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Relations And Functions

Class 11 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsLet \(R=\{(1,a),(2,b),(3,a)\}\) be a relation from \(A=\{1,2,3\}\) to \(B=\{a,b,c\}\). Which of the following statements is correct?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 28Expert MathematicsIf \(A=\{1,2,3\}\) and \(B=\{0,1,2\}\), how many functions from \(A\) to \(B\) satisfy \(f(1)<f(2)<f(3)\)?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 28Expert MathematicsIf f: Z → Z is given by f(n) = (n² + n)/2, which statement is correct?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 28Medium MathematicsIf \(A=\{a,b,c,d\}\) and \(B=\{1,2,3\}\), how many functions from \(A\) to \(B\) have range exactly \(\{1,2\}\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 28Expert MathematicsThe relation \(R=\{(x,y):y^2=x+1,\ x\in X,\ y\in Y\}\), where \(X=\{0,3,8\}\) and \(Y=\{-3,-2,-1,1,2,3\}\), is considered from \(X\) to \(Y\). What is the correct conclusion?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 28Expert MathematicsIf R = {(x, y): x = |y|, x ∈ {0, 1, 2}, y ∈ {−2, −1, 0, 1, 2}} is considered from X = {0, 1, 2} to Y = {−2, −1, 0, 1, 2}, what is R?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 30Medium MathematicsIf f: A → B has |A| = 5 and |B| = 2, the number of all relations is 2¹⁰. How many of these are functions?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 30Hard MathematicsIf R = {(x, y): y = x², x ∈ [−2, 2], y ∈ [0, 4]}, what is correct about R?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 30Medium MathematicsIf A = {1, 2, 3}, B = {1, 2, 3}, why cannot f(x) = x² be called a function from A to B?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 30Medium MathematicsIf \(A=\{1,2,3\}\), \(B=\{1,4,9,16\}\), and \(R=\{(x,y):y=x^2\}\) is a relation from \(A\) to \(B\), which of the following statements is correct?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 30Hard MathematicsWhat is correct about the relation R = {(x, y): y = |x|, x ∈ {−2, −1, 0, 1, 2}, y ∈ {0, 1, 2}}?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 30Medium MathematicsIf f: ℝ → ℝ is given by f(x) = |x − 2| + 3, what is its range?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 30Medium MathematicsIf A = {1, 2, 3}, B = {0, 1}, and R = {(x, y): y ≡ x (mod 2)}, what is correct about R?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 30Medium MathematicsIf f: ℝ → ℝ is given by f(x) = 1/(x² − 9), what should be the domain to make it a valid real function?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 30Medium MathematicsThe relation \(R=\{(x,y): y^2=x,\ x\in X,\ y\in Y\}\) is defined from \(X=\{1,4,9\}\) to \(Y=\{-3,-2,-1,1,2,3\}\). Why is this relation not a function?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 30Hard MathematicsLet f:{1,2,3}→{2,3,4}, f(x)=x+1, and g:{1,2,3}→{2,3,4,5}, g(x)=x+1. Are f and g equal functions?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 29Medium MathematicsLet \(A=\{1,2,3,4\}\) and define \(f:A\to\mathbb{Z}\) by \(f(x)=(-1)^x\). What is the range of \(f\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 29Hard MathematicsIf in an arrow diagram of a relation, one element of A points to two different elements of B, what is the conclusion?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 29Easy MathematicsLet A={0,1,2,3} and f(x)=x²−3x+2. Which ordered pair will not be in the graph of f?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 29Medium MathematicsLet A={1,2,3,4}, B={a,b}, and f(1)=a, f(2)=a, f(3)=b, f(4)=b. Which statement is correct?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 29Medium