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Binomial Theorem question

2024 · 31 Jan · Shift 1 · Q47

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PYQ Library
JEE Main
Mathematics
Binomial Theorem
2024 · 31 Jan · Shift 1 · Q47

Binomial Theorem question

2024 · 31 Jan · Shift 1 · Q47

JEE MainMathematicsBinomial TheoremMCQ+4 / −1

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_{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

A
$2: 1: 4$
B
$1: 1: 4$
C
$1: 2: 4$
D
$4: 1: 4$

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