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Relations And Functions

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsA student says about the function \(h:\mathbb{R}\to\mathbb{R}\), where \(h(x)=x^3-3x\): “Since \(h(1)=h(-2)=-2\), \(h\) is not onto.” What is the correct evaluation of this statement?Class 12Relations and FunctionsOnto functionLevel 25ExpertMathematicsIf (f:\mathbb{R}\to \mathbb{R}) is defined by (f(x)=\begin{cases}x^2,&x\ge0\-x^2,&x<0\end{cases}), choose the correct statement about (f).Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsChoose the correct option for (f:\mathbb{R}\to \mathbb{R}), (f(x)=x^3+e^x).Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsIf (f:(-\infty,1]\to [0,\infty)), (f(x)=x^2-2x+1), what is the correct statement about (f)?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsWhat is the correct conclusion for (f:[1,\infty)\to [0,\infty)), (f(x)=x^2-2x+1)?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsIf (f:\mathbb{R}\to [1,\infty)), (f(x)=\sqrt{x^2+1}), what type is (f)?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsIf (f:\mathbb{R}\to \mathbb{R}), (f(x)=\sqrt{x^2+1}), choose the correct option about (f).Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsWhat is the correct conclusion about (f:\mathbb{R}\to [4,\infty)), (f(x)=|x-2|+|x+2|)?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsIf (f:\mathbb{R}\to [0,\infty)), (f(x)=|x-2|+|x+2|), what is the correct statement?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsIf (f:\mathbb{R}\to \mathbb{R}), (f(x)=\lceil x\rceil), what type is (f)?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsWhat is the correct conclusion for (f:\mathbb{R}\to \mathbb{Z}), (f(x)=\lceil x\rceil)?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsIf (f:\mathbb{Z}\to {n\in\mathbb{Z}:n\ge0}), (f(n)=n^2), what is correct about (f)?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsChoose the correct statement for (f:\mathbb{Z}\to \mathbb{Z}), (f(n)=n^2).Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsIf (f:\mathbb{Z}\to {0,1,2}), where (f(n)) is the remainder when (n) is divided by (3), what type is (f)?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsWhat is the correct conclusion for \(f:\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\to [-1,1]\), \(f(x)=\sin x\)?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsIf \(f:\left[0,\frac{\pi}{2}\right]\to [-1,1]\), \(f(x)=\sin x\), which statement is correct?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsChoose the correct option for (f:[0,\pi]\to [-1,1]), (f(x)=\cos x).Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsIf (f:[-1,1]\to [0,1]), (f(x)=x^3), what is the correct conclusion about (f)?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsWhich statement is correct about (f:[-1,1]\to [-1,1]), (f(x)=x^3)?Class 12Relations and FunctionsOnto functionLevel 25HardMathematicsIf (f:\mathbb{R}\to \mathbb{R}), (f(x)=x^5-x), what type is (f)?Class 12Relations and FunctionsOnto functionLevel 25Hard