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MCQ (Single Correct Answer)

MHT CET 2024 16th May Morning Shift
Range of the function $\mathrm{f}(x)=\frac{x^2+x+2}{x^2+x+1}, x \in \mathbb{R}$ is
MHT CET 2024 15th May Evening Shift
If $[x]^2-5[x]+6=0$, where $[\cdot]$ denotes the greatest integer function, then
MHT CET 2024 15th May Morning Shift
Let $\mathrm{f}(x)=(x+1)^2-1, x \geqslant-1$, then the set $\left\{x / f(x)=f^{-1}(x)\right\}$ is
MHT CET 2024 11th May Evening Shift
If $\mathrm{f}:[1, \infty) \rightarrow[2, \infty)$ is given by $\mathrm{f}(x)=x+\frac{1}{x}$ then $\mathrm{f}^{-1}(x)$ equals
MHT CET 2024 11th May Morning Shift
If $[x]^2-5[x]+6=0$, where $[x]$ denotes the greatest integer function, then
MHT CET 2024 10th May Evening Shift
Let $\mathrm{f}(x)=\frac{a x}{x+1}, x \neq-1$, then for $\alpha=$ ________, $\mathrm{f}(\mathrm{f}(x))=x$.
MHT CET 2024 10th May Morning Shift
The domain of definition of the function $y(x)$ is given by the equation $2^x+2^y=2$, is
MHT CET 2024 9th May Evening Shift
The domain of definition of the function $f(x)$ given by the equation $2^x+2^y=2$ is
MHT CET 2024 4th May Evening Shift
If $\mathrm{f}(x)=\frac{x}{2-x}, \mathrm{~g}(x)=\frac{x+1}{x+2}$, then (gogof) $(x)=$
MHT CET 2024 3rd May Evening Shift
The domain of definition of $\mathrm{f}(x)=\frac{\log _2(x+3)}{x^2+3 x+2}$ is
MHT CET 2024 3rd May Morning Shift
If $g(x)=x^2+x-1$ and (gof) $(x)=4 x^2-10 x+5$, then $\mathrm{f}(2)$ is equal to
MHT CET 2024 2nd May Morning Shift
For a suitable chosen real constant a, let a function $f: \mathbb{R}-\{-\mathrm{a}\} \rightarrow \mathbb{R}$ be defined by $f(x)=\frac{a-x}{a+x}$. Fur...
MHT CET 2023 14th May Evening Shift
If $$\mathrm{f}(x)=\frac{2 x-3}{3 x-4}, x \neq \frac{4}{3}$$, then the value of $$\mathrm{f}^{-1}(x)$$ is
MHT CET 2023 14th May Morning Shift
The range of the function $$\mathrm{f}(x)=\frac{x^2}{x^2+1}$$ is
MHT CET 2023 14th May Morning Shift
The function $$\mathrm{f}(x)=[x] \cdot \cos \left(\frac{2 x-1}{2}\right) \pi$$, where $$[\cdot]$$ denotes the greatest integer function, is discontinu...
MHT CET 2023 13th May Evening Shift
The domain of the definition of the function $$y(x)$$ is given by the equation $$2^x+2^y=2$$ is
MHT CET 2023 13th May Morning Shift
If $$3 \mathrm{f}(x)-\mathrm{f}\left(\frac{1}{x}\right)=8 \log _2 x^3, x>0$$, then $$\mathrm{f}(2), \mathrm{f}(4)$$, $$f(8)$$ are in
MHT CET 2023 12th May Evening Shift
If $$\mathrm{f}(x)=x^2+1$$ and $$\mathrm{g}(x)=\frac{1}{x}$$, then the value of $$\mathrm{f}(\mathrm{g}(\mathrm{g}(\mathrm{f}(x))))$$ at $$x=1$$ is...
MHT CET 2023 12th May Morning Shift
If $$\mathrm{g}(x)=1+\sqrt{x}$$ and $$\mathrm{f}(\mathrm{g}(x))=3+2 \sqrt{x}+x$$ then $$\mathrm{f}(\mathrm{f}(x))$$ is
MHT CET 2023 12th May Morning Shift
The approximate value of $$\sin \left(60^{\circ} 0^{\prime} 10^{\prime \prime}\right)$$ is (given that $$\sqrt{3}=1.732,1^{\circ}=0.0175^{\circ}$$ )...
