JEE MAIN Inequation Previous Year Questions (PYQs) – Page 1 of 2

Let $A = \{x \in \mathbb{R} : [x + 3] + [x + 4] \le 3\}$, and $B = \left\{ x \in \mathbb{R} : 3^x \left( \sum_{r=1}^{\infty} \frac{3}{10^r} \right)^{x - 3} < 3^{-3x} \right\}$, where $[\,]$ denotes the greatest integer function. Then,

The number of real roots of the equation $x|x-2|+3|x-3|+1=0$ is:

Let x, y > 0. If x³y² = 2¹⁵, then the least value of 3x + 2y is

$A={(\alpha,\beta)\in\mathbb{R}\times\mathbb{R}:\ |\alpha-1|\le 4\ \text{and}\ |\beta-5|\le 6}$ $B={(\alpha,\beta)\in\mathbb{R}\times\mathbb{R}:\ 16(\alpha-2)^2+9(\beta-6)^2\le 144}.$ Then

$S = \{\, x \in [-6,3] \setminus \{-2,2\} \;:\; \dfrac{|x+3|-1}{|x|-2} \geq 0 \,\}$ $T = \{\, x \in \mathbb{Z} \;:\; x^{2} - 7|x| + 9 \leq 0 \,\}$ Then the number of elements in $S \cap T$ is :

Let $S = {x \in \mathbb{R} : x \ge 0 \text{ and } 2\lvert\sqrt{x}-3\rvert + \sqrt{x}(\sqrt{x}-6)+6=0}$. Then $S$ :

Let $f:R \to R$ and $g:R \to R$ be two functions defined by $f(x) = {\log _e}({x^2} + 1) - {e^{ - x}} + 1$ and $g(x) = {{1 - 2{e^{2x}}} \over {{e^x}}}$. Then, for which of the following range of $\alpha$, the inequality $f\left( {g\left( {{{{{(\alpha - 1)}^2}} \over 3}} \right)} \right) > f\left( {g\left( {\alpha -{5 \over 3}} \right)} \right)$ holds ?

Let [x] denote the greatest integer less than or equal to x. Then the domain of $ f(x) = \sec^{-1}(2[x] + 1) $ is:

The equation $x^{2}-4x+[x]+3 = x[x]$, where $[x]$ denotes the greatest integer function, has:

 no solution  

The sum of the squares of the roots of $|x - 2|^2 + |x - 2| - 2 = 0$ and the squares of the roots of $x^2 - 2|x - 3| - 5 = 0$, is: