Let a be the sum of all coefficients in the expansion of (1-2 x+2 x²)²⁰²³(3-4 x²+2 x³)²⁰²⁴ and b= lim x → 0 ((∫₀ˣ (log (1+t))/(t²⁰²⁴+1) d t)/(x²)). If the equation c x²+d x+e=0 and 2 b x²+a x+4=0 have a common root, where c, d, e R, then d: c: e equals

Binomial Theorem and Its Simple Applications: JEE Main 2024 Mathematics question

JEE Main 2024 · 31 Jan, Morning shift · Q2959

JEE Main 202431 Jan, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

Let

a

be the sum of all coefficients in the expansion of

\left(1-2 x+2 x^2\right)^{2023}\left(3-4 x^2+2 x^3\right)^{2024}

and

b=\lim _\limits{x \rightarrow 0}\left(\frac{\int_0^x \frac{\log (1+t)}{t^{2024}+1} d t}{x^2}\right)

. If the equation

c x^2+d x+e=0

and

2 b x^2+a x+4=0

have a common root, where

c, d, e \in \mathbb{R}

, then

\mathrm{d}: \mathrm{c}:

e equals