Mathematics · 2026
JEE Main · 23 January 2026, Shift 1 · Q6
The sum of all possible values of n ∈ N, so that the coefficients of x, x^2 and x^3 in the expansion of (1+x^2)^2(1+x)^n, are in arithmetic…
The sum of all possible values of $\displaystyle \mathrm{n} \in \mathbf{N}$, so that the coefficients of $\displaystyle x, x^2$ and $\displaystyle x^3$ in the expansion of $\displaystyle \left(1+x^2\right)^2(1+x)^{\mathrm{n}}$, are in arithmetic progression is :
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle 9$
More from Binomial Theorem
- If the sum of the coefficients of x^7 and x^14 in the expansion of (1/x^3-x^4)^n, x ≠ 0, is zero, then the value of n is ____.2026
- The number of elements in the set S={(r, k): k ∈ Z. and.^36 C_r+1=(6(^35 C_r))/((k^2-3))}, is:2026
- If for 3 ≤ r ≤ 30,(^30 C_30-r)+3(^30 C_31-r)+3(^30 C_32-r)+(^30 C_33-r)=^m C_r, then m equals:2026
- If the coefficients of the middle terms in the binomial expansions of (1+α x)^26 and (1-α x)^28, α ≠ 0, are equal, then the value of α is:2026
- In the expansion of (9 x-1/(3 √x))^18, x>0, if the term independent of x is (221)k, then k is equal to:2026
- Let the smallest value of k ∈ N, for which the coefficient of x^3 in (1+x)^3+(1+x)^4+(1+x)^5+…+(1+x)^99+(1+k x)^100, x ≠ 0, is (43 n+101/4)(^100 C_3)…2026
- The coefficient of x^2 in the expansion of (2 x^2+1/x)^10, x ≠ 0, is:2026
- If 26(2^3/3(^12 C_2)+2^5/5(^12 C_4)+2^7/7(^12 C_6)+⋯+(2^13)/13(^12 C_12))=3^13-α, then α is equal to:2026
JEE Main 2026 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.