Chapter 3

Chapter 3:Miscellaneous Exercise Prove that(Class 11 Chapter 3 Miscellaneous Exercise trigonometry ) Question 1: Solution: Given, Using formula Question 2: Solution: Taking Using formula: and Question 3: Solution: Taking Using formula: and ) Question 4: Solution: Taking Using formulae: and ) Question 5: Solution: Taking Using formulae: Again using formula: Question 6:  Solution: Taking Using … Read more

 EXERCISE 3.4(Trigonometric function) Find the principal and general solutions of the following equations(Ex 3.4 Trigonomety ncert maths solution class 11) Question 1: Solution: Given, Since ‘‘ positive in Ist and IIIrd quadrant Then, Hence the principal solution are Given, Hence the general solution is Question 2: Solution: Given, Since ‘‘ positive in Ist and IVth … Read more

  EXERCISE 3.2(Trigonometric Function) Find the values of other five trigonometric functions in Exercises 1 to 5.(Ex 3.2 Trigonomety ncert maths solution class 11) Question 1: , x lies in third quadrant. Solution: Given, Since, We know that Since x lies in third quadrant We know that Since, Now Question 2: , x lies in … Read more

 EXERCISE 3.1(Trigonometric function) 1. Find the radian measures corresponding to the following degree measures:(Ex 3.1 Trigonometric function ncert solution class 11) (i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520° Solution: (i) Since, Radian Then, (ii) And degree Then, degree Since, Radian Then, Radian (iii) Since, Radian Then, radian (iv) Since, radian Then, radian … Read more

EXERCISE 3.3 (Matrix) class 12 maths exercise 3.3 solution Question1: Find the transpose of each of the following matrices: (i) (ii) (iii) Solution: (i) Let Then (ii) Let Then (iii) Let Then Question2: and Then verify that (i) (ii) Solution:  (i) and Now Hence (ii)  Then Thus Question 5: For the matrices A and B, … Read more

Chapter 3 ( Miscellaneous) class 12 maths chapter 3 Miscellaneous solution Question 1: Let ,show that , where I is the identity matrix of order 2 and. Solution: It is given that LHS. RHS. Since, Hence, We shall prove the result by using the principle of mathematical induction. For n=1, we have: P(1): Therefore, the … Read more

 EXERCISE 3.2 (MATRIX) Class 12 ncert solution math exercise 3.2 matrix Question 1: A= ,B=,C= Find each of the following (a) (b) (c) (d) (e) Solution:(a) (b) (c) (d) (e) Question 2: Compute the following: (a) (b) (c) (d) Solution: (a) (b) (c)  (d)  Question 3: Compute the indicated products: (a) (b) (c) (d) (e) … Read more

EXERCISE 3.1 (MATRIX) Class 12 ncert solution math exercise 3.1 matrix Question 1: (i) The order of the matrix (ii) The number of elements (iii) Write the elements Solution: (i) Since, in the given matrix, the number of rows is 3 and the number of columns is 4 , the order of the matrix is … Read more