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

MathematicsLet the function \(f:\mathbb{R}\to\mathbb{R}\) be defined by \(f(x)=|3x+2|-6\). Which of the following statements is correct?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 33Expert MathematicsWhat is the domain of the function \(f(x)=\frac{x+1}{\sqrt{x^2-4}}\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 32Expert MathematicsWhich statement is correct about the function \(f:\mathbb{R}\to\mathbb{R}\), where \(f(x)=x^3-3x\)?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 32Hard MathematicsWhat is called the range of a function?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 32Easy MathematicsIn the function \(f:A\to\mathbb{R}\), what does the set \(A\) represent?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 31Easy MathematicsIf (f:mathbb{R} omathbb{R}) has range ([5,infty)) and (f(x)=a(x-2)^2+b), where (a>0), which of the following pairs is possible?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 30Expert MathematicsIf the function \(f:\{1,2,3,4,5,6,7,8,9\}\to\{0,1\}\) is defined by \(f(n)=1\) when \(n\) is divisible by \(3\), and \(f(n)=0\) otherwise, what is \(f^{-1}(\{1\})\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 30Expert MathematicsIf (A={1,2,3,4,5,6}) and (B={a,b}), how many functions from (A) to (B) satisfy (f(2)=a) or (f(5)=b)?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 30Expert MathematicsIf A = {1,2,3,4,5}, B = {1,2,3,4,5}, and R = {(x,y): x + y is odd}, why is R not a function?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 30Medium 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 relationLevel 30Hard 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 relationLevel 30Expert 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 MathematicsIf the function \(f:\{1,2,3,4,5,6,7,8\}\to\{0,1\}\) is defined by \(f(n)=1\) when \(n\) is divisible by \(4\), and \(f(n)=0\) otherwise, what is \(f^{-1}(\{1\})\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 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 (A={1,2,3,4,5}) and (B={a,b}), how many functions from (A) to (B) satisfy (f(1)=a) or (f(5)=b)?Class 11Relations and FunctionsFunctions as a special kind of relationLevel 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}) 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 29Expert MathematicsIf \(f:\{1,2,3,4,5,6\}\to\{0,1\}\) is defined by \(f(n)=0\) when \(n\) is divisible by \(3\), and \(f(n)=1\) otherwise, what is \(f^{-1}(\{0\})\)?Class 11Relations and FunctionsReal-Valued Functions, Their Domain and RangeLevel 28Expert