JEE MAIN Function Previous Year Questions (PYQs) – Page 15 of 15
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Let $f(x)=\log_e x$ and $g(x)=\dfrac{x^{4}-2x^{3}+3x^{2}-2x+2}{2x^{2}-2x+1}$. Then the domain of $f\circ g$ is:
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Solution
If $f(x) =
\begin{cases}
\int_{0}^{x} \left( 5 + |1 - t| \right) dt, & x > 2 \\
5x + 1, & x \leq 2
\end{cases}$, then
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Solution
If the domain of the function
$\sin^{-1}\!\left(\dfrac{3x-22}{2x-19}\right)+\log_e\!\left(\dfrac{3x^2-8x+5}{x^2-3x-10}\right)$
is $(\alpha,\beta)$, then $3\alpha+10\beta$ is equal to:
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Solution
Let $R$ be a relation on $\mathbb{R}$, given by $R=\{(a,b):\,3a-3b+\sqrt{7}\text{ is an irrational number}\}$. Then $R$ is:
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Solution
Let $f(x)=
\begin{cases}
x^{3}-x^{2}+10x-7, & x\le 1,\\
-2x+\log_{2}(b^{2}-4), & x>1.
\end{cases}$
Then the set of all values of $b$ for which $f(x)$ has maximum value at $x=1$ is:
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Solution
Let $S=\left\{x:\ x\in\mathbb{R}\ \text{and}\ (\sqrt{3}+\sqrt{2})^{\,x^{2}-4}+(\sqrt{3}-\sqrt{2})^{\,x^{2}-4}=10\right\}$. Then $n(S)$ is equal to:
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Solution
Let $f,g:(1,\infty)\to\mathbb{R}$ be defined as $f(x)=\dfrac{2x+3}{5x+2}$ and $g(x)=\dfrac{2-3x}{1-x}$. If the range of the function $f\circ g:[2,4]\to\mathbb{R}$ is $[\alpha,\beta]$, then $\dfrac{1}{\beta-\alpha}$ is equal to
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Solution
JEE MAIN
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