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Binomial Theorem
Multinomial Expansion, Number of Terms
jee_adv_2026_mock_p2
Grade 12
Question:
The number of terms in the expansion of (1 + x + x^2 + x^3)^6 is:
A. 16
B. 19
C. 22
D. 25
Step-by-Step Solution
Key Concept: Use (1 + x + x^2 + x^3) = (1 - x^4)/(1 - x).
Step 1: (1 + x + x^2 + x^3)^6 = (1 - x^4)^6 (1 - x)^-6. Step 2: The degree of the polynomial is 18. Step 3: Coefficient of x^n is Σ_{r=0}^{min(6, floor(n/4))} (-1)^r C(6,r) C(5 + n - 4r, 5). Step 4: All coefficients for n = 0 to 18 are non-zero. Hence 19 terms.
Correct Answer:B
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