JEE Mains · Maths · STD 11 - 12. limits
\(\mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{\left( {1 - cos2x} \right)\left( {3 + \cos x} \right)}}{{x\;tan4x}}\) =
- A \( - \frac{1}{4}\)
- B \(\frac{1}{2}\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\(\mathop {\lim }\limits_{x \to 0} \frac{{\left( {1 - \cos 2x} \right)\left( {3 + \cos x} \right)}}{{x\,\tan 4x}}\) \( = \mathop {\lim }\limits_{x \to 0} \frac{{2{{\sin }^2}x\left( {3 + \cos x} \right)}}{{x \times \frac{{\tan 4x}}{{4x}} \times 4x}}\)…
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
- \(\mathop \smallint \limits_2^4 \frac{{\log {x^2}}}{{\log {x^2} + {\rm{log}}\left( {36 - 12x + {x^2}} \right)}}\;dx = \)JEE Mains 2015 Medium
- \(\int_{\frac{3 \sqrt{2}}{4}}^{\frac{3 \sqrt{3}}{4}} \frac{48}{\sqrt{9-4 x^2}} d x\) is equal toJEE Mains 2023 Medium
- A multiple choice examination has \(5\) questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get \(4\) or more correct answers just by guessing is :JEE Mains 2013 Medium
- The integral \(\int_{0}^{\frac{\pi}{2}} \frac{1}{3+2 \sin x+\cos x} d x\) is equal to.JEE Mains 2022 Medium
- If the system of linear equations \(x - 2y + kz = 1\) ; \(2x + y + z = 2\) ; \(3x - y - kz = 3\) Has a solution \((x, y, z) \ne 0\), then \((x, y)\) lies on the straight line whose equation isJEE Mains 2019 Hard
- Three numbers are in an increasing geometric progression with common ratio \(\mathrm{r}\). If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference \(\mathrm{d}\). If the fourth term of GP is \(3 \mathrm{r}^{2}\), then \(\mathrm{r}^{2}-\mathrm{d}\) is equal to:JEE Mains 2021 Hard
More PYQs from JEE Mains
- Let the domain of the function \(f(x)=\log _{4}\left(\log _{5}\left(\log _{3}\left(18 x-x^{2}-77\right)\right)\right)\) be \((a, b)\). Then the value of the integral \(\int_{a}^{b} \frac{\sin ^{3} x}{\left(\sin ^{3} x+\sin ^{3}(a+b-x)\right)} d x\) is equal to \(.....\)JEE Mains 2021 Hard
- If \(\cos ec\,\theta = \frac{{p + q}}{{p - q}}\) \(\left( {p \ne q \ne 0} \right)\), then \(\left| {\cot \left( {\frac{\pi }{4} + \frac{\theta }{2}} \right)} \right|\) is equal toJEE Mains 2014 Hard
- If \(\sin \left(\frac{y}{x}\right)=\log _0|x|+\frac{\alpha}{2}\) is the solution of the differential equation \(x \cos \left(\frac{y}{x}\right) \frac{d y}{d x}=y \cos \left(\frac{y}{x}\right)+x\) and \(y(1)=\frac{\pi}{3}\), then \(\alpha^2\) is equal toJEE Mains 2024 Hard
- Let a relation \(R\) on \(\mathbb{N} \times \mathbb{N}\) be defined as : \(\left(\mathrm{x}_1, \mathrm{y}_1\right) \mathrm{R}\left(\mathrm{x}_2, \mathrm{y}_2\right)\) if and only if \(\mathrm{x}_1 \leq \mathrm{x}_2\) or \(\mathrm{y}_1 \leq \mathrm{y}_2\) Consider the two statements : (\(I\)) \(\mathrm{R}\) is reflexive but not symmetric. (\(II\)) \(\mathrm{R}\) is transitive Then which one of the following is true?JEE Mains 2024 Medium
- Let \(f : R \rightarrow R\) be a function such that \(f(x)=\frac{x^2+2 x+1}{x^2+1}\). ThenJEE Mains 2023 Hard
- If the line \(y =4+ kx , k >0\), is the tangent to the parabola \(y = x - x ^{2}\) at the point \(P\) and \(V\) is the vertex of the parabola, then the slope of the line through \(P\) and \(V\) isJEE Mains 2022 Hard