JEE MAIN Function Previous Year Questions (PYQs) – Page 14 of 15
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The remainder when $(11)^{1011} + (1011)^{11}$ is divided by $9$ is
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Solution
Let $f:\mathbb{R}-\{2,6\}\to\mathbb{R}$ be the real-valued function defined as $f(x)=\dfrac{x^{2}+2x+1}{x^{2}-8x+12}$. Then the range of $f$ is:
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If the domain of the function $f(x)=\log_{7}!\big(1-\log_{4}(x^{2}-9x+18)\big)$ is $(\alpha,\beta)\cup(\gamma,\delta)$, then $\alpha+\beta+\gamma+\delta$ is equal to
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Let g : N $\to$ N be defined as g(3n + 1) = 3n + 2, g(3n + 2) = 3n + 3, g(3n + 3) = 3n + 1, for all n $\ge$ 0. Then which of the following statements is true?
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Solution
Let $A=\{1,2,3,4\}$ and $B=\{1,4,9,16\}$. Then the number of many-one functions $f:A\to B$ such that $1\in f(A)$ is equal to:
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Let $f:[0,\infty ) \to [0,\infty )$ be defined as $f(x) = \int_0^x {[y]dy} $ where [x] is the greatest integer less than or equal to x. Which of the following is true?
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Solution
Let $f:\mathbb{R}\to\mathbb{R}$ be a continuous function satisfying $f(0)=1$ and $f(2x)-f(x)=x$ for all $x\in\mathbb{R}$. If $\lim_{n\to\infty}{f(x)-f\left(\dfrac{x}{2^{n}}\right)}=G(x)$, then $\displaystyle \sum_{r=1}^{10} G(r^{2})$ is equal to
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For $x \in (0, 3/2)$, let $f(x) = \sqrt{x}$, $g(x) = \tan x$ and $h(x) = \dfrac{1 - x^2}{1 + x^2}$.
If $\phi(x) = (h \circ f \circ g)(x)$, then $\phi\left(\dfrac{\pi}{3}\right)$ is equal to :
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Solution
Let $f:\mathbb{R}\to\mathbb{R}$ be a continuous function such that
$f(3x) - f(x) = x$.
If $f(8) = 7$, then $f(14)$ is equal to :
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Solution
Let $f(x)=x^5+2e^{x/4}$ for all $x\in\mathbb R$.
Consider a function $g(x)$ such that $(g\circ f)(x)=x$ for all $x\in\mathbb R$.
Then the value of $8g'(2)$ is:
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Solution
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