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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।

MathematicsThe relation R = {(x,y): y² = x − 1, x ∈ {2,5,10}, y ∈ {−3,−2,−1,1,2,3}} is considered from X = {2,5,10} to Y = {−3,−2,−1,1,2,3}. What is the correct conclusion?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 30Hard MathematicsIf A = {1, 2} and B = {a, b, c}, how many subsets of A × B are not functions from A to B?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 29Hard MathematicsIf \(f:\mathbb{R}\to\mathbb{R}\) has range \([-2,\infty)\) and \(f(x)=(x-a)^2+b\), which of the following pairs \((a,b)\) is possible?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 29Expert MathematicsIf A = {1, 2, 3, 4, 5} and B = {0, 1}, how many functions f: A → B have at least two inputs with image 1?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 29Hard MathematicsFor the function defined by \(f(x)=\frac{1}{|x+1|-3}\), what is its largest possible real domain?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 29Expert MathematicsIf \(f:\{1,2,3,4,5\}\to\{1,2,3\}\) is defined by \(f(x)=\max(1,4-x)\), what is its range?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 29Expert MathematicsIf f: ℝ → ℝ is given by f(x) = (x² + 4)/(x² + 1), what is its range?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 29Hard MathematicsThe relation \(R=\{(x,y): |x+y|=2,\ x\in\{-2,0,2\},\ y\in\{-4,-2,0,2,4\}\}\) is considered from the domain \(\{-2,0,2\}\) to the codomain \(\{-4,-2,0,2,4\}\). Why is this relation not a function?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 29Expert MathematicsIf f: {0, 1, 2, 3} → {0, 1, 2, 3} is given by f(x) = x² − 2x + 1, is f a valid function?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 29Medium MathematicsIf \(f:\{0,1,2,3,4\}\to\{0,1,2,3,4\}\) is defined by the remainder obtained when \(3x\) is divided by \(5\), what is the range of \(f\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 29Expert MathematicsIf A = {1, 2, 3, 4}, B = {1, 2, 3, 4}, and R = {(x, y): x − y is odd}, why is R not a function?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 29Medium MathematicsIf \(A=\{1,2,3,4,5,6\}\) and \(B=\{0,1\}\), how many functions from \(A\) to \(B\) have exactly 3 inputs whose image is 1?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 29Expert MathematicsThe relation R = {(x,y): x² + y² = 4, x ∈ {-2,0,2}, y ∈ {-2,0,2}} is considered from X to Y. Why is it not a function?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 29Medium MathematicsIn which option is the relation not a function from A = {0,1,2,3} to B = {p,q,r}, even though every element of A appears as a first component?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 29Medium MathematicsIf f: R → R is given by f(x) = {x + 1 for x ≤ 2; x² for x ≥ 2}, why is it not a function?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 28Hard MathematicsIf A={1,2,3,4} and B={0,1}, how many functions f:A→B have at least one input with image 1?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 28Expert MathematicsIf \(f:\mathbb{R}\to\mathbb{R}\) is defined by \(f(x)=\begin{cases}x+2,&x<0\\x^2,&x>0\end{cases}\), why is it not a function from \(\mathbb{R}\) to \(\mathbb{R}\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 28Expert MathematicsThe relation R = {(x,y): |x-y| = 1, x ∈ {1,2,3}, y ∈ {1,2,3,4}} is considered from X to Y. Why is it not a function?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 28Medium MathematicsIf f: {1,2,3,4} → {1,2,3,4} is given by f(x) = x² - 4x + 5, which statement is correct?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 28Medium MathematicsIf f: R → R is given by f(x) = x² + 2x + 5, what is the range of f?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 28Medium