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  • Class 12
    • Chapter 1
      • Class 12 ncert solution math exercise 1.1
      • Class 12 ncert solution math exercise 1.2
    • Chapter 2
      • Class 12 ncert solution math exercise 2.1
      • Class 12 ncert solution math exercise 2.2
      • Class 12 ncert solution math chapter 2 Miscellaneous
    • Chapter 3
      • Class 12 ncert solution math exercise 3.1 matrix
      • Class 12 ncert solution math exercise 3.2 matrix
      • class 12 maths exercise 3.3 solution
      • class 12 maths chapter 3 Miscellaneous solution
    • Chapter 4
      • Class 12 ncert solution math exercise 4.1
      • Class 12 ncert solution math exercise 4.3 determinants
      • Class 12 ncert solution math exercise 4.4
      • class 12 maths exercise 4.5 ncert solution
      • Class 12 ncert solution math exercise 4.6
    • Chapter 5
      • Class 12 ncert solution math exercise 5.1
      • Class 12 ncert solution math exercise 5.2
      • Class 12 ncert solution math exercise 5.3
      • Class 12 ncert solution math exercise 5.4
      • Class 12 ncert solution math exercise 5.5 differentiation
      • Class 12 ncert solution math exercise 5.6
      • Class 12 ncert solution math exercise 5.7 differentiation
      • Class 12 ncert solution math chapter 5 miscellaneous
    • Chapter 6
      • class 12 maths ex 6.1 ncert solution
      • class 12 maths ex 6.2 ncert solution
      • class 12 maths ex 6.3 ncert solution
      • class 12 maths ex 6.5 ncert solution
      • class 12 maths chapter 6 Miscellaneous ncert solution
    • Chapter 7
      • Ex 7.1 integration ncert solution maths class 12
      • Ex 7.2 integration ncert solution maths class 12
      • Ex 7.3 integration ncert maths solution class 12
      • Ex 7.4 integration ncert maths solution class 12
      • Ex 7.5 integration ncert maths solution class 12
      • Ex 7.6 integration ncert maths solution class 12
      • Ex 7.7 integration ncert maths solution class 12
      • Ex 7.9 integration ncert maths solution class 12
      • Ex 7.10 integration ncert maths solution class 12
      • Ex 7.11 integration ncert maths solution class 12
      • Chapter 7 Miscellaneous integration ncert maths class 12
    • chapter 8
      • Exercise 8.1 ncert math solution class 12
      • Exercise 8.2 ncert math solution class 12
  • Class 11
    • Chapter 1
      • Ex 1.1 ncert maths solution class 11
      • Ex 1.2 sets ncert maths solution class 11
      • Ex 1.3 sets ncert maths solution class 11
      • Ex 1.4 sets ncert maths solution class 11
      • Ex 1.5 sets ncert maths solution class 11
      • Ex 1.6 sets ncert maths solution class 11
      • Miscellaneous exercise sets ncert maths solution class 11
    • Chapter 2
      • Ex 2.1 sets ncert maths solution class 11
      • Ex 2.2 sets ncert maths solution class 11
      • Ex 2.3 sets ncert maths solution class 11
      • Chapter 2 Miscellaneous sets ncert maths solution class 11
    • Chapter 3
      • Trigonometry formulae for class 11
      • Ex 3.1 Trigonometric function ncert solution class 11
      • Ex 3.2 Trigonomety ncert maths solution class 11
      • Ex 3.3 Trigonomety ncert maths solution class 11
      • Ex 3.4 Trigonomety ncert maths solution class 11
      • Class 11 Chapter 3 Miscellaneous Exercise trigonometry
    • Chapter 4
      • Exercise 4.1 ncert math solution class 11
    • Chapter 5
      • Exercise 5.1 complex no. ncert math solution class 11
      • Exercise 5.2 complex no. ncert math solution class 11
      • Exercise 5.3 complex no. ncert math solution class 11
      • Chapter 5 Miscellaneous ncert math solution class 11
    • Chapter 6
      • Ex 6.1 Linear Inequalities ncert math solution class 11
      • Ex 6.2 Linear Inequalities ncert math solution class 11
      • Ex 6.3 Linear Inequalities ncert math solution class 11
      • Chapter 6 Miscellaneous ncert math solution class 11
    • Chapter 7
      • Exercise 7.1 ncert solutions maths class-11
      • Exercise 7.2 ncert solutions maths class 11
      • Exercise 7.3 ncert solutions maths class 11
      • Exercise 7.4 ncert solutions maths class 11
      • Chapter 7 Miscellaneous Ncert math solution class 11
  • Class 10
    • Trigonometric formulae for class 10
    • 1. Real Number
      • Exercise 1.1 real number class 10 ncert maths solutions
      • Exercise 1.2 real number class 10 ncert maths solutions
  • Question-Answer
    • Class 12
      • R= {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive
      • R={(a, b): a ≤  b³} is reflexive, symmetric or transitive
      • f(x) = 5x^2+6x-9 prove that f is bijective.
      • A and B throw a die alternatively till one of them gets 6
      • Two balls are drawn at random one by one with replacement
      • Find the equations of the diagonals of the parallelogram