MHT CET 2023 11th May Evening Shift
If $$\mathrm{f}(x)=\frac{3 x+4}{5 x-7}$$ and $$\mathrm{g}(x)=\frac{7 x+4}{5 x-3}$$, then $$\mathrm{f}(\mathrm{g}(x))=$$
MHT CET 2023 11th May Morning Shift
The domain of the function given by $$2^x+2^y=2$$ is
MHT CET 2023 10th May Evening Shift
Let $$\mathrm{f}(x)=\mathrm{e}^x-x$$ and $$\mathrm{g}(x)=x^2-x, \forall x \in \mathrm{R}$$, then the set of all $$x \in \mathrm{R}$$, where the functi...
MHT CET 2023 10th May Morning Shift
$$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R} ; \mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$$ are two functions such that $$\mathrm{f}(x)=2 x-3, \...
MHT CET 2023 9th May Morning Shift
$$\mathrm{f}: \mathbb{R}-\left(-\frac{3}{5}\right) \rightarrow \mathbb{R}$$ is defined by $$f(x)=\frac{3 x-2}{5 x+3}$$, then $$f \circ f(1)$$ is...
MHT CET 2023 9th May Morning Shift
The number of discontinuities of the greatest integer function $$\mathrm{f}(x)=[x], x \in\left(-\frac{7}{2}, 100\right)$$
MHT CET 2022 11th August Evening Shift
If $$[x]$$ is greatest integer function and $$2[2 x-5]-1=7$$, then $$x$$ lies in
MHT CET 2021 24th September Evening Shift
If $$f(x)=2\{x\}+5 x$$, where $$\{x\}$$ is fractional part function, then $$f(-1.4)$$ is
MHT CET 2021 24th September Morning Shift
If $$f(x)=\frac{x}{2 x+1}$$ and $$g(x)=\frac{x}{x+1}$$, then $$(f \circ g)(x)=$$
MHT CET 2021 23rd September Evening Shift
The domain of the function $$\log _{10}\left(x^2-5 x+6\right)$$ is
MHT CET 2021 23th September Morning Shift
Range of the function $$f(x)=3+2^x+4^x$$ is
MHT CET 2021 22th September Evening Shift
If $$f(x)=[8 x]-3$$, where $$[x]$$ is greatest integer function of $$x$$, then $$f(\pi)=$$ (where $$\pi=3,14$$)
MHT CET 2021 22th September Morning Shift
The domain of the function $$f(x)=\sqrt{x-1}+\sqrt{6-x}$$ is
MHT CET 2021 21th September Morning Shift
If f(x) = 3[x] + 5{x + 1}, where [x] is greatest integer function of x and {x} is fractional part function of x, then f($$-$$1.32) =
MHT CET 2021 20th September Evening Shift
Let $$A=[a, b, c, d], B=[1,2,3]$$. Relation $$R_1, R_2, R_3, R_4$$ are as follows : $$\begin{aligned} & R_1=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{...
MHT CET 2021 20th September Morning Shift
The domain of the function $$f(x)=\frac{1}{\sqrt{x+|x|}}$$ is
MHT CET 2020 19th October Evening Shift
The range of the function $f(x)=\frac{x-3}{5-x}, x \neq 5$ is
MHT CET 2020 16th October Evening Shift
For $$f(x)=[x]$$, where $$[x]$$ is the greatest integer function, which of the following is true, for every $$x \in \mathbf{R}$$
MHT CET 2020 16th October Evening Shift
The domain of the function $$f(x)=\sqrt{x}$$ is
MHT CET 2020 16th October Morning Shift
The approximate value of the function $$f(x)=x^3-3 x+5$$ at $$x=1.99$$ is
MHT CET 2020 16th October Morning Shift
If $$f(x)=\frac{2 x+3}{3 x-2}, x \neq \frac{2}{3}$$, then the function $$f$$ of is
MHT CET 2019 3rd May Morning Shift
The domain of the real valued function $f(x)=\sqrt{\frac{x-2}{3-x}}$ is......
MHT CET 2019 3rd May Morning Shift
Which of the following function has period 2?
MHT CET 2019 2nd May Evening Shift
If $f(x)=3 x+6, g(x)=4 x+k$ and $f \circ g(x)=g \circ f(x)$ then $k=$
MHT CET 2019 2nd May Morning Shift
If $f(x)=3 x-2$ and $g(x)=x^2$, then $(f \circ g)(x)=$
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