal points by John Napier.

Basic Maths GK Questions

1. Who is the Father of Mathematics?

Answer: Archimedes

2. Who discovered Zero (0)?

Answer: Aryabhatta

3. Roman Number of 400?

Answer: CD

4. Roman Number of 500?

Answer: D

5. Roman Number of 600?

Answer: DC

6. Roman Number of 900?

Answer: CM

7. Roman Number of 1000?

Answer: M

8. Angles greater than 90 degrees but less than 180 degrees are called?

Answer: Obtuse angles

9. How many sides are there in a Heptagon?

Answer: 7

10. Solid shape that has four equal triangles?

Answer: Tetrahedron

11. What part of a Revolution have you turned through if you stand facing west and turn clockwise to face South?

Answer: ¾

12. Who discovered ∮ the Contour Integral sign?

Answer: Arnold Sommerfeld

13. Who discovered Existential Quantifier ∃ (there exists)?

Answer: Giuseppe Peano

14. Who invented ± Plus-Minus sign?

Answer: William Oughtred

15. Father of Cryptology?

Answer: Leon Battista Alberti

16. What is the shape of a Brick in India?

Answer: Cuboid

17. Where did the “Magic Square” originate?

Answer: Ancient China

18. Which movie is based on Srinivasa Ramanujan?

Answer: The Man Who Knew Infinity

19. Number between 50 and 60, which is a multiple of 7 and 8?

Answer: 56

20. Who invented “∇” the Nabla symbol?

Answer: William Rowan Hamilton

21. Who is known as Human Computer?

Answer: Shakuntala Devi

22. Name of the symbol φ ?

Answer: Golden ratio

23. Name of the symbol Δ ?

Answer: Delta

24. How many Centimeters make a Decameter?

Answer: 1000

25. What is the name of the following sequences 0,1,1,2,3,5,8….?

Answer: The Fibonacci Sequences

26. Who discovered “/” Division Slash (solidus)?

Answer: Thomas Twining

27. Ashok has an equal number of one rupee, five rupees, and 10 rupees notes. If he has ₹320 with him, what will be the number of each rupee note?

Answer: 20

28. What is the other name of the Perimeter of a Circle?

Answer: Circumference

29. Who discovered the Proportionality Sign ∝ ?

Answer: William Emerson (1768)

30. Who discovered the partial differential sign ∂ (curly d or Jacobi’s delta)?

Answer: Marquis de Condorcet

31. Who discovered Partial Derivatives?

Answer: Adrien-Marie Legendre (1786)

32. Who discovered Gamma-Function “Γ” ?

Answer: Leonhard Euler

33. Who discovered Laplace Transform?

Answer: Pierre-Simon Laplace

34. Who invented the Factorial symbol “!” ?

Answer: Christian Kramp

35. Who said the phrase “There is no permanent place in the world for ugly mathematics”?

Answer: Godfrey Harold Hardy

36. Who is the Father of Analytic Geometry?

Answer: René Descartes and Pierre de Fermat

37. Who invented Parentheses ( ) ?

Answer: Niccolò Tartaglia

38. Who invented “∫” Integral sign?

Answer: Gottfried Leibniz

39. Who discovered Matrix Notation […] ?

Answer: Gerhard Kowalewski

40. Who is the “Father of Mathematics”?

Answer: Archimedes

41. Name of the polygon that has 15 sides?

Answer: Pentadecagon

42. Who discovered an easy method to find all the Prime Numbers?

Answer: Eratosthenes

43. What is the average of the first 50 Natural Numbers?

Answer: 25.5

44. What is an angle greater than 180 degrees but less than 360 degrees called?

Answer: Reflex angle

45. The Smallest Perfect Number?

Answer: 6 (Six)

46. Who invented the Radical symbol √ ̅ ( square root)?

Answer: René Descartes

47. Mr. Harold ranked 7th from the top and 26th from the bottom, How many students are there in the class?

Answer: 32

48. Who discovered ” ∀ ” universal quantifier (for all)?

Answer: Gerhard Gentzen

49. A number between 30 and 50 which is a common multiple of 6 and 8. What is the number when it is added to 45?

Answer: 93

50. Roman Number of 40?

Answer: XL

51. What is the Line called which cuts a pair of Parallel lines?

Answer: Transversal

52. Who developed the Chinese Remainder Theorem?

Answer: Sun Tzu

53. Who developed Descartes’ Theorem?

Answer: René Descartes in 1643

54. Who created the Theory of Probability?

Answer: Blaise Pascal and Pierre de Fermat

55. Who was the first person to use Algebra for solving Astronomical Problems?

Answer: Brahmagupta (7th century)

56. Which equation was solved by Rafael Bombelli using Imaginary numbers?

Answer: Cubic equations in 1572

57. Who discovered Binomial Theorem?

Answer: Al-Karaji

58. Who discovered Divergence Theorem?

Answer: Joseph Louis Lagrange

59. Who discovered Taylor Series?

Answer: Brook Taylor in 1712

60. Calculate the Rate of Interest for a certain sum of money that becomes 5 times its principal Amount in 10 years?

Answer: 40%

61. Which Theorem did André-Marie Ampère discover in 1825?

Answer: Stokes’ theorem.

