Q JEE MAIN 2026

The sum of squares of all the real solutions of the equation $\log _{(x+1)}\left(2 x^2+5 x+3\right)=4-\log _{(2 x+3)}\left(x^2+2 x+1\right)$ is...

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Q Jee Main 2026

If the set of all solutions of $\left|x^2+x-9\right|=|x|+\left|x^2-9\right|$ is $[\alpha, \beta] \cup[\gamma, \infty)$, then $\left(\alpha^2+\beta^2+\gamma^2\right)$ is equal to:

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Q JEE Main 2024

The number of real solutions of the equation $x|x+5|+2|x+7|-2=0$ is $\_\_\_\_$ .

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Q Jee Main 2024

Let the set $C=\left\{(x, y) \mid x^2-2^y=2023, x, y \in \mathbb{N}\right\}$. Then $\sum_{(x, y) \in C}(x+y)$ is equal to

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Q JEE MAIN 2026

The sum of all the real solutions of the equation $\log _{(x+3)}\left(6 x^2+28 x+30\right)=5-2 \log _{(6 x+10)}\left(x^2+6 x+9\right)$ is equal...

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Q JEE MAIN 2026

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

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Q JEE MAIN_2026_

The number of distinct real solutions of the equation $x|x+4|+3|x+2|+10=0$ is

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Q JEE MAIN 2026

Let $\mathrm{A}=\left\{x:\left|x^2-10\right| \leq 6\right\}$ and $\mathrm{B}=\{x:|x-2|>1\}$. Then

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Q JEE MAIN 2026

The sum of all the roots of the equation $(x-1)^2-5|x-1|+6=0$, is :

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Q JEE MAIN 2019

The domain of the definition of the function $f(x)=\frac{1}{4-x^2}+\log _{10}\left(x^3-x\right)$ is :

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Q JEE MAIN 2021

The number of the real roots of the equation $(x+1)^2+|x-5|=\frac{27}{4}$ is $\_\_\_\_$ .

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Q JEE MAIN 2021

The value of $3+\frac{1}{4+\frac{1}{3+\frac{1}{4+\frac{1}{3+\infty}}}}$ is equal to

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Q JEE MAIN 2021

The number of solutions of the equation $\log _4(x-1)=\log _2(x-3)$ is

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Q JEE MAIN 2022

Let $A=\{x \in R:|x+1|

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Q JEE MAIN 2025

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

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Q JEE MAIN 2023

If the solution curve f(x, y)=0 of the differential equation $...

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Q JEE MAIN_2025

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

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Q JEE MAIN 2023

The number of real roots of the equation $x|x|-5|x+2|+6=0$, is

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Q JEE-Main 2023

The sum of all the roots of the equation is :$\left|x^2-8 x+15\right|-2 x+7=0$ is :

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Q JEE MAIN 2023

The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^2 \geq 0$ is

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Q JEE MAIN 2023

The number of elements in the set $\left\{n \in \mathbb{Z}:\left|n^2-10 n+19\right|

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Q JEE MAIN 2023

Let $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be three distinct positive real numbers such that $(2 \mathrm{a})^{\log _{\mathrm{a}} \mathrm{a}}=(\mathrm{bc})^{\log _{\mathrm{a}} \mathrm{b}}$ and $...

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Q JEE MAIN 2023

Let $\alpha, \beta, \gamma$ be the three roots of the equation $x^3+b x+c=0$. If $\beta \gamma=1=-\alpha$, then $...

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Q JEE-Main 2023

The sum of all the roots of the equation $\left|x^2-8 x+15\right|-2 x+7=0$ is :

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Q JEE MAIN 2024

The number of distinct real roots of the equation $|x||x+2|-5|x+1|-1=0$ is

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Q JEE MAIN 2024

The sum of all the solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is is:

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Q JEE MAIN 2024

Let $S$ be the set of positive integral values of a for which $\frac{\mathrm{ax}^2+2(\mathrm{a}+1) \mathrm{x}+9 \mathrm{a}+4}{\mathrm{x}^2-8 \mathrm{x}+32}

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Q JEE MAIN 2025

Let $\mathrm{A}=\left\{x \in(0, \pi)-\left\{\frac{\pi}{2}\right\}: \log _{(2 / \pi)}|\sin x|+\log _{(2 / \pi)}|\cos x|=2\right\}$ and $B=\{x \geq 0: \sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0\}$. Then $...

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Q JEE MAIN 2025

The sum, of the squares of all the roots of the equation $...

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Q JEE MAIN 2025

The product of all solutions of the equation $\mathrm{e}^{5\left(\log _{\mathrm{c}} x\right)^2+3}=x^8, x>0$, is :

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