- Who is known as the Father of Geometry?
Answer: Euclid - What is the value of π (Pi) up to 5 decimal places?
Answer: 3.14159 - Euler’s formula relates to which branch of mathematics?
Answer: Topology - What is the sum of the interior angles of a triangle?
Answer: 180° - Which number is known as the ‘Ramanujan Number’?
Answer: 1729 - Who developed the concept of Calculus independently in the 17th century?
Answer: Isaac Newton and Gottfried Wilhelm Leibniz - What is the derivative of sin(x)?
Answer: cos(x) - Who is known as the ‘Prince of Indian Mathematics’?
Answer: Srinivasa Ramanujan - Which theorem states that the sum of the squares of the two legs of a right-angled triangle equals the square of the hypotenuse?
Answer: Pythagorean Theorem - What is the value of the golden ratio (φ)?
Answer: Approximately 1.61803
Geometry & Shapes
- What is the sum of the interior angles of a quadrilateral?
Answer: 360° - How many faces does a cube have?
Answer: 6 - What is the name of a polygon with 10 sides?
Answer: Decagon - Which shape has no edges and no vertices?
Answer: Circle - What is the area of a circle formula?
Answer: πr² - What is the volume of a sphere formula?
Answer: (4/3)πr³ - How many sides does a hexagon have?
Answer: 6 - What is the perimeter of a rectangle formula?
Answer: 2(l + b) - How many diagonals does a hexagon have?
Answer: 9 - What is the surface area of a cylinder formula?
Answer: 2πr(h + r)
Algebra & Numbers
- What is the square root of 144?
Answer: 12 - Which number is known as the ‘perfect number’ between 1 and 10?
Answer: 6 - What is the value of 2 raised to the power of 10?
Answer: 1024 - What is the sum of the first 10 prime numbers?
Answer: 129 - What is the least common multiple (LCM) of 12 and 15?
Answer: 60 - What is the greatest common divisor (GCD) of 36 and 60?
Answer: 12 - Which number is known as the ‘Fibonacci number’ after 13?
Answer: 21 - What is the value of 7 factorial (7!)?
Answer: 5040 - Which number is known as the ‘amicable number’ between 220 and 284?
Answer: 220 - What is the sum of the first 100 natural numbers?
Answer: 5050
Statistics & Probability
- What is the mean of the numbers 2, 4, 6, 8, and 10?
Answer: 6 - What is the median of the numbers 1, 3, 5, 7, and 9?
Answer: 5 - What is the mode of the numbers 2, 4, 4, 6, 8?
Answer: 4 - What is the probability of rolling a 3 on a fair six-sided die?
Answer: 1/6 - What is the standard deviation of the numbers 2, 4, 6, 8, and 10?
Answer: 2.83 (approximately) - What is the range of the numbers 5, 10, 15, 20, and 25?
Answer: 20 - In a normal distribution, what percentage of data lies within one standard deviation of the mean?
Answer: Approximately 68% - What is the formula for the variance of a population?
Answer: σ² = Σ(x – μ)² / N - What is the probability of drawing an Ace from a standard deck of 52 playing cards?
Answer: 4/52 or 1/13 - What is the expected value of rolling a fair six-sided die?
Answer: 3.5
Mathematical History & Mathematicians
- Who is known as the ‘Father of Modern Mathematics’?
Answer: René Descartes - Who developed the concept of the Cartesian coordinate system?
Answer: René Descartes - Who is credited with the invention of the abacus?
Answer: The Chinese - Who formulated the laws of motion and universal gravitation?
Answer: Isaac Newton - Who is known for his work on the theory of probability and statistics?
Answer: Pierre-Simon Laplace - Who is known for his work on the theory of numbers and prime numbers?
Answer: Carl Friedrich Gauss - Who is known for his work on the theory of relativity?
Answer: Albert Einstein - Who is known for his work on the theory of sets and infinity?
Answer: Georg Cantor - Who developed the concept of mathematical induction?
Answer: Pierre de Fermat - Who is known for his work on the theory of groups and symmetry?
Answer: Évariste Galois
Calculus & Analysis
- What is the derivative of cos(x)?
Answer: -sin(x) - What is the integral of sin(x)?
Answer: -cos(x) + C - What is the derivative of e^x?
