WBJEE · Maths · Area Under Curves
The area of the region lying above \(X\) -axis, and included between the circle \(x^{2}+y^{2}=2 a x\) and the parabola \(y^{2}=a x, a>0\) is
- A \(8 \pi a^{2}\)
- B \(a^{2}\left(\frac{\pi}{4}-\frac{2}{3}\right)\)
- C \(\frac{16 \pi a^{2}}{9}\)
- D \(\pi\left(\frac{27}{8}+3 a^{2}\right)\)
Answer & Solution
Correct Answer
(B) \(a^{2}\left(\frac{\pi}{4}-\frac{2}{3}\right)\)
Step-by-step Solution
Detailed explanation
Given, equation of circle \(x^{2}+y^{2}=2 a x\) \(\Rightarrow\) \((x-a)^{2}+y^{2}=a^{2}\) and equation of parabola is \(y^{2}=a x, a>0\) Intersection points of circle and parabola \(\begin{array}{lr}\Rightarrow & x^{2}+a x=2 a x \\ \Rightarrow & x^{2}=a x\end{array}\)…
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 \(f: R \rightarrow R\) be differentiable at \(x=0\). If f(0)=0 and f'(0)=2, then the value of \[
\left.\lim _{x \rightarrow 0} \frac{1}{x} \mid f(x)+f(2 x)+f(3 x)+\ldots+f(2015 x)\right] \text{ is}
\]WBJEE 2015 Medium - The function \(f(x)=a \sin |x|+b e^{| x \mid} \quad\) is differentiable at \(x=0\) whenWBJEE 2014 Medium
- If \(f(x)=\frac{e^x}{1+e^x}, l_1=\int_{f(-a)}^{f(a)} x g(x(1-x)) d x\) and \(l_2=\int_{f(-a)}^{f(a)} g(x(1-x)) d x\), then the value of \(\frac{l_2}{l_1}\) isWBJEE 2024 Medium
- A ray of light along \(x+\sqrt{3}y=\sqrt{3}\) gets reflected upon reaching \(x\)-axis, the equation of the reflected ray isWBJEE 2021 Easy
- \(\mathrm{A}\) student appears for tests 1 , 11 and \(\mathrm{III}\). The student is successful if he passes in tests I,II or I, III. The probabilities of the student passing in tests I. II and III are respectively,
p,q and \(1 / 2 .\) If the probability of the student to be successful is \(1 / 2 .\) ThenWBJEE 2018 Easy - If \(f(x)\) is an odd differentiable function defined on \((-\infty, \infty)\) such that \(f^{\prime}(3)=2,\) then \(f^{\prime}(-3)\) is equal toWBJEE 2016 Medium
More PYQs from WBJEE
- An electric current \(^{\prime} I^{\prime}\) enters and leaves a uniform circular wire of radius \(r\) through diametrically opposite points. A particle carrying a charge \(q\) moves along the axis of the circular wire with speed \(v\). What is the magnetic force experienced by the particle when it passes through the centre of the circle?WBJEE 2019 Medium
- An interference pattern is obtained with two coherent sources of intensity ratio \(\mathrm{n}: 1\). The ratio \(\frac{\mathrm{I}_{\text {Max }}-\mathrm{I}_{\text {Min }}}{\mathrm{I}_{\text {Max }}+\mathrm{I}_{\text {Min }}}\) will be maximum ifWBJEE 2023 Easy
-
As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius 'r' concentrically inside a square of side ' \(a\) ', where \(a: r=8: \pi\). A battery B drives a current through the wire. If the battery B and the gap G are of negligible sizes, determine the strength of magnetic field at the common centre \(O\).WBJEE 2020 Medium - \(\beta-emission\) is always accompanied byWBJEE 2014 Easy
-
In the given circuit, the binary inputs at \(A\) and \(B\) are both 1 in one case and both 0 in the next case. The respective outputs at \(Y\) in these two cases will beWBJEE 2017 Easy - The least positive value of \(t\), so that the lines \(x=t+\alpha, y+16=0 \quad\) and \(\quad y=\alpha x\) are concurrent, isWBJEE 2015 Medium