JEE 2023 — Mathematics PYQ

Step 1: Variables ko separate karein

Di gayi equation hai:

Ise hum aise likh sakte hain:

Step 2: Dono side integrate karein

Step 3: Constant $C$ ki value nikaalein

Hamein condition di gayi hai: $y(1)=e$. Iska matlab jab $x=1$, tab $y=e$:

Ab hamari equation bani:

Isse $y$ (yaani $f(x)$) ke liye solve karte hain:

Step 4: Limit calculate karein

Ab hamein ${\lim }_{x\to 0^{+}}f(x)$ nikalna hai:

Jab $x\to 0^{+}$ hota hai, tab $\frac{1}{x}\to \infty$ hota hai.

Iska matlab exponent $(2-\frac{1}{x})\to -\infty$ jayega.

Hum jaante hain ki $e^{-\infty }=0$.

Isliye:

Correct Option:

Sahi jawab option (3) 0 hai.