JEE Mains · Maths · STD 11 - 12. limits
The value of \(\lim _{h \rightarrow 0} 2\left\{\frac{\sqrt{3} \sin \left(\frac{\pi}{6}+h\right)-\cos \left(\frac{\pi}{6}+h\right)}{\sqrt{3} h(\sqrt{3} \cosh -\sinh )}\right\}\) is
- A \(\frac{4}{3}\)
- B \(\frac{2}{\sqrt{3}}\)
- C \(\frac{3}{4}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{4}{3}\)
Step-by-step Solution
Detailed explanation
\(L=\lim _{h \rightarrow 0} 2\left(\frac{\sqrt{3}\left(\frac{1}{2} \cosh +\frac{\sqrt{3}}{2} \sinh \right)-\left(\frac{\sqrt{3}}{2} \cosh -\frac{\sinh }{2}\right)}{(\sqrt{3} h)(\sqrt{3})}\right)\) \(L=\lim _{h \rightarrow 0} \frac{4 \sinh }{3 h}\) \(\Rightarrow L=\frac{4}{3}\)
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 \(\mathrm{f}(\mathrm{x})\) be a polynomial of degree \(3\) such that \(\mathrm{f}(\mathrm{k})=-\frac{2}{\mathrm{k}}\) for \(\mathrm{k}=2,3,4,5 .\) Then the value of \(52-10 \mathrm{f}(10)\) is equal to :JEE Mains 2021 Hard
- The mean and variance of seven observations are \(8\) and \(16\), respectively. If \(5\) of the observations are \(2, 4, 10, 12, 14,\) then the product of the remaining two observations isJEE Mains 2019 Hard
- Let the latus ractum of the parabola \(y ^{2}=4 x\) be the common chord to the circles \(C _{1}\) and \(C _{2}\) each of them having radius \(2 \sqrt{5}\). Then, the distance between the centres of the circles \(C _{1}\) and \(C _{2}\) isJEE Mains 2020 Medium
- If the integral \(525 \int_0^{\frac{\pi}{2}} \sin 2 x \cos ^{\frac{11}{2}} x\left(1+\cos ^{\frac{5}{2}} x\right)^{\frac{1}{2}} d x\) is equal to \((n \sqrt{2}-64)\), then \(n\) is equal toJEE Mains 2024 Hard
- For \(k \in N\), let \(\frac{1}{\alpha(\alpha+1)(\alpha+2) \ldots(\alpha+20)}=\sum_{k=0}^{20} \frac{A_{k}}{a+k}\), where \(a\,>\,0\). Then the value of \(100\left(\frac{A_{14}+A_{15}}{A_{13}}\right)^{2}\) is equal to \(....\)JEE Mains 2021 Hard
- Let \(f: R \rightarrow R\) be a function defined as \(f(x)=\left\{\begin{array}{cl}\frac{\sin (a+1) x+\sin 2 x}{2 x} & , \text { if } x<0 \\ b & , \text { if } x=0 \\ \frac{\sqrt{x+b x^{3}}-\sqrt{x}}{b x^{5 / 2}} & , \text { if } x>0\end{array}\right.\) . If \(f\) is continuous at \(x=0,\) then the value of \(a + b\) is equal to ....... .JEE Mains 2021 Hard
More PYQs from JEE Mains
- A value of \(\theta \in (0, \pi /3)\), for which \(\left| {\begin{array}{*{20}{c}}
{1 + {{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\
{{{\cos }^2}\,\theta }&{1 + {{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\
{{{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{1 + 4\,\cos \,6\theta }
\end{array}} \right| = 0\), isJEE Mains 2019 Hard - A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is \(q\). If \(p : q = m\) \(: n\), where \(m\) and \(n\) are coprime, then \(m + n\) is equal to \(..........\).JEE Mains 2023 Hard
- Number of \(4-\)digit numbers (the repetition of digits is allowed) which are made using the digits \(1, 2, 3\) and \(5\) , and are divisible by \(15\) , is equal to \(............\).JEE Mains 2023 Hard
- Let \(\overrightarrow{O A}=\vec{a}, \overrightarrow{O B}=12 \vec{a}+4 \vec{b}\), and \(\overrightarrow{O C}=\vec{b}\), where \(O\) is the origin. If \(S\) is the parallelogram with adjacent sides \(O A\) and \(O C\), then find the value of \(\frac{\text { area of quadrilateral } O A B C}{\text { area of } S} .\)JEE Mains 2024 Hard
- For \(x \in R,x \ne 0\), if \(y(x)\) is a differentiable function such that \(x\int\limits_1^x {y\left( t \right)} dt = \left( {x + 1} \right)\int\limits_1^x {ty\left( t \right)} dt\) , then \(y(x)\) equals (where \(C\) is a constant)JEE Mains 2016 Hard
- In an examination, there are \(5\) multiple choice questions with \(3\) choices, out of which exactly one is correct There are \(3\) marks for each correct answer, \(-2\) marks for each wrong answer and \(0\) mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets \(5\) marks is. . . . . ... . .JEE Mains 2022 Hard