# Tag Archives: NCERT Solutions Class-12

Chapter 4 Determinants- Exercise 4.2 | Set 1 Question 11. (i) (ii) Solution: (i) L.H.S.= ∵ L.H.S.=R.H.S Hence proved (ii)  ∵ L.H.S.=R.H.S Hence proved Question… Read More
Using the properties of determinants and without expanding in Exercise 1 to 7, prove that: Question 1.  Solution: L.H.S.=            … Read More
Question 1. Find the transpose of each of the following matrices: (i)   (ii)  (iii)  Solution: (i) Let A = ∴Transpose of A = A’ =… Read More
Question 1. Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A={ 1, 2,3, . .… Read More
Write minors and cofactors of the elements of the following determinants:  Question 1.  (i)  (ii)  Solution:  (i)  Finding minors of the elements of the determinant: … Read More
Question 1. Find area of the triangle with vertices at the point given in each of the following :  (i) (1, 0), (6, 0), (4,… Read More
Chapter 3 Matrices – Exercise 3.4 | Set 1  Question 11.  Solution: } Question 12.  Solution: Here, both the elements of R2 of L.H.S. are… Read More
Using elementary transformations, find the inverse of each of the matrices, if it exists in Exercises 1 to 6. Question 1. Solution: Question 2. Solution:… Read More
Chapter 4 Determinants   – Exercise 4.6 | Set 1 Question 11. 2x + y + z = 1             … Read More
Examine the consistency of the system of equations in Exercises 1 to 6. Question 1. x + 2y = 2          … Read More
Question 1.  Let f : {1, 3, 4} -> {1, 2, 5} and g : {1, 2, 5} -> {1, 3} be given by f… Read More
Chapter 1 Relations And Functions – Exercise 1.1 | Set 1 Question 11. Show that the relation R in the set A of points in… Read More
Question 1. Show that the function f: R* ⇢ R* defined by f(x)=(1/x) is one-one and onto, where R* is the set of all non-zero… Read More
Evaluate the determinants from the following Questions. Question 1.  Solution: The determinant of a 2 x 2 matrix  Hence,  Question 2. (i)  Solution:  from trigonometric… Read More
Find the principal values of the following: Question 1. sin-1(-1/2) Solution: Let sin-1(-1/2) = y then, sin y = -1/2 Range of principal value for… Read More