JEE Mains · Maths · STD 11 - 12. limits
If \(\mathop {\lim }\limits_{x \to \infty } {\left( {1 + \frac{a}{x} - \frac{4}{{{x^2}}}} \right)^{2x}} = {e^3},\) then \('a'\) is equal to
- A \(2\)
- B \(\frac {3}{2}\)
- C \(\frac {1}{2}\)
- D \(\frac {2}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac {3}{2}\)
Step-by-step Solution
Detailed explanation
\(\,\mathop {\lim }\limits_{x \to \infty } {\left( {1 + \frac{a}{x} - \frac{4}{{{x^2}}}} \right)^{2x}}\,\,\,\,\,\,\,\,\,\left( {{1^{\infty \,}}from} \right)\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(\arg ( z )\) represent the principal argument of the complex number \(z\). The, \(| z |=3\) and \(\arg ( z -1)-\) \(\arg ( z +1)=\frac{\pi}{4}\) intersectJEE Mains 2022 Medium
- If \(\frac{ dy }{ dx }+2 y \tan x =\sin x , 0< x <\frac{\pi}{2}\) and \(y \left(\frac{\pi}{3}\right)=\) 0 , then the maximum value of \(y(x)\) is.JEE Mains 2022 Hard
- The square of the distance of the point \(\left(\frac{15}{7}, \frac{32}{7}, 7\right)\) from the line \(\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}\) in the direction of the vector \(\hat{i}+4 \hat{j}+7 \hat{k}\) is :JEE Mains 2025 Medium
- If \(a, b\) and \(c\) be three distinct numbers in \(G.P.\) and \(a + b + c = xb\) then \(x\) can not beJEE Mains 2019 Hard
- The term independent of \(x\) in the expression of \(\left(1-x^{2}+3 x^{3}\right)\left(\frac{5}{2} x^{3}-\frac{1}{5 x^{2}}\right)^{11}, x \neq 0\) isJEE Mains 2022 Hard
- A survey shows that \(63 \%\) of the people in a city read newspaper \(A\) whereas \(76 \%\) read newspaper \(B\). If \(x \%\) of the people read both the newspapers, then a possible value of \(x\) can beJEE Mains 2020 Medium
More PYQs from JEE Mains
- The shortest distance between the lines \(\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}\) and \(\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}\) is \(......\).JEE Mains 2023 Hard
- The area (in \(sq.\, units\)) of the region bounded by the curves \(x^{2}+2 y-1=0, y^{2}+4 x-4=0\) and \(y^{2}-4 x-\) \(4=0\), in the upper half plane is \(....\)JEE Mains 2021 Hard
- A function \(f(x)\) is given by \(f(x)=\frac{5^{x}}{5^{x}+5}\), then the sum of the series \(f\left(\frac{1}{20}\right)+f\left(\frac{2}{20}\right)+f\left(\frac{3}{20}\right)+\ldots \ldots+f\left(\frac{39}{20}\right)\) is equal to ....... .JEE Mains 2021 Medium
- The value of the integral \(\int \limits_{-1}^{1} \log _{ e }(\sqrt{1- x }+\sqrt{1+ x }) dx\) is equal to:JEE Mains 2021 Hard
- If the mean and variance of five observations are \(\frac{24}{5}\) and \(\frac{194}{25}\) respectively and the mean of first four observations is \(\frac{7}{2}\), then the variance of the first four observations in equal toJEE Mains 2024 Hard
- If \(\int_{-\pi / 2}^{\pi / 2} \frac{8 \sqrt{2} \cos x d x}{\left(1+e^{\sin x}\right)\left(1+\sin ^4 x\right)}=\alpha \pi+\beta \log _e(3+2\) \(\sqrt{2}\) ), where \(\alpha, \beta\) are integers, then \(\alpha^2+\beta^2\) equals ...........JEE Mains 2024 Hard