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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।

MathematicsWhich statement is correct about (R={(x,y):2x+y=12,\ x\in{1,2,3,4},\ y\in{4,6,8,10}})?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (f:\mathbb{Z}\to\mathbb{Z}) is given by (f(n)=\frac{n^5-n}{5}), which statement is correct?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf A = {r, s, t, u} and B = {1, 2, 3, 4}, how many functions from A to B have range exactly {1, 3, 4}?Class 11Relations and FunctionsFunctions as a special kind of relationHard MathematicsA function (f:\mathbb{R}\to\mathbb{R}) is to be defined by (f(x)=\sqrt{a x^2-6a+9}). Which condition on (a) is necessary and sufficient 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): 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 relationHard MathematicsIf (A={1,2,3,4,5,6}) and (B={0,1,2}), how many functions from (A) to (B) satisfy (f(1)=f(2)), (f(3)=f(4)), and (f(5)\ne f(6))?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\begin{cases}2x-1,&x\le3\x+2,&x\ge3\end{cases}), which statement is correct?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\begin{cases}x+3,&x\le1\x^2+1,&x\ge1\end{cases}), why is it not a function?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsWhich statement is correct for (R={(x,y):y=\sqrt{x-1},\ x\in{1,2,5,10},\ y\in{0,1,2,3}})?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (f:A\to B) is a function and (|A|=6), (|B|=4), how many ordered pairs will the graph of (f) contain?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (f:{1,2,3,4,5}\to{1,2,3,4,5}) is given by (f(x)=x) when (x) is prime and (f(x)=6-x) otherwise, what is the range?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (R={(x,y):y=|2x-3|,\ x\in{0,1,2,3}}), why is (R) a function?Class 11Relations and FunctionsFunctions as a special kind of relationExpert 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 relationHard MathematicsIf (R={(x,y):y=\frac{2}{x-1},\ x\in{0,1,2},\ y\in\mathbb{R}}) is considered from (X={0,1,2}) to (\mathbb{R}), what is correct?Class 11Relations and FunctionsFunctions as a special kind of relationExpert 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 relationHard MathematicsIn which option is (R) a function from (A={1,2,3}) to (B={4,5,6}), but (R^{-1}) is not a function?Class 11Relations and FunctionsFunctions as a special kind of relationExpert MathematicsIf (A={1,2,3,4}) and (B={a,b,c,d,e}), how many functions from (A) to (B) have all four images distinct?Class 11Relations and FunctionsFunctions as a special kind of relationExpert 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 relationExpert 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 relationMedium MathematicsIf (R={(x,y):x=y^5,\ x\in{-32,-1,0,1,32},\ y\in{-2,-1,0,1,2}}), which statement about (R) is correct?Class 11Relations and FunctionsFunctions as a special kind of relationExpert