Answer: e^x - What is the derivative of ln(x)?
Answer: 1/x - What is the limit of (1 + 1/n)^n as n approaches infinity?
Answer: e - What does the Fundamental Theorem of Calculus connect?
Answer: Differentiation and integration - What is the second derivative of x³?
Answer: 6x - What is the integral of x^2 dx?
Answer: (x³)/3 + C - What is the derivative of tan(x)?
Answer: sec²(x) - What is the antiderivative of 1/x?
Answer: ln|x| + C - What does ∫ f'(x) dx equal?
Answer: f(x) + C
Vectors & 3D Geometry
- What is the dot product of two perpendicular vectors?
Answer: 0 - What is the cross product of two parallel vectors?
Answer: Zero vector - What is the magnitude of vector a = 3i + 4j?
Answer: 5 - If two vectors are a = i + 2j and b = 2i + 4j, are they parallel?
Answer: Yes - What is the angle between two identical vectors?
Answer: 0° - Which product (dot or cross) gives a scalar?
Answer: Dot product - Which product (dot or cross) gives a vector?
Answer: Cross product - What is the direction ratio of a line parallel to vector 2i + 3j + 4k?
Answer: 2:3:4 - What is the distance formula between two points in 3D?
Answer: √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
Matrices & Determinants
- What is the determinant of a 2×2 matrix \[a,b\[a, b\[a,b, c,dc, dc,d]?
Answer: ad – bc - What is the identity matrix?
Answer: A square matrix with 1’s on the diagonal and 0’s elsewhere - What is the inverse of a matrix A such that A * A⁻¹ = ?
Answer: Identity matrix - When is a matrix non-invertible?
Answer: When its determinant is 0 - What type of matrix has only one row?
Answer: Row matrix - If A is a 2×3 matrix and B is a 3×2 matrix, what will be the order of AB?
Answer: 2×2 - What is the transpose of a matrix?
Answer: Rows become columns and columns become rows - What is a diagonal matrix?
Answer: A matrix with all off-diagonal elements zero - What is the trace of a matrix?
Answer: Sum of diagonal elements - What is the determinant of the identity matrix of order 3?
Answer: 1
Logic & Reasoning in Mathematics
- What does the symbol ⇒ mean in logic?
Answer: Implies - What is a tautology in logic?
Answer: A statement that is always true - What is the contrapositive of “If A, then B”?
Answer: If not B, then not A - What is the negation of “All A are B”?
Answer: Some A are not B - What does the symbol ∀ mean?
Answer: For all - What does the symbol ∃ mean?
Answer: There exists - Which logic gate gives true output only if both inputs are true?
Answer: AND gate - Which logic gate gives true output if either input is true?
Answer: OR gate - What is the truth value of (True AND False)?
Answer: False - What is the result of (True OR False)?
Answer: True
Real-life Applications of Math
- Which mathematical method is used in encryption of digital data?
Answer: Number theory (especially prime numbers) - Which mathematical concept is essential in computer graphics?
Answer: Matrices and vectors - Which mathematical tool is used for predicting weather?
Answer: Differential equations - Which branch of mathematics is used in economics for optimization?
Answer: Calculus - What mathematical principle is used in credit card verification?
Answer: Luhn algorithm - Which mathematical method is used in medical imaging (CT scans)?
Answer: Fourier transforms - Which field of math helps in AI and machine learning?
Answer: Linear algebra - Which mathematical area is used in making Google Maps?
Answer: Graph theory and geometry - Which concept helps in analyzing risk in insurance?
Answer: Probability and statistics - Which branch of math deals with patterns and sequences?
Answer: Algebra
Bonus Rapid-Fire
- Value of i² (imaginary number)?
Answer: -1 - Binary number system base?
Answer: 2 - Is zero an even number?
Answer: Yes - Who developed Boolean algebra?
Answer: George Boole - What is the sum of interior angles of a pentagon?
Answer: 540° - What is 0 factorial (0!)?
Answer: 1 - What is the result of any number raised to the power 0?
Answer: 1 - What is the base-10 logarithm of 1000?
Answer: 3 - Name a number that is both square and cube of an integer.
Answer: 64 (8² = 64, 4³ = 64) - What is the binary equivalent of decimal number 10?
Answer: 1010
