Let a be the sum of all coefficients in the expansion of (1-2 x+2 x^2) ^{2023} (3-4 x^2+2 x^3) ^{2024} and b=\lim_{x \to 0} ( {\int_{0}^{x} {\log (1+t)}/{t^{2024}+1} \dt}/{x^2}). If the equations 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 R, then d: c : e equals [31-Jan-2024 Shift 1]

JEE Main 31-Jan-2024 Shift 1 Solved Paper

Section: Mathematics

Question : 2 of 90

Marks: +1, -0

Let a be the sum of all coefficients in the expansion of (1−2x+2x2)2023(3−4x2+2x3)2024 and b=

lim

x→0

(‌

∫

log(1+t)

t2024+1

‌dt

). If the equations cx2+dx+e=0 and 2bx2+ax+4=0 have a common root, where c,d,e∈R, then d:c : e equals

[31-Jan-2024 Shift 1]

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