enEnglishguગુજરાતી
JEE Mains · Maths · STD 11 - 12. limits
\(\mathop {\lim }\limits_{x \to 0} \frac{{x\,\tan \,2x - 2x\,\tan \,x}}{{{{\left( {1 - \cos \,2x} \right)}^2}}}\) equals
- A \(1\)
- B \( - \frac{1}{2}\)
- C \( \frac{1}{4}\)
- D \( \frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \( \frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Let, \(L = \,\,\,\mathop {\lim }\limits_{x \to 0} \frac{{\left( {x\tan 2x - 2x\tan \,x} \right)}}{{{{\left( {1 - \cos \,2x} \right)}^2}}} = \mathop {\lim }\limits_{x \to 0} K\) (say)…
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 the maximum area of the triangle that can be inscribed in the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{4}=1\), a \(>2\), having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the \(y\)-axis, be \(6 \sqrt{3}\). Then the eccentricity of the ellispe isJEE Mains 2022 Hard
- \(50 \tan \left(3 \tan ^{-1}\left(\frac{1}{2}\right)+2 \cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)+4 \sqrt{2} \tan \left(\frac{1}{2} \tan ^{-1}(2 \sqrt{2})\right)\) is equal toJEE Mains 2022 Hard
- \(2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)\) isJEE Mains 2022 Medium
- Let \(f\) and \(g\) be twice differentiable functions on \(R\) such that \(f^{\prime \prime}(x)=g^{\prime \prime}(x)+6 x\) \(f^{\prime}(1)=4 g^{\prime}(1)-3=9\) \(f(2)=3 g(2)=12\) Then which of the following is NOT true ?JEE Mains 2023 Hard
- The equations of two sides of a variable triangle are \(x =0\) and \(y =3\), and its third side is a tangent to the parabola \(y^2=6 x\). The locus of its circumcentre is :JEE Mains 2023 Hard
- Let \(A=\{0,1,2,3,4,5\}\). Let \(R\) be a relation on A defined by \((x, y) \in R\) if and only if max \(\{x, y\} \in\{3,4\}\). Then among the statements \(\left(\mathrm{S}_1\right)\) : The number of elements in R is 18 , and \(\left(\mathrm{S}_2\right)\) : The relation R is symmetric but neither reflexive nor transitiveJEE Mains 2025 Medium
More PYQs from JEE Mains
- Let the Mean and Variance of five observations \(x_1=1, x_2=3, x_3=a, x_4=7\) and \(x_5=b, a \gt b\), be 5 and 10 respectively. Then the Variance of the observations \(n+x_n, n=1,2, \ldots \ldots . .5\) isJEE Mains 2025 Medium
- If the set \(R=\{(a, b) ; a+5 b=42, a, b \in \mathbb{N}\}\) has \(m\) elements and \(\sum_{n=1}^m\left(1-i^{n !}\right)=x+i y\), where \(I=\sqrt{-1}\), then the value of \(m+x+y\) is :JEE Mains 2024 Hard
- The coefficient of \(x^{10}\) in the expansion of \((1 + x)^2 (1 + x^2)^3 ( 1 + x^3)^4\) is euqal toJEE Mains 2018 Hard
- Two different families \(A\) and \(B\) are blessed with equal number of children. There are \(3\) tickets to be distributed amongst the children of these families so that no child gets more than one ticket . If the probability that all the tickets go to the children of the family \(B\) is \(\frac {1}{12}\) , then the number of children in each family is?JEE Mains 2018 Hard
- Let there be three independent events \(E _{1}, E _{2}\) and \(E _{3}\). The probability that only \(E _{1}\) occurs is \(\alpha\), only \(E _{2}\) occurs is \(\beta\) and only \(E _{3}\) occurs is \(\gamma .\) Let \('p'\) denote the probability of none of events occurs that satisfies the equations \((\alpha-2 \beta) p =\alpha \beta\) and \((\beta-3 \gamma) p =2 \beta \gamma .\) All the given probabilities are assumed to lie in the interval \((0,1)\) Then, \(\frac{\text { Probability of occurrence of } E _{1}}{\text { Probability of occurrence of } E _{3}}\) is equal to ..........JEE Mains 2021 Hard
- If \(A=\) \(\left[ {\begin{array}{*{20}{c}}{5a}&{ - b}\\3&2\end{array}} \right]\) and \(A\;adj\;A = A\;{A^T},\) then \(5a+b \) to :JEE Mains 2016 Medium