MAH-CET 2025 — Mathematics PYQ

Solving Steps:

1. General Term ($T_{r+1}$):

Expansion $(a+b{)}^n$ ka general term hota hai:

Yahan $a=4^{1/5}$, $b=7^{1/10}$, aur $n=45$:

2. Condition for Rational Terms:

Ek term rational tab hoga jab $4$ aur $7$ ki powers integers honi chahiye:

• $\frac{45-r}{5}$ ek integer hona chahiye $⟹(45-r)$ 5 se divide hona chahiye. Iska matlab $r$ ko 5 ka multiple hona chahiye.

• $\frac{r}{10}$ ek integer hona chahiye $⟹r$ ko 10 ka multiple hona chahiye.

Dono conditions ko satisfy karne ke liye, $r$ ko $LCM(5,10)=10$ ka multiple hona chahiye.

3. Possible values of $r$:

Humein pata hai $0\le r\le 45$. Toh $r$ ki values hongi:

Total rational terms = 5

4. Total Number of Terms:

Expansion $(a+b{)}^{45}$ mein total terms $n+1$ hote hain:

5. Number of Irrational Terms: