If $\alpha, \beta$ are the roots of the equation $x^{2} - \left(5 + 3\sqrt{\log_{3}5} - 5\sqrt{\log_{5}3}\right)x + 3\left(3^{\tfrac{1}{3}\log_{3}5} - 5^{\tfrac{2}{3}\log_{5}3} - 1\right) = 0$, then the equation, whose roots are $\alpha + \tfrac{1}{\beta}$ and $\beta + \tfrac{1}{\alpha}$, is:
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If for $p\ne q\ne 0$, the function $f(x)=\dfrac{\sqrt[7]{p(729+x)}-3}{\sqrt[3]{729+qx}-9}$ is continuous at $x=0$, then:
Topic: JEE Main 2022 (27 July Evening Shift)
Let $f(x)=2+|x|-|x-1|+|x+1|,;x\in\mathbb{R}$.
Consider
(S1): $f'!\left(-\tfrac{3}{2}\right)+f'!\left(-\tfrac{1}{2}\righ…
Topic: JEE Main 2022 (27 July Evening Shift)
Let the sum of an infinite G.P., whose first term is $a$ and the common ratio is $r$, be $5$. Let the sum of its first …
Topic: JEE Main 2022 (27 July Evening Shift)
The area of the region enclosed by $y\le 4x^{2}$, $x^{2}\le 9y$ and $y\le 4$ is equal to:
Topic: JEE Main 2022 (27 July Evening Shift)
The value of $\displaystyle \int_{0}^{2}!\left(,|2x^{2}-3x|+\big[x-\tfrac{1}{2}\big]\right),dx$, where $[\cdot]$ is the…
Topic: JEE Main 2022 (27 July Evening Shift)
Consider a curve $y=y(x)$ in the first quadrant as shown in the figure. Let the area $A_{1}$ be twice the area $A_{2}$.…
Topic: JEE Main 2022 (27 July Evening Shift)
The equations of the sides $AB$, $BC$ and $CA$ of a triangle $ABC$ are $2x+y=0$, $x+py=39$ and $x-y=3$ respectively and…
Topic: JEE Main 2022 (27 July Evening Shift)
If the length of the perpendicular drawn from the point $P(a,4,2),;a>0$ on the line $\dfrac{x+1}{2}=\dfrac{y-3}{3}=\…
Topic: JEE Main 2022 (27 July Evening Shift)
A six faced die is biased such that
$3 \times P(\text{a prime number}) = 6 \times P(\text{a composite number}) = 2 \tim…
Topic: JEE Main 2022 (27 July Evening Shift)
