JEE Mains · Maths · STD 12 - 8. Application and integration
If the area of the larger portion bounded between the curves \(x^2+y^2=25\) and \(y=|x-1|\) is \(\frac{1}{4}(b \pi+c), b, c \in N\), then \(b+c\) is equal to
- A 55
- B 66
- C 77
- D 88
Answer & Solution
Correct Answer
(C) 77
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{x}^2+\mathrm{y}^2=5 \\ & \mathrm{x}^2+(\mathrm{x}-1)^2=25 \Rightarrow \mathrm{x}=4 \\ & \mathrm{x}^2+(-\mathrm{x}+1)^2=5 \Rightarrow \mathrm{x}=-3 \\ & \mathrm{~A}=25 \pi-\int_{-3}^4 \sqrt{25-\mathrm{x}^2} \mathrm{dx}+\frac{1}{2} \times 4 \times…
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
- The integral \(\int {\frac{{dx}}{{{{(x + 1)}^{\frac{3}{4}}}{{(x - 2)}^{\frac{5}{4}}}}}} \) is equal toJEE Mains 2015 Hard
- The value of the integral \(\int \limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{x+\frac{\pi}{4}}{2-\cos 2 x} d x\) is :JEE Mains 2023 Hard
- Let \(f: R \rightarrow R\) be defined as \(f(x)=\left[\begin{array}{ll}{\left[e^{x}\right],} \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,x<0 \\ a e^{x}+[x-1], \,\,\,\,\,\,\,\,\,0 \leq x<1 \\ b+[\sin (\pi x)], \,\,\,\,\,\,\,\,\,\,\,\,1 \leq x<2 \\ {\left[e^{-x}\right]-c,} \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,x \geq 2\end{array}\right.\) where a,b,c \(\in R\) and \([t]\) denotes greatest integer less than or equal to \(t.\) Then, which of the following statements is true \(?\)JEE Mains 2022 Hard
- The area of the bounded region enclosed by the curve \(y=3-\left|x-\frac{1}{2}\right|-|x+1|\) and the \(x-\)axis isJEE Mains 2022 Hard
- Let the solution curve \(y=y(x)\) of the differential equation \(\left(1+ e ^{2 x }\right)\left(\frac{ dy }{ dx }+ y \right)=1\) pass through the point \(\left(0, \frac{\pi}{2}\right)\). Then, \(\lim _{x \rightarrow \infty} e ^{x} y(x)\) is equal to.JEE Mains 2022 Hard
- An are \(P Q\) of a circle subtends a right angle at its centre \(O\). The mid point of the arc \(P Q\) is \(R\). If \(\overline{O P}=\vec{u}, \overline{O R}=\vec{v}\) and \(\overrightarrow{O Q}=\alpha \vec{u}+\beta \vec{v}\), then \(\alpha, \beta^2\) are the roots of the equationJEE Mains 2023 Hard
More PYQs from JEE Mains
- The area enclosed by the curves \(y^2+4 x=4\) and \(y-2 x=2\) is :JEE Mains 2023 Medium
- The minimum value of the function \(f(x)=\int \limits_0^2 e^{|x-t|} d t\) isJEE Mains 2023 Hard
- The largest value of \(a,\) for which the perpendicular distance of the plane containing the lines \(\vec{r}=(\hat{i}+\hat{j})+\lambda(\hat{i}+a \hat{j}-\hat{k})\) and \(\vec{r}=(\hat{i}+\hat{j})+\mu(-\hat{i}+\hat{j}-a \hat{k})\) from the point \((2,1,4)\) is \(\sqrt{3}\), is\(...\)JEE Mains 2022 Hard
- The local maximum value of the function \(f(x)=\left(\frac{2}{x}\right)^{x^{2}}, x>0\), isJEE Mains 2021 Hard
- If \(A = \dfrac{\sin 3^\circ}{\cos 9^\circ} + \dfrac{\sin 9^\circ}{\cos 27^\circ} + \dfrac{\sin 27^\circ}{\cos 81^\circ}\) and \(B = \tan 81^\circ - \tan 3^\circ\), then \(\dfrac{B}{A}\) is equal to _____.JEE Mains 2026 Medium
- Let PQR be a triangle. The points \(A , B\) and \(C\) are on the sides \(QR , RP\) and \(PQ\) respectively such that \(\frac{ QA }{ AR }=\frac{ RB }{ BP }=\frac{ PC }{ CQ }=\frac{1}{2}\). Then \(\frac{\operatorname{Area}(\triangle PQR )}{\operatorname{Area}(\triangle ABC )}\) is equal to \(........\)JEE Mains 2023 Hard