JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Sets Relations and Functions

The number of relations, defined on the set $\{\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\}$, which are both reflexive and symmetric, is equal to:

Let $\mathrm{A}=\{2,3,5,7,9\}$. Let R be the relation on A defined by x Ry if and only if $2\mathrm{x}\le 3\mathrm{y}$. Let $\ell$ be the number of elements in R, and m be the minimum number of elements required to be added in R to make it a symmetric relation. Then …

Let the relation R on the set $\mathrm{M}=\{1,2,3,\dots ,16\}$ be given by
$\mathrm{R}=\{(\mathrm{x},\mathrm{y}):4\mathrm{y}=5\mathrm{x}-3,\mathrm{x},\mathrm{y}\in \mathrm{M}\}$.
Then the minimum number of elements required to be added in R, in order to make the relation …

If the domain of the function $f(x)={\sin }^{-1}\left(\frac{5-x}{3+2x}\right)+\frac{1}{{\log }_e(10-x)}$ is $(-\infty ,\alpha ]\cup [\beta ,\gamma )-\{\delta \}$, then $6(\alpha +\beta +\gamma +\delta )$ is equal to

The number of elements in the relation $R=\{(x,y):4x^2+y^2<52,x,y\in \mathbb{Z}\}$ is

Let the domain of the function
$\mathrm{f}(\mathrm{x})={\log }_3{\log }_5\left(7-{\log }_2\left({\mathrm{x}}^2-10\mathrm{x}+85\right)\right)+{\sin }^{-1}\left(\left|\frac{3\mathrm{x}-7}{17-\mathrm{x}}\right|\right)$ be $(\alpha ,\beta ]$. Then $\alpha +\beta$ is equal to :