1
JEE Main 2022 (Online) 26th July Morning Shift
Numerical
+4
-1
Change Language

If for some $$\mathrm{p}, \mathrm{q}, \mathrm{r} \in \mathbf{R}$$, not all have same sign, one of the roots of the equation $$\left(\mathrm{p}^{2}+\mathrm{q}^{2}\right) x^{2}-2 \mathrm{q}(\mathrm{p}+\mathrm{r}) x+\mathrm{q}^{2}+\mathrm{r}^{2}=0$$ is also a root of the equation $$x^{2}+2 x-8=0$$, then $$\frac{\mathrm{q}^{2}+\mathrm{r}^{2}}{\mathrm{p}^{2}}$$ is equal to ____________,

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2
JEE Main 2022 (Online) 26th July Morning Shift
Numerical
+4
-1
Change Language

The number of 5-digit natural numbers, such that the product of their digits is 36 , is __________.

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3
JEE Main 2022 (Online) 26th July Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

The series of positive multiples of 3 is divided into sets : $$\{3\},\{6,9,12\},\{15,18,21,24,27\}, \ldots$$ Then the sum of the elements in the $$11^{\text {th }}$$ set is equal to ____________.

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4
JEE Main 2022 (Online) 26th July Morning Shift
Numerical
+4
-1
Change Language

The number of distinct real roots of the equation $$x^{5}\left(x^{3}-x^{2}-x+1\right)+x\left(3 x^{3}-4 x^{2}-2 x+4\right)-1=0$$ is ______________.

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