RD Sharma Chapter 3 : Binary Operation Exercise 3.1 Solutions Determine whether the operation define a binary operation or not: ′⋆′on N defined by a∗b=ab ∀ a,b∈N Watch Solution Determine whether the operation define a binary operation or not:‘O’ on Z defined by aOb=ab ∀ a,b∈ Z Watch Solution Determine whether the operation define a […]
RD Sharma Chapter 2 : Functions Multiple Choice Questions (MCQs) Solutions Let A = {xϵR :–1≤x≤1} =B and C={xϵR :X ≥ 0} and let S={(x, y) ϵA×B :x^2+y^2=1} and S0={(x, y)ϵA×C :x^2+y^2=1} Then A. S defines a function from A to B B. S0 defines a function from A to C C. S0 defines a
RD Sharma Chapter 2 : Functions Very Shorts Answer Questions Solutions Which one of the following graphs represent a function ? Watch Solution Which one of the following graphs represent a one-one function ? Watch Solution If A = {1, 2, 3} and B = {a, b}, write total number of functions from A to
RD Sharma Chapter 2 : Functions Exercise 2.4 Solutions State with reasons whether the following function has inverse : (i) f : [1, 2, 3, 4] → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)} Watch Solution State with reasons whether the following function has inverse : (ii) g : {5, 6,
RD Sharma Chapter 2 : Functions Exercise 2.3 Solutions Find fog and gof, if f(x) = e^x ,g(x) = loge x Watch Solution Find fog and gof, if f(x) = x^2 ,g(x) = cos x Watch Solution Find fog and gof, if f(x) = ∣x∣, g(x) = sin x Watch Solution Find fog and gof, if
RD Sharma Chapter 2 : Functions Exercise 2.2 Solutions Find gof and fog when f: R → R and g: R → R is defined by f(x) = 2x+3 and g(x) = x^2 +5 Watch Solution Find gof and fog when f: R → R and g: R → R is defined by f(x) = 2x
RD Sharma Chapter 2 : Functions Exercise 2.1 Solutions (Step-by-Step Guide) Give an example of a function (i) Which is one – one but not onto. Watch Solution Give an example of a function (ii) Which is not one – one but onto. Watch Solution Give an example of a function (iii) Which is neither
RD Sharma Chapter 1: Relations Multiple Choice Questions (MCQs) Solutions Let R be a relation on the set N given by R = {a, b) : a = b – 2, b greater than 6}. Then (a) (2, 4) ∈ R (b) (3,8) ∈ R (c) (6, 8) ∈ R (d) (8,7) ∈ R Watch Solution
RD Sharma Chapter 1 : Relation Very Shorts Question Answer (VSAQs) Solutions Write the domain of the relation R defined on the set Z of integers as follows: (a, b) ϵ R ⟺ a^2 + b^2 = 25 Watch Solution If R = {( x ,y): x^2 + y^2 ≤ 4; x ,y ϵ Z} is
RD Sharma Chapter 1 : Relation Exercise 1.2 Solutions Show that the relation R defined by R = {(a, b): a – b is divisible by 3; a, b ∈ Z} is an equivalence relation. Watch Solution Show that the relation R on the set Z of integers, given by R = {(a, b) :