Home Question Details Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 7 Question Type Exercise More Details Previous Question Next Question Show that the relation R in the set A of all the books in a library of a college, given by (mathrm{R}={(x, y): x)
Abstract ClassesHome Previous Question Next Question Factor Theorem : If (p(x)) is a polynomial of degree (n geq 1) and (a) is any real number, then (x-a) is a factor of (p(x)), if and only if (p(a)=0). Proof: By the Remainder Theorem, (p(x)=(x-a) q(x)+p(a)).(i) If (p(a)=0), then (p(x)=(x-a) q(x)), which shows that (x-a) is a factor
Abstract ClassesHome Previous Theorem Next Theorem Remainder Theorem : Let (p(x)) be any polynomial of degree greater than or equal to one and let a be any real number. If (p(x)) is divided by the linear polynomial (x-a), then the remainder is (p(a)). Proof : Let (p(x)) be any polynomial with degree greater than or equal
Abstract ClassesQuestion Details Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 5 Question Type Exercise More Details Previous Question Next Question Check whether the relation (mathrm{R}) in (mathbf{R}) defined by (mathrm{R}=left{(a, b): a leq b^3right}) is reflexive, symmetric or transitive. Expert Answer Solution: (R=left{(a, b): a
Abstract ClassesQuestion Details Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 4 Question Type Exercise More Details Previous Question Next Question Show that the relation (R) in (R) defined as (R={(a, b): a leq b}), is reflexive and transitive but not symmetric. Expert Answer (A=(-infty, infty))
Abstract ClassesQuestion Details Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 3 Question Type Exercise More Details Previous Question Next Question Check whether the relation (R) defined in the set ({1,2,3,4,5,6}) as (mathbf{R}={(a, b): b=a+1}) is reflexive, symmetric or transitive. Expert Answer (mathrm{R}={(mathrm{a}, mathrm{b}): mathrm{b}=mathrm{a}+1}) in
Abstract ClassesQuestion Details Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 2 Question Type Exercise More Details Previous Question Next Question Question-2. Show that the relation (mathbf{R}) in the set (mathbf{R}) of real numbers, defined as (mathrm{R}=left{(a, b): a leq b^2right}) is neither reflexive nor symmetric
Abstract ClassesQuestion Details Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 1 Question Type Exercise More Details Previous Question Next Question Question 1. Determine whether each of the following relations are reflexive, symmetric and transitive : (i) Relation (R) in the set (A={1,2,3, ldots ldots, 13,14})
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