1
JEE Main 2024 (Online) 8th April Evening Shift
Numerical
+4
-1
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The number of distinct real roots of the equation $$|x+1||x+3|-4|x+2|+5=0$$, is _______

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2
JEE Main 2024 (Online) 6th April Evening Shift
Numerical
+4
-1
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Let $$\alpha, \beta$$ be roots of $$x^2+\sqrt{2} x-8=0$$. If $$\mathrm{U}_{\mathrm{n}}=\alpha^{\mathrm{n}}+\beta^{\mathrm{n}}$$, then $$\frac{\mathrm{U}_{10}+\sqrt{2} \mathrm{U}_9}{2 \mathrm{U}_8}$$ is equal to ________.

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3
JEE Main 2024 (Online) 6th April Morning Shift
Numerical
+4
-1
Change Language

Let $$x_1, x_2, x_3, x_4$$ be the solution of the equation $$4 x^4+8 x^3-17 x^2-12 x+9=0$$ and $$\left(4+x_1^2\right)\left(4+x_2^2\right)\left(4+x_3^2\right)\left(4+x_4^2\right)=\frac{125}{16} m$$. Then the value of $$m$$ is _________.

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4
JEE Main 2024 (Online) 5th April Evening Shift
Numerical
+4
-1
Change Language

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

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