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Functions As A Special Kind Of Relation

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

MathematicsWhat is the range of (R={(x,y):y=\frac{x}{x-1},\ x\in{0,2,3},\ y\in\mathbb{R}})?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (f:A\to B) and (|A|=2), (|B|=4), what are the numbers of all relations and all functions respectively?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (f:[0,4]\to\mathbb{R}) is given by (f(x)=\sqrt{x}+\sqrt{4-x}), what is the maximum value of (f)?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsA relation (R\subseteq A\times B) has (A={1,2,3}) and (B={p,q}). If (R) has exactly (3) ordered pairs, when will (R) be a function?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (f:\mathbb{R}-{-1}\to\mathbb{R}) is given by (f(x)=\frac{x^2-1}{x+1}), which value will not belong to the range?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsWhich option gives a valid function (f:\mathbb{N}\to\mathbb{N})?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (f:{1,2,3,4}\to{1,2,3,4}) is given by (f(x)=5-x), which statement about the inverse relation (f^{-1}) is correct?Class 11Relations and FunctionsFunctions as a special kind of relationExpert 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 relationExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is to be defined by (f(x)=\frac{1}{x^2+ax+1}), which condition on (a) makes it a function on all of (\mathbb{R})?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsThe relation (R={(x,y):x^2+y^2=1,\ x\in{-1,0,1},\ y\in{-1,0,1}}) is considered from (X={-1,0,1}) to (Y={-1,0,1}). Why is it not a function?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (f:A\to B) is a function and its graph is a subset of (A\times B), which statement is always true?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (A=\emptyset) and (B=\emptyset), what is the number of functions from (A) to (B)?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsThe function (f:[-1,3]\to\mathbb{R}) is given by (f(x)=|x-1|+|x-3|). What is its range?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsWhich option is not a function from (A={1,2,3,4}) to (B={a,b,c}) even though every element of (A) occurs as a first component?Class 11Relations and FunctionsFunctions as a special kind of relationExpert 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 relationExpert MathematicsIf (f:\mathbb{R}-{2}\to\mathbb{R}) is given by (f(x)=\frac{x^2-4}{x-2}), what is the range?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsWhat is the correct conclusion about (R={(x,y):xy=6,\ x\in{1,2,3,6},\ y\in{1,2,3,6}})?Class 11Relations and FunctionsFunctions as a special kind of relationExpert 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 relationMedium MathematicsA function (f:\mathbb{R}\to\mathbb{R}) is to be defined by (f(x)=\sqrt{ax^2+4}). What is the correct condition on (a) for it to be a function on all of (\mathbb{R})?Class 11Relations and FunctionsFunctions as a special kind of relationExpert 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 relationExpert