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JEE MAIN 2022

25-06-2022 S2

Question

The line $y=x+1$ meets the ellipse $\frac{x^2}{4}+\frac{y^2}{2}=1$ at two points $P$ and $Q$. If $r$ is the radius of the circle with PQ as diameter then $(3 r)^2$ is equal to

Select the correct option:

A

20

B

12

C

11

D

8

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

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Mathematics

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The number of species from the following that have pyramidal geometry around the central atom is $\_\_\_\_$
$...

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The number of unpaired d-electrons in $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}$ is $\_\_\_\_$

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A first row transition metal in its +2 oxidation state has a spin-only magnetic moment value of 3.86 BM. The...

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QJEE Main 20242024

For a strong electrolyte, a plot of molar conductivity against (concentration) ${ }^{1 / 2}$ is a straight line, with...

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Given below are two statements:
Statement I : The correct order of first ionization enthalpy values of Li, Na, F...

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QJEE Main 20242024

Choose the Incorrect Statement about Dalton's Atomic Theory

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Let the slope of the line $45 x+5 y+3=0$ be $27 r_1+\frac{9 r_2}{2}$ for some $r_1, r_2 \in R$. Then...

JEE MainMathematicsEasy

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QJee Main 20242024

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

JEE MainMathematicsMedium

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QJee Main 20242024

Remainder when $64^{32^{32}}$ is divided by 9 is equal to

JEE MainMathematicsMedium

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QJee Main 20242024

Let $f(x)=\sqrt{\lim _{r \rightarrow x}\left\{\frac{2 r^2\left[(f(r))^2-f(x) f(r)\right]}{r^2-x^2}-r^3 e^{\frac{f(r)}{r}}\right\}}$ be differentiable in $(-\infty, 0) \cup(0, \infty)$ and $f(1)=1$. Then the value...

JEE MainMathematicsHard

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Q JEE MAIN 20242024

The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is

JEE MainMathematicsEasy

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QJee Main 20242024

Let $O$ be the origin, and $M$ and $N$ be the points on the lines $\frac{x-5}{4}=\frac{y-4}{1}=\frac{z-5}{3}$ and $\frac{x+8}{12}=\frac{y+2}{5}=\frac{z+11}{9}$ respectively such...

JEE MainMathematicsMedium

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QJEE Main 20242024

Fuel cell, using hydrogen and oxygen as fuels,
A. has been used in spaceship
B. has as efficiency...

JEE MainChemistryEasy

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QJEE Main 20242024

If an iron (III) complex with the formula $\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_{\mathrm{x}}(\mathrm{CN})_{\mathrm{y}}\right]^{-}$has no electron in its $\mathrm{e}_{\mathrm{g}}$ orbital, then the value of $\mathrm{x}+\mathrm{y}$...

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QJee Main 20242024

Let the area of the region $\left\{(x, y): 0 \leq x \leq 3,0 \leq y \leq \min \left\{\mathrm{x}^2+2,2 \mathrm{x}+2\right\}\right\}$ be...

JEE MainMathematicsMedium

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QJEE Main 20242024

The correct order of the first ionization enthalpy is

JEE MainChemistryEasy

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QJEE MAIN 20242024

The variance $\sigma^2$ of the data

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QJee Main 20242024

If $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1-\sin 2 x} d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}$, where $\alpha, \beta$ and $\gamma$ are rational numbers, then $...

JEE MainMathematicsMedium

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