      • A line l passes through point (-1,3,-2) and is perpendicular
      • A function f:[-4,4] → [0,4] is given by f(x) = √16 – x²
      • Show that right circular cone of least curve surface
      • If 20 m of wire is available for fencing off a flower-bed
      • Prove that the volume of the largest cone that can be
      • A wire of length 28 m is to be cut into two pieces
      • Show that the right circular cylinder of given surface
      • Show that of all the rectangles inscribed in a given fixed circle
      • A square piece of tin of side 18 cm is to be made into a box
      • A rectangula sheet of tin 45 cm by 24 cmis to be made into
      • Show that of all the rectangles inscribed in a given fixed circle
      • If y^x = e^(y-x), then prove that dy/dx = (1 + logy)^2/log y
      • If tan inverse y/x = log root x^2 + y^2, then prove that
      • Find the value of dy/dx at θ = pi/4, if x = aeθ(sin θ – cos θ)
      • If cos y = x cos (a + y) with cos a ≠ ± 1 then prove that
      • int root cotx + root tanx dx
      • Three friends go for coffee. They decide who will pay the bill
      • 13. Probability
        • In a certain collage, 4% of boys and 1% of girls
        • An urn contains 5 red and 2 black balls. Two balls
        • Two group are competing for the position on the Board
        • The probabilities of two students A and B coming
        • A and B throw a pair of dice alternately A wins the game
        • A, B and C throw a pair of dice in that order alternately
        • The probability that A hits a target is 1/3 and the
        • In a group of 50 scouts in a camp, 30 are well trained
        • A bag I contains 5 red and 4 white balls and a bag II
    • Class 10
      • Prove that root 2 is an irrational number
      • Prove that root 5 is an irrational number
      • Prove that 2-root 3 is irrational, given that root 3 is irrational
      • Prove that root p + root q is irrational
      • Prove that root 2 + root 5 is irrational
      • Prove that root n is not a rational number
      • rahul-had-some-bananas-and-he-divided-them-into-two-lots
      • Ruhi invested a certain amount of money in two schemes
      • find the value of k for which the pair of equation
      • Find the zeros of the quadratic polynomial x² + 7x + 12
      • If we add 1 to the numerator and subtract 1 from the
      • If α and β are the zeros of the quadratic polynomial
      • If Ritu were younger by 5 years than what she really is
      • The sum of areas of two squares is 157 m²
      • If the equation (1 + m²)x² + 2 mcx + c² – a² = 0 has equal
      • A train covers a distance of 480 km at a uniform speed
      • A train travels 360 km at a uniform speed If the speed
      • In a flight of 600 km an aircraft was slowed due to
      • Arithemetic Progression
        • A child puts one five-rupees coin of her savings in the
        • Ramkali would require Rs 5000 for getting her daughter
        • The first term of an A.P. is -5 and the last term is 45
        • Show that the sum of all terms of an A.P. whose first term is a
        • Yasmeen saves ₹ 32 during the first month ₹ 36
        • A sum of ₹ 4,250 is to be used to give 10 cash prizes
  • Multiple Choice
    • Class 12 relation and functions multiple choice
    • class 12 inverse trigonometric functions multiple choice
    • Class 12 matrix multiple choice question
    • Class 12 determinants multiple choice question
    • Class 12 continuity and differentiability multiple choice
    • Class 12 application of derivatives multiple choice
    • Class 12 integration multiple choice question gmath
    • Class 12 application of integral multiple choice question
    • Class 12 differential equation multiple choice question
    • Class 12 vectors multiple choice question
    • Multiple choice question of 3 dimensional geometry
    • Class 12 multiple choice question of linear programming
    • Class 12 multiple choice of probability
  • Revision notes
    • class 12 revision of cbse math part-I 2022-2023
    • Class 12 revision of cbse math part-II 2022-2023
  • Case Study Question
    • Class 12
      • 1. Relation and function
        • Case study relation and function 1 chapter 1 class 12
        • Case study relation and function 2 chapter 1 class 12
        • Case study relation and function 3 chapter 1 class 12
        • Case study relation and function 4 chapter 1 class 12
      • 2. Inverse Trigonometry
        • Case study inverse trigonometric 1 chapter 2 class 12
        • Case study inverse trigonometry 2 chapter 2 class 12
      • 3. Matrix
        • Case study problem matrix 1 chapter 3 class 12
        • Case study problem matrix 2 chapter 3 class 12
        • Case study problem matrix 3 chapter 3 class 12
      • 4. Determinant
        • Case study problem determinant 1 chapter 4 class 12
        • Case study problem determinant 2 chapter 4 class 12
        • Case study problem determinant 3 chapter 4 class 12
        • Case study problem determinant 4 chapter 4 class 12
        • Case study problem determinant 5 chapter 4 class 12
      • 6. Application of derivative
        • Case study application of derivative 1 chapter 6 class 12
        • Case study application of derivative 2 chapter 6 class 12
        • Case study application of derivative 3 chapter 6 class 12
        • Case study application of derivative 4 chapter 6 class 12
        • Case study application of derivative 5 chapter 6 class 12
        • The relation between the height of the plant
      • 8. Application of Integral
        • Case study application of integral 1 chapter 8 class 12
        • Case study application of integral 2 chapter 8 class 12
        • Case study application of integral 3 chapter 8 class 12
        • Case study application of integral 4 chapter 8 class 12
        • Case study application of integral 5 chapter 8 class 12
      • 9. Differential equation
        • Case study Differential equation chapter 9 class 12
      • 10 vector
        • Case study problem vector 1 chapter 10 class 12
        • Case study problem vector 2 chapter 10 class 12
        • Case study three dimension geometry 1 chapter 11 class 12
      • 11. Three dimesion geometry
        • Case study three dimension geometry 2 chapter 11 class 12
      • 12. Linear programming
        • Case study linear programming 1 chapter 12 class 12
        • Case study linear programming 2 chapter 12 class 12
        • Case study linear programming 3 chapter 12 class 12
        • Case study linear programming 4 chapter 12 class 12
        • Case study linear programming 5 chapter 12 class 12
      • 13. Probability
        • Case study problem probability 1 chapter 13 class 12
        • Case study problem probability 2 chapter 13 class 12
        • Case study problem probability 3 chapter 13 class 12
        • Case study problem probability 4 chapter 13 class 12
        • Case study problem probability 5 chapter 13 class 12
        • Case study problem probability 6 chapter 13 class 12
        • Case study problem probability 7 chapter 13 class 12
        • Case study problem probability 8 chapter 13 class 12
        • Case study problem probability 9 chapter13 class 12
        • Recent studies suggest that roughly 12 % of the world
        • Engine displacement is the measure of the cylinder volume
        • The use of electric vehicle will curb air pollution
    • Class 10
      • Chapter 1
        • Class 10 Case based problem of Chapter 1 Real Number 1
        • Class 10 Case based problem of Chapter 1 Real Number 2
        • Class 10 Case based problem of Chapter 1 Real Number 3
      • Chapter 2
        • Class 10 Case based problem of Chapter 2 Polynomials 1
        • Class 10 Case based problem of Chapter 2 Polynomials 2
        • Class 10 Case based problem of Chapter 2 Polynomials 3
      • Chapter 3
        • Class 10 Case based problem of Chapter 3 Pair of Linear eq 1
        • Class 10 Case based problem of Chapter 3 Pair of Linear eq 2
      • Chapter 4
        • Class 10 Case based problem of Chapter 4 quadratic eq 1
        • Class 10 Case based problem of Chapter 4 Quadratic eq 2
      • Chapter 5
        • Class 10 Case based problem of Chapter 5 A.P. 1
        • Class 10 Case based problem of Chapter 5 A.P. 2
      • Chapter 6: Triangles
        • Class 10 Case based problem of Chapter 6 Triangles 1
        • Class 10 Case based problem of Chapter 6 Triangles 2
      • Chapter 7: Coordinate Geometry
        • Class 10 Case study of Chapter 7 coordinate geometry
      • chapter 8: Introduction to trigonometry
        • Class 10 Case study Chapter 8 introduction to Trigonometry
      • chapter 11
        • Class 10 case study chapter 11 Area related to circle
        • Class 10 case study Chapter 11 Area related to circle 2
  • Linear Algebra
    • Vector spaces
      • Vector Space and properties of Vector space
  • Other
    • CBSE 12th and 10th Class Date Sheet 2024
    • sbi clerk mains admit card 2025 download
  • Game
    • Lionel Messi
    • Cristiano Ronaldo
    • Sachin Tendulkar
    • MS Dhoni
    • Virat kohli The indian cricketer
    • Rohit Sharma Cricket Legend
    • Hardik Pandya
  • Last year question paper
    • CBSE Class 10 mathematics Paper  2023-2024

Question-Answer

Three friends go for coffee. They decide who will pay the bill

03/01/2023 by Team Gmath

    Three friends go for coffee. They decide who will pay the bill, by each tossing a coin and and then letting the “odd person” pay. There is no odd person if all three tosses produce the same result. It there is no odd person in the first round , they make a second … Read more

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