JEE Mains · Maths · STD 11 - 12. limits
If \(\lim _{x \rightarrow 0} \frac{a x-\left(e^{4 x}-1\right)}{a x\left(e^{4 x}-1\right)}\) exists and is equal to \(b\), then the value of \(a-2 b\) is ....... .
- A \(10\)
- B \(3\)
- C \(5\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{\operatorname{ax}-\left(e^{4 x}-1\right)}{\operatorname{ax}\left(e^{4 x}-1\right)} \quad\left(\frac{0}{0}\right)\) \(=\lim _{x \rightarrow 0} \frac{\operatorname{ax}-\left(e^{4 x}-1\right)}{\operatorname{ax} \cdot 4 x} \quad\) Use…
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
- The area (in sq. units) of the region bounded by the parabola, \(y = x^2 + 2\) and the lines, \(y = x + 1, x = 0\) and \(x = 3\), isJEE Mains 2019 Hard
- If all the words (with or without meaning) having five letters, formed using the letters of the word \(SMALL\) and arranged as in a dictionary; then the position of the word \(SMALL\) is :JEE Mains 2016 Hard
- The square of the distance of the point \(P(5, 6, 7)\) from the line \(\dfrac{x-2}{2} = \dfrac{y-5}{3} = \dfrac{z-2}{4}\) is equal to:JEE Mains 2026 Medium
- Let \({f_k}\left( x \right) = \frac{1}{k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)\;,x \in R\) and \(k \ge 1\), then \({f_4}\left( x \right) - {f_6}\left( x \right)\) is equal toJEE Mains 2014 Hard
- Let \(R\) be a relation on \(Z \times Z\) defined by\( (a, b)\)\(R(c, d)\) if and only if \(ad - bc\) is divisible by \(5\) . Then \(\mathrm{R}\) isJEE Mains 2024 Medium
- The missing value in the following figure is
JEE Mains 2021 Medium
More PYQs from JEE Mains
- If the system of linear equations \(2 x + y - z =7\) ; \(x-3 y+2 z=1\) ; \(x +4 y +\delta z = k\), where \(\delta, k \in R\) has infinitely many solutions, then \(\delta+ k\) is equal toJEE Mains 2022 Medium
- Let the set of all positive values of \(\lambda\), for which the point of local minimum of the function \(\left(1+x\left(\lambda^2-x^2\right)\right)\) satisfies \(\frac{x^2+x+2}{x^2+5 x+6}<0\), be \((\alpha, \beta)\). Then \(\alpha^2+\beta^2\) is equal to ...........JEE Mains 2024 Hard
- A student score the following marks in five tests : \(45, 54, 41, 57, 43\). His score is not known for the sixth test. If the mean score is \(48\) in the six tests, then the standard deviation of the marks in six tests is:JEE Mains 2019 Hard
- Let \(A=\{1,3,7,9,11\}\) and \(B=\{2,4,5,7,8,10,12\}\). Then the total number of one-one maps \(\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}\), such that \(\mathrm{f}(1)+\mathrm{f}(3)=14\), is :JEE Mains 2024 Hard
- Let \(\mathrm{T}_{\mathrm{r}}\) be the \(\mathrm{r}^{\text {th }}\) term of an A.P. If for some \(\mathrm{m}, \mathrm{T}_{\mathrm{m}}=\frac{1}{25}, \mathrm{~T}_{25}=\frac{1}{20}\), and \(20 \sum_{\mathrm{r}=1}^{25} \mathrm{~T}_{\mathrm{r}}=13\), then \(5 \mathrm{~m} \sum_{\mathrm{r}=\mathrm{m}}^{2 \mathrm{~m}} \mathrm{~T}_{\mathrm{r}}\) is equal toJEE Mains 2025 Medium
- If \(I _{ n }=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \cot ^{ n } x dx ,\) then :JEE Mains 2021 Hard