JEE 2023 — Mathematics PYQ

1. Domain nikalne ke liye condition:

Hum jaante hain ki ${\sec }^{-1}(u)$ ka domain hota hai $|u|\ge 1$.

Yahan $u=\frac{2x}{5x+3}$ hai, isliye:

Iska matlab hai ki ya toh $\frac{2x}{5x+3}\ge 1$ hoga, ya $\frac{2x}{5x+3}\le -1$ hoga.

2. Case 1: $\frac{2x}{5x+3}\ge 1$ ko solve karna:

Wavy curve method se, yahan se hame milta hai:

3. Case 2: $\frac{2x}{5x+3}\le -1$ ko solve karna:

Iska solution hoga:

4. Dono cases ko milane par (Domain):

Domain = $[-1,-3/5)\cup (-3/5,-3/7]$

Sawal ke anusar, domain $[\alpha ,\beta )\cup (\gamma ,\delta ]$ hai.

Isliye:

• $\alpha =-1$

• $\beta =-3/5$

• $\gamma =-3/5$

• $\delta =-3/7$

5. Expression ki value nikalna:

Hame $|3\alpha +10(\beta +\gamma )+21\delta |$ ki value nikalni hai: