Class 12

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 6 Application of Derivatives Miscellaneous Exercise Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 6 Application of Derivatives Miscellaneous Exercise Question 1. (a) () Solution: (b) (33) : Question 2. Show that the functions given by f(x) = has a maximum at […]

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 12 Linear Programming Miscellaneous Exercise Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 12 Linear Programming Miscellaneous Exercise Question 1. How many packets of each type of foods P and Q should be used to maximise the amount of vitamin A in

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise Question 1. Prove that the determinant independent of θ. Solution: Let ∆ = Expanding with the help of elements of I row, we get ∆ =

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Question 1. Show that the three lines with direction cosines , , ; , , and , , are mutually perpendicular. Solution:

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 Question 1. If a line makes angles 90°, 135° and 45° with x, y and z axes respectively, find its direction cosines.

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise Question 1. Write down a unit vector in XY plane making an angle of 30° with the positive direction of x-axis. Solution: Let OX,

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.3 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.3 Question 1. 2x + 3y = sin x Solution: 2x + 3y = sin x. Differentiating w.r.t. x, 2x + 3 =

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.2 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.2 Question 1. sin(x² + 5) Solution: Let y = sin(x² + 5) Put x² + 5 = t ∴ y = sin

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.6 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.6 Question 1. x + 2y = 2 2x + 3y = 3 Solution: x + 2y = 2 2x + 3y = 3 Let A =

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4 Question 1. Solution: Let y = . where x ≠ nπ, x ∈ Z. Question 2. Solution: Let y = Put sin-1x

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.5 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.5 Question 1. cos x . cos 2x . cos 3x Solution: Let y – cos x . cos 2.x . cos 3x.

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 9 Differential Equations Ex 9.4 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 9 Differential Equations Ex 9.4 For each of the differential equations in questions 1 to 10, find the general solution: Question 1. = Solution: ∴ y = 2 tan

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 13 Probability Ex 13.1 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 13 Probability Ex 13.1 Question 1. Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P(E/F) and

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.8 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.8 Question 1. Verify Rolle’s Theorem for the function f(x) = x² + 2x – 8, x ∈ [- 4, 2]. Solution: Now,

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 6 Application of Derivatives Ex 6.5 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 6 Application of Derivatives Ex 6.5 Question 1. Find the maximum and minimum values, if any, of the following functions given by (i) f(x) = (2x – 1)²

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 6 Application of Derivatives Ex 6.3 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 6 Application of Derivatives Ex 6.3 Question 1. Find the slope of the tangent to the curve y = 3×4 – 4x at x = 4. Solution: The

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Miscellaneous Exercise Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 5 Continuity and Differentiability Miscellaneous Exercise Question 1. (3x² – 9x + 5)9 Solution: Let y = (3x² – 9x + 5)9 = 9, where u = 3x²

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 9 Differential Equations Miscellaneous Exercise Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 9 Differential Equations Miscellaneous Exercise Question 1. For each of the differential equations given below, indicate its order and degree (if defined): (i) + 5x()2 – 6y = log

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 8 Application of Integrals Ex 8.1 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 8 Application of Integrals Ex 8.1 Question 1. Find the area of the region bounded by the curve y2 = x and the lines x = 1, x

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 9 Differential Equations Ex 9.1 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 9 Differential Equations Ex 9.1 Determine orders and degrees (if defined) of the differential equations given ¡n questions 1 to 10: Question 1. + sin(y”’) = 0 Solution: ∴