Class 12

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 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 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 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 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 4.4 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 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 4.3 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. =

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.1 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 4 Determinants Ex 4.1 Question 1. Solution: = 2 x (-1) – 4 x (-5) = – 2 + 20 = 18 Question 2. (i) (ii) Solution: (i) = cos

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 3 Matrices Ex 3.3 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 3 Matrices Ex 3.3 Question 1. Find the transpose of each of the following matrices: (i) (ii) (iii) Solution: Question 2. If A = + B = , then verify

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 2 Inverse Trigonometric Functions Ex 2.1 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 2 Inverse Trigonometric Functions Ex 2.1 Find the principal values of the following: Question 1. sin-1(-) Solution: Let sin-1(-) = y ∴ sin y = = – sin

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 1 Relations and Functions Miscellaneous Exercise Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 1 Relations and Functions Miscellaneous Exercise Question 1. Let R → R be defined as f(x) = 10x + 7. Find the function g : R → R

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 1 Relations and Functions Ex 1.4 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 1 Relations and Functions Ex 1.4 Question 1. Determine whether or not each of the definitions of * given below gives a binary operation. In the event that

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 1 Relations and Functions Ex 1.3 Textbook Questions and Answers. Gujarat Board Textbook Solutions Class 12 Maths Chapter 1 Relations and Functions Ex 1.3 Question 1. Let f : {1. 3 4} → {1,2, 5} and g: {1, 2, 5} → {1,3} be given by f