1
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
Change Language
The total number of isoelectronic species from the given set is ___________.

$\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Al}, \mathrm{Mg}^{2+}, \mathrm{Na}^{+}, \mathrm{O}^{+}, \mathrm{Mg}, \mathrm{Al}^{3+}, \mathrm{F}$
Your input ____
2
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $x=x(y)$ be the solution of the differential equation

$2(y+2) \log _{e}(y+2) d x+\left(x+4-2 \log _{e}(y+2)\right) d y=0, y>-1$

with $x\left(e^{4}-2\right)=1$. Then $x\left(e^{9}-2\right)$ is equal to :
A
$\frac{4}{9}$
B
$\frac{32}{9}$
C
$\frac{10}{3}$
D
3
3
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $\int\limits_{0}^{1} \frac{1}{\left(5+2 x-2 x^{2}\right)\left(1+e^{(2-4 x)}\right)} d x=\frac{1}{\alpha} \log _{e}\left(\frac{\alpha+1}{\beta}\right), \alpha, \beta>0$, then $\alpha^{4}-\beta^{4}$ is equal to :
A
-21
B
21
C
19
D
0
4
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The total number of three-digit numbers, divisible by 3, which can be formed using the digits $1,3,5,8$, if repetition of digits is allowed, is :
A
21
B
22
C
18
D
20
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