1
JEE Advanced 2022 Paper 1 Online
MCQ (Single Correct Answer)
+3
-1
LIST-I contains metal species and LIST-II contains their properties.
List-I | List-II |
---|---|
(I) $\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}$ |
(P) $t_{2 \mathrm{g}}$ orbitals contain 4 electrons |
(II) $\left[\mathrm{RuCl}_{6}\right]^{2-}$ | (Q) $\mu$ (spin-only $)=4.9 \mathrm{BM}$ |
(III) $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ |
(R) low spin complex ion |
(IV) $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ |
(S) metal ion in $4+$ oxidation state |
(T) $d^{4}$ species |
[Given: Atomic number of $\mathrm{Cr}=24, \mathrm{Ru}=44, \mathrm{Fe}=26$ ]
Match each metal species in LIST-I with their properties in LIST-II, and choose the correct option
2
JEE Advanced 2022 Paper 1 Online
MCQ (Single Correct Answer)
+3
-1
Match the compounds in LIST-I with the observations in LIST-II, and choose the correct option.
List-I | List-II |
---|---|
(I) Aniline |
(P) Sodium fusion extract of the compound on boiling with $\mathrm{FeSO}_{4}$, followed by acidification with conc. $\mathrm{H}_{2} \mathrm{SO}_{4}$, gives Prussian blue color. |
(II) $o$-Cresol | (Q) Sodium fusion extract of the compound on treatment with sodium nitroprusside gives blood red color. |
(III) Cysteine |
(R) Addition of the compound to a saturated solution of $\mathrm{NaHCO}_{3}$ results in effervescence. |
(IV) Caprolactam |
(S) The compound reacts with bromine water to give a white precipitate. |
(T) Treating the compound with neutral $\mathrm{FeCl}_{3}$ solution produces violet color. |
3
JEE Advanced 2022 Paper 1 Online
Numerical
+3
-0
Considering only the principal values of the inverse trigonometric functions, the value of
$$ \frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^{2}}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^{2}}+\tan ^{-1} \frac{\sqrt{2}}{\pi} $$
is
$$ \frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^{2}}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^{2}}+\tan ^{-1} \frac{\sqrt{2}}{\pi} $$
is
Your input ____
4
JEE Advanced 2022 Paper 1 Online
Numerical
+3
-0
Let $$\alpha$$ be a positive real number. Let $$f: \mathbb{R} \rightarrow \mathbb{R}$$ and $$g:(\alpha, \infty) \rightarrow \mathbb{R}$$ be the functions defined by
$$ f(x)=\sin \left(\frac{\pi x}{12}\right) \quad \text { and } \quad g(x)=\frac{2 \log _{\mathrm{e}}(\sqrt{x}-\sqrt{\alpha})}{\log _{\mathrm{e}}\left(e^{\sqrt{x}}-e^{\sqrt{\alpha}}\right)} . $$
Then the value of $$\lim \limits_{x \rightarrow \alpha^{+}} f(g(x))$$ is
$$ f(x)=\sin \left(\frac{\pi x}{12}\right) \quad \text { and } \quad g(x)=\frac{2 \log _{\mathrm{e}}(\sqrt{x}-\sqrt{\alpha})}{\log _{\mathrm{e}}\left(e^{\sqrt{x}}-e^{\sqrt{\alpha}}\right)} . $$
Then the value of $$\lim \limits_{x \rightarrow \alpha^{+}} f(g(x))$$ is
Your input ____
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Chemistry
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Mathematics
18
Physics
18
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