JAMIA 2024 — Mathematics PYQ
JAMIA | Mathematics | 2024The coefficient of the middle term in the expansion of (2+3x)4 is
Choose the correct answer:
- A.
5!
- B.
6
- C.
216
(Correct Answer) - D.
8!
216
Explanation
Step 1: Middle term ki sankhya pata karein
Yahan n=4 hai, jo ek even (sam) sankhya hai.
Is expansion mein total terms n+1=4+1=5 honge.
Middle term (2n+1)th term hota hai.
Step 2: General term ka formula use karein
Binomial expansion (a+b)n ka general term hota hai:
Yahan a=2, b=3x, aur n=4 hai. 3rd term ke liye hum r=2 lenge:
Step 3: Calculation karein
Ab values calculate karte hain:
-
(24)=2×14×3=6
-
(2)4−2=22=4
-
(3x)2=9x2
Inhe multiply karne par:
Step 4: Final Answer
Middle term ka coefficient (gunank) 216 hai.
Explanation
Step 1: Middle term ki sankhya pata karein
Yahan n=4 hai, jo ek even (sam) sankhya hai.
Is expansion mein total terms n+1=4+1=5 honge.
Middle term (2n+1)th term hota hai.
Step 2: General term ka formula use karein
Binomial expansion (a+b)n ka general term hota hai:
Yahan a=2, b=3x, aur n=4 hai. 3rd term ke liye hum r=2 lenge:
Step 3: Calculation karein
Ab values calculate karte hain:
-
(24)=2×14×3=6
-
(2)4−2=22=4
-
(3x)2=9x2
Inhe multiply karne par:
Step 4: Final Answer
Middle term ka coefficient (gunank) 216 hai.

