Skip to content

Gmath

  • 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
      • 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
    • 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
      • 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
    • 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
  • Case Study
    • 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
      • 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
      • 11. Three dimesion geometry
        • Case study three dimension geometry 1 chapter 11 class 12
        • 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
  • 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

If cos y = x cos (a + y) with cos a ≠ ± 1 then prove that

02/06/2023 by Dileep namdev

Question: If , with , then prove that . Hence show that . ……..      [CBSC  2016] Solution: Given, Differentiating with respect to y on both sides, we get Differentiating both sides w.r.t. x, we get Some other question: Q 1: If , Prove that .    ……..[CBSC 2020] Solution: For solution click here … Read more

Categories Question-Answer Leave a comment

Find the value of dy/dx at θ = pi/4, if x = aeθ(sin θ – cos θ)

02/06/202301/06/2023 by Dileep namdev

Question: Find the value of at , if and .          ……..   [CBSC 2008, 2014] Solution: Given, and Taking, Differentiating with respect to θ, we get Again taking, Differentiating with respect to θ, we get Some other question: Q 1: If , Prove that .    ……..[CBSC 2020] Solution : For solution … Read more

Categories Question-Answer Leave a comment

If tan inverse y/x = log root x^2 + y^2, then prove that

01/06/202301/06/2023 by Dileep namdev

Question: If , Prove that .    ……..[CBSC 2020] Solution: Given, Differentiating with respect to x, we have, Some other question: Q 1: If , then prove that Q 2: Find the value of at , if and .          ……..   [CBSC 2008, 2014]

Categories Question-Answer Leave a comment

If y^x = e^(y-x), then prove that dy/dx = (1 + logy)^2/log y

01/06/202330/05/2023 by Dileep namdev

Question: If , then prove that Solution: Given, Taking logrithm both sides, we get log Differentiating both sides with respect to y, we get Some other question Q 1 :If tan inverse y/x = log root x^2 + y^2, then prove that Q 2: Find the value of at , if and .      … Read more

Categories Question-Answer Leave a comment

Class 10 Case study Chapter 8 introduction to Trigonometry

03/06/202329/05/2023 by Dileep namdev

Class 10 Case study Chapter 8 introduction to Trigonometry Case Study:1     An electrician wanted to repair a street lamp at a height of 15 feet. He places his ladder such that its foot is 8 feet from the foot of the lamp post as shown in the figure below: (A) Find the value … Read more

Categories Case Study Leave a comment

Class 10 Case study of Chapter 7 coordinate geometry

27/05/2023 by Dileep namdev

Class 10 Case study of Chapter 7 coordinate geometry  Case study:1                 To conduct Annual day activities, in a rectangular shaped school ground PQRS, lines have been drawn with chalk powder at a distance of 1 m each.  10 banners have been placed at a distance of 10 … Read more

Categories Case Study Leave a comment

If α and β are the zeros of the quadratic polynomial

26/05/202326/05/2023 by Dileep namdev

Question:             If α and β are the zeros of the quadratic polynomial f(x) = ax² + bx + c, then evaluate: (i)  (ii)  (iii) (iv) (v)  (vi) Solution: Since α and β are the zeros of the quadratic polynomial f(x) = ax² + bx + c and (i) We … Read more

Categories Question-Answer Leave a comment

If we add 1 to the numerator and subtract 1 from the

30/05/202326/05/2023 by Dileep namdev

Question:1                    If we add 1 to the numerator and subtract 1 from the denominator, a fraction becomes 1. It also becomes 1/2 if we add 1 to the denominator. What is the fraction. Solution: Let the fraction Then, according to the first condition, we have ……..(i) … Read more

Categories Question-Answer Leave a comment

Find the zeros of the quadratic polynomial x² + 7x + 12

02/06/202325/05/2023 by Dileep namdev

Question:1               Find the zeros of the quadratic polynomial x² + 7x + 12, and verify the relation between the zeros and its coefficients. Solution: We  have, f(x) = x² + 7x + 12 f(x) = x² + 7x + 12 ⇒ f(x) = x² + 4x + 3x … Read more

Categories Question-Answer Leave a comment

Class 10 Case based problem of Chapter 6 Triangles 2

23/05/202321/05/2023 by Dileep namdev
Class 10 Case based problem of Chapter 6 Triangles 2

Class 10 Case based problem of Chapter 6 Triangles 1 Class 10 Case based problem of Chapter 6 Triangles 2  Case study:1 While browsing through the catalogue of wooden shelves. Ravi came across this beautiful triangular shaped shelf. A shelf DE parallel to the base BC could be used for displaying small plants and showpieces … Read more

Categories Case Study Leave a comment
Older posts
Page1 Page2 … Page19 Next →

Recent Posts

  • If cos y = x cos (a + y) with cos a ≠ ± 1 then prove that
  • Find the value of dy/dx at θ = pi/4, if x = aeθ(sin θ – cos θ)
  • If tan inverse y/x = log root x^2 + y^2, then prove that
  • If y^x = e^(y-x), then prove that dy/dx = (1 + logy)^2/log y
  • Class 10 Case study Chapter 8 introduction to Trigonometry

Recent Comments

No comments to show.
© 2023 Gmath • Built with GeneratePress