Class 12

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.8 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.8 Evaluate the following definite integrals as limits of the sum: Question 1. x dx Solution: Question 2. (x + 1) dx Solution: Compare (x + 1) […]

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.7 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.7 Integrate the following functions: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: Question 7. Solution: Question

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.6 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.6 Integrate the following functions: Question 1. x sin x Solution: Let I = ∫x sin x dx We know that ∫uv dx = u∫v dx –

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.3 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.3 Find the integrals of the following: Question 1. sin2(2x + 5) Solution: Question 2. sin3x cos4x Solution: Question 3. cos2x cos4x cos6x Solution: Question 4. sin3(2x

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Miscellaneous Exercise Integrate the following functions w.r.t x (questions from 1 to 24): Question 1. Solution: Let = = + + ⇒ 1 = A(1 + x)(1 –

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 8 Application of Integrals Miscellaneous Exercise Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 8 Application of Integrals Miscellaneous Exercise Question 1. Find the area under the following given curves and given lines: (i) y = x2, x = 1, x =

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 8 Application of Integrals Ex 8.2 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 8 Application of Integrals Ex 8.2 Question 1. Find the area of the circle 4×2 + 4y2 = 9 which is interior to the parabola x2 = 4y.

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.11 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.11 By using properties of definite integrals, evaluate the following: Question 1. cos2x Solution: Question 2. dx Solution: Question 3. dx Solution: Question 4. Solution: Question 5.

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.10 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.10 Evaluate the following integrals: Question 1. dx Solution: Let I = dx. Put x2 + 1 = t, 2x dx = dt. When x = 1,

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.9 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.9 Evaluate the following definite integrals: Question 1. (x + 1)dx Solution: Question 2. dx Solution: = log 3 – log 2 = log . Question 3.

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.2 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.2 Integrate the following: Question 1. Solution: Question 2. Solution: Question 3. Solution: I = ∫dt = log t + C = log |1 + log x|

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.1 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.1 Find an antiderivative (or integral) of the following by the method of inspection: Question 1. sin 2x Solution: We know that cos 2x = – 2sin

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.5 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.5 Question 1. Solution: A11 = (-1)1+1 M11 = 4 A12 = (-1)1+2 M12 = – 3 A21 = (-1)2+1 M21 = – 2 A22 = (-1)2+2

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.5 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.5 Integrate the following functions: Question 1. Solution: may be written as = + ∴ x = A(x + 2) + B(x + 1) Put x =

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.4 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.4 Integrate the following functions: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: Question 7. Solution: Question

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 9 Differential Equations Ex 9.2 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 9 Differential Equations Ex 9.2 In each of the questions 1 to 10, verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 3 Matrices Miscellaneous Exercise Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 3 Matrices Miscellaneous Exercise Question 1. Let A = . Show that (aI + bA)n + nan-1bA, where I is the identity matrix of order n ∈ N Solution: Apply

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.4 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.4 Write minors and cofactors of elements of the following determinants: Question 1. (i) (ii) Solution: (i) ∆ = Minor of a11 is M11 = 3, Minor

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.3 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.3 Question 1. Find the area of the triangle with vertices at the points given in each of the following: (i) (1, 0), (6, 0), (4, 3)

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.2 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.2 Question 1. = 0 Solution: Operating C1 → C1 + C2, we get = = 0, since 1st and 3rd columns are identical. Question 2. =