62. Who developed the Analytic number theory?

Answer: Peter Gustav Lejeune Dirichlet

63. Which problem was solved by Jean le Rond d’Alembert in 1747?

Answer: Vibrating string problem (one-dimensional wave equation)

64. Who proved the Fundamental Theorem of Arithmetic?

Answer: Euclid (sometimes called Euclid of Alexandria)

65. Who proved that the value of π lies between 3 + 1/7 (approx. 3.1429) and 3 + 10/71 (approx. 3.1408)?

Answer: Archimedes (260 BC)

66. Which theorem did Thomas Bayes prove in 1761?

Answer: Bayes’ theorem

67. Who Proved that “π” Pi is Irrational?

Answer: Johann Heinrich Lambert

68. Which Numerals have been modified by Arab mathematicians to form the modern Arabic Numeral system?

Answer: Indian Numerals

69. Most famous Theorem of Triangles in Geometry?

Answer: Pythagoras’ Theorem

70. Which rule did Shridhara (A.K.A Sridharacharya from India) give?

Answer: Volume of a sphere and the formula for solving quadratic equations

71. Who first introduced the Trigonometric Functions (sine and cosine) and methods of calculating their Approximate Numerical Values?

Answer: Aryabhata

72. Roman Number of 40?

Answer: XL

73. What Number that is twice the sum of their digits (other than zero)?

Answer: 18

74. Which is the only even Prime Number?

Answer: 2

75. Roman Number of 50?

Answer: L

76. Roman Number of 60?

Answer: LX

77. Roman Number of 70?

Answer: LXX

78. Roman Number of 90?

Answer: XC

79. Roman Number of 100?

Answer: C

80. Find the missing number in the series 5, 10, 17, _, 37, 50, 65, 82?

Answer: 26

81. Which is the smallest Perfect Number?

Answer: 6

82. Who discovered + and – ?

Answer: Johannes Widman

83. Who discovered intersection ∩ and union ∪ ?

Answer: Giuseppe Peano

84. What is the next Prime Number after 13?

Answer: 17

85. Which is the only number that cannot be used as a Divisor?

Answer: Zero

86. Who is known as the prince of Mathematics in India?

Answer: Srinivasa Ramanujan

87. Who said the phrase “Number rules the Universe”?

Answer: Pythagoras

88. Which number is Known as Ramanujan-Hardy Number?

Answer: 1729

89. What is the name of the number system with base 2?

Answer: Binary

90. How many seconds are there in one hour?

Answer: 3600 Seconds

91. Who discovered the identity sign ≡ (for congruence relation)?

Answer: Carl Friedrich Gauss

92. Which number system does not have the symbol for zero?

Answer: Roman Numerals

93. Who discovered Number Line?

Answer: John Wallis

94. Who discovered strict inequality signs < and > ?

Answer: Thomas Harriot

95. What number do we get when we multiply all of the numbers on a Telephone Number Pad?

Answer: Zero

96. Who discovered the division sign ÷ ?

Answer: Johann Rahn

97. Who discovered the ⌊x⌋ greatest integer ≤ x (floor) and ⌈x⌉ smallest integer ≥ x (ceiling)?

Answer: Kenneth E. Iverson

98. What is the name for the longest side of a Right Angled Triangle?

Answer: Hypotenuse

99. Which number does not have a Reciprocal?

Answer: zero

100. Who discovered Mathematical Induction?

Answer: Giovanni Vacca

101. What Phobia is the fear of Numbers?

Answer: Arithmophobia

102. How many zeros are there in One Trillion?

Answer: 12 Zeros (1,000,000,000,000)

103. What comes after a Trillion?

Answer: Quadrillion

104. Name the Polygon that has 15 Sides?

Answer: Pentadecagon

105. Father of Trigonometry?

Answer: Hipparchus

106. Father of Science?

Answer: Galileo Galilei

107. Who discovered Line Graph, Bar Chart, Circle Graph?

Answer: William Playfair

108. Who discovered ∇ (delta)?

Answer: William Rowan Hamilton

109. Who invented Boolean Algebra?

Answer: George Boole in 1847

110. Who invented Unknown or variable quantities x, y, z ?

Answer: Rene Descartes

111. How many Faces are there in a Pyramid?

Answer: 4

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