1
JEE Main 2023 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is :
A
$[2 \sqrt{2}, \sqrt{11}]$
B
$[\sqrt{5}, \sqrt{13}]$
C
$[\sqrt{2}, \sqrt{7}]$
D
$[\sqrt{5}, \sqrt{10}]$
2
JEE Main 2023 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The solution of the differential equation

$\frac{d y}{d x}=-\left(\frac{x^2+3 y^2}{3 x^2+y^2}\right), y(1)=0$ is :
A
$\log _e|x+y|+\frac{x y}{(x+y)^2}=0$
B
$\log _e|x+y|-\frac{x y}{(x+y)^2}=0$
C
$\log _e|x+y|+\frac{2 x y}{(x+y)^2}=0$
D
$\log _e|x+y|-\frac{2 x y}{(x+y)^2}=0$
3
JEE Main 2023 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $x=(8 \sqrt{3}+13)^{13}$ and $y=(7 \sqrt{2}+9)^9$. If $[t]$ denotes the greatest integer $\leq t$, then :
A
$[x]$ is odd but $[y]$ is even
B
$[x]$ and $[y]$ are both odd
C
$[x]+[y]$ is even
D
$[x]$ is even but $[y]$ is odd
4
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1
Change Language
Let $A=\{1,2,3,5,8,9\}$. Then the number of possible functions $f: A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to ___________.
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