MHT CET · Maths · Area Under Curves
The area included between the parabolas \(y^{2}=5 x\) and \(x^{2}=5 y\) is
- A \(\frac{25}{7}\) sq. units
- B \(\frac{25}{3}\) sq. units
- C \(\frac{25}{4}\) sq. units
- D \(25 \mathrm{sq}\). units
Answer & Solution
Correct Answer
(B) \(\frac{25}{3}\) sq. units
Step-by-step Solution
Detailed explanation
(C)
Prabolas\(y^{2}=5 x\) and \(x^{2}=5 y\) intersect at
\(\frac{x^{2}}{5}=5 x \Rightarrow x^{*}=5^{3} x \Rightarrow x\left(x^{3}-125\right)=0 \Rightarrow x=\) \(0.5 \Rightarrow y=0,5\)
Let points of intersection be \(Q(0,0)\) and \(A(5.5)\). Required area is shaded. Ares included becween the parabolas
\(=\int \sqrt{5 x}-\frac{x}{5} d x\)
\(\left.=\frac{\sqrt{5} x}{3}-\frac{x^{3}}{15}=\frac{2}{3}\right)(\sqrt{5})(5 \sqrt{5})-\frac{125}{15}\)
\(=\frac{50}{3}-\frac{125}{15}=\frac{25}{3}\)
Prabolas\(y^{2}=5 x\) and \(x^{2}=5 y\) intersect at
\(\frac{x^{2}}{5}=5 x \Rightarrow x^{*}=5^{3} x \Rightarrow x\left(x^{3}-125\right)=0 \Rightarrow x=\) \(0.5 \Rightarrow y=0,5\)
Let points of intersection be \(Q(0,0)\) and \(A(5.5)\). Required area is shaded. Ares included becween the parabolas
\(=\int \sqrt{5 x}-\frac{x}{5} d x\)
\(\left.=\frac{\sqrt{5} x}{3}-\frac{x^{3}}{15}=\frac{2}{3}\right)(\sqrt{5})(5 \sqrt