JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region, inside the circle \((x-2 \sqrt{3})^2+y^2=12\) and outside the parabola \(y^2=2 \sqrt{3} x\) is :
- A \(3 \pi+8\)
- B \(6 \pi-16\)
- C \(3 \pi-8\)
- D \(6 \pi-8\)
Answer & Solution
Correct Answer
(B) \(6 \pi-16\)
Step-by-step Solution
Detailed explanation
Required area \(=2 \int_0^{2 \sqrt{3}}\left(\sqrt{4 \sqrt{3} x-x^2}-\sqrt{2 \sqrt{3} x}\right) d x \) \( =2 \int_0^{2 \sqrt{3}}\left(\sqrt{12-(x-2 \sqrt{3})^2}-\sqrt{2 \sqrt{3} x}\right) d x \)…
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
- 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
- Let \(\mathrm{A}\) and \(\mathrm{B}\) be two square matrices of order \(3\) such that \(|A|=3\) and \(|B|=2\). Then \(\left|\mathrm{A}^{\mathrm{T}} \mathrm{A}(\operatorname{adj}(2 \mathrm{~A}))^{-1}(\operatorname{adj}(4 \mathrm{~B}))(\operatorname{adj}(\mathrm{AB}))^{-1} \mathrm{AA}^{\mathrm{T}}\right|\) is equal to :JEE Mains 2024 Hard
- Let \(S\) be the set containing all \(3 \times 3\) matrices with entries from \(\{-1,0,1\}\). The total number of matrices \(A \in S\) such that the sum of all the diagonal elements of \(A ^{ T } A\) is \(6\) is.JEE Mains 2022 Hard
- The value of the definite integral \(\int_{\pi / 24}^{5 \pi / 24} \frac{d x}{1+\sqrt[3]{\tan 2 x}} \text { is }\)JEE Mains 2021 Hard
- Let \({f_k}\left( x \right) = \frac{1}{k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)\) where \(x \in R\;\) and \(k \ge 1\). Then \({f_4}\left( x \right) - {f_6}\left( x \right) \) is equalsJEE Mains 2014 Hard
- If the function \(f(x)=\left(\frac{1}{x}\right)^{2 x} ; x>0\) attains the maximum value at \(\mathrm{x}=\frac{1}{\mathrm{e}}\) then :JEE Mains 2024 Hard
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 \(f\left( n \right) = \left[ {\frac{1}{3} + \frac{{3n}}{{100}}} \right]n\) , where \([n]\) denotes the greatest integer less than or equal to \(n\). Then \(\sum\limits_{n = 1}^{56} {f\left( n \right)} \) is equal toJEE Mains 2014 Hard
- The differential equation satisfied by the system of parabolas \(y ^{2}=4 a ( x + a )\) isJEE Mains 2021 Hard
- Let \(\alpha \) and \(\beta \) be the roots of the quadratic equation \({x^2}\,\sin \,\theta - x\,\left( {\sin \,\theta \cos \,\,\theta + 1} \right) + \cos \,\theta = 0\,\left( {0 < \theta < {{45}^o}} \right)\) , and \(\alpha < \beta \). Then \(\sum\limits_{n = 0}^\infty {\left( {{\alpha ^n} + \frac{{{{\left( { - 1} \right)}^n}}}{{{\beta ^n}}}} \right)} \) is equal toJEE Mains 2019 Hard
- \(\frac{2^{3}-1^{3}}{1 \times 7}+\frac{4^{3}-3^{3}+2^{3}-1^{3}}{2 \times 11}+\)\(\frac{6^{3}-5^{3}+4^{3}-3^{3}+2^{3}-1^{3}}{3 \times 15}+\ldots .+\) \(\frac{30^{3}-29^{3}+28^{3}-27^{3}+\ldots+2^{3}-1^{3}}{15 \times 63}\)is equal to.JEE Mains 2022 Hard
- If the vector \(\vec b = 3\hat j + 4\hat k\) is written as the sum of a vector \({\vec {b_1}}\) , parallel to \(\vec a = \hat i + \hat j\) and a vector \({\vec {b_2}}\) , perpendicular to \(\vec a\) , then \({\vec {b_1}} \times {\vec {b_2}}\) is equal toJEE Mains 2017 Hard