Mathematics · 2014
JEE Main · 12 April 2014, Shift 1 · Q73
If 1+x^4+x^5=Σ_i =0^5 a_i (1+x)^i, for all x in R, then a_2 is:
If $\displaystyle 1+x^4+x^5=\sum_{\mathrm{i}=0}^5 \mathrm{a}_{\mathrm{i}}(1+x)^{\mathrm{i}}$, for all $\displaystyle x$ in $\displaystyle \mathbf{R}$, then $\displaystyle \mathrm{a}_2$ is :
Official answer
(1)
$\displaystyle -4$
More from Binomial Theorem
- The term independent of x in the expansion of [(x+1)/(x^2 / 3-x^1 / 3+1)-(x-1)/(x-x^1 / 2)]^10, x ≠ 1, is equal to \ \ \ \.2021
- Suppose Σ_r=0^2023 r^2^2023 C_r=2023 × α × 2^2022. Then the value of α is ____2023
- If Σ_r=0^5 (^11 C_2 r+1)/(2 r+2)=m/n, gcd(m, n)=1, then m-n is equal to ____.2025
- The coefficient of x^18 in the expansion of (x^4-1/x^3)^15 is ____2023
- In the expansion of (1+x)(1-x^2)(1+3/x+3/x^2+1/x^3)^5, x ≠ 0, the sum of the coefficients of x^3 and x^-13 is equal to ____2024
- 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
- If the coefficient of a^7 b^8 in the expansion of (a+2 b+4 ab)^10 is K · 2^16, then K is equal to \ \ \ \.2021
- If the fourth term in the Binomial expansion of (2/x+x^log_8 x)^6(x>0) is 20 × 8^7, then a value of x is:2019
JEE Main 2014 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.