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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।

MathematicsIf (A={1,2,3,4}) and (B={0,1,2}), how many functions from (A) to (B) satisfy (f(1)=f(2)) and (f(3)\ne f(4))?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (A=\emptyset) and (B={1,2,3}), how many functions are there from (A) to (B)?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsIf (f:A\to B) is a function and (A) is not an empty set, what is the correct conclusion if (f) is the empty relation?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsWhich option gives a function from (A={1,2,3,4}) to (B={0,1})?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) has (f(x)=\frac{x-a}{x^2-4}), which statement is correct?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsIf (f:\mathbb{R}\to[0,\infty)) is given by (f(x)=x^2+2x+2), what is the range?Class 11Relations and FunctionsFunctions as a special kind of relationHard 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 relationMedium 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 relationHard MathematicsIf (f:{1,2,3,4}\to{1,2,3,4}) is given by (f(x)=x) when (x) is even and (f(x)=5-x) when (x) is odd, what is the range?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsIf (A={1,2,3}) and (B={1,2}), how many subsets of (A\times B) are functions from (A) to (B)?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsWhich piecewise rule will not define a function on (\mathbb{R})?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\begin{cases}x+1,&x<0\x^2,&x\ge0\end{cases}), what is (f(0))?Class 11Relations and FunctionsFunctions as a special kind of relationHard 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 relationMedium MathematicsWhich option gives a valid function (g:\mathbb{N}\to\mathbb{N})?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsIf (A={a,b,c}) and (B={1,2,3,4}), how many functions from (A) to (B) satisfy (f(a)=2)?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is to be given by (f(x)=\sqrt{4-x^2}), which is the correct domain?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsWhat is the range of the relation (R={(x,y):y=\frac{x}{|x|},\ x\in{-3,-2,-1,1,2,3}})?Class 11Relations and FunctionsFunctions as a special kind of relationHard 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 relationMedium MathematicsIf (f:{1,2,3,4,5}\to{0,1}) is given by (f(x)=0) when (x) is even and (f(x)=1) when (x) is odd, what is (f^{-1}({0}))?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2), why is (f^{-1}) as a relation not a function from (\mathbb{R}) to (\mathbb{R})?Class 11Relations and FunctionsFunctions as a special kind of relationHard