1
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
Change Language
If the CFSE of $\left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$ is $-96.0 \mathrm{~kJ} / \mathrm{mol}$, this complex will absorb maximum at wavelength ___________ $\mathrm{nm}$. (nearest integer)

Assume Planck's constant (h) $=6.4 \times 10^{-34} \mathrm{Js}$, Speed of light $(\mathrm{c})=3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$ and Avogadro's

Constant $\left(\mathrm{N}_{\mathrm{A}}\right)=6 \times 10^{23} / \mathrm{mol}$
Your input ____
2
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
Change Language
The rate constant for a first order reaction is $20 \mathrm{~min}^{-1}$. The time required for the initial concentration of the reactant to reduce to its $\frac{1}{32}$ level is _______ $\times 10^{-2} \mathrm{~min}$. (Nearest integer)

(Given : $\ln 10=2.303$ and $$ \log 2=0.3010 \text { )}$$
Your input ____
3
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}-\hat{j}+2 \hat{k}$ and $\vec{c}=5 \hat{i}-3 \hat{j}+3 \hat{k}$ be three vectors. If $\vec{r}$ is a vector such that, $\vec{r} \times \vec{b}=\vec{c} \times \vec{b}$ and $\vec{r} \cdot \vec{a}=0$, then $25|\vec{r}|^{2}$ is equal to :
A
336
B
449
C
339
D
560
4
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $f: \mathbb{R}-\{2,6\} \rightarrow \mathbb{R}$ be real valued function

defined as $f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}$.

Then range of $f$ is
A
$ \left(-\infty,-\frac{21}{4}\right] \cup[1, \infty) $
B
$\left(-\infty,-\frac{21}{4}\right) \cup(0, \infty) $
C
$\left(-\infty,-\frac{21}{4}\right] \cup[0, \infty) $
D
$\left(-\infty,-\frac{21}{4}\right] \cup\left[\frac{21}{4}, \infty\right)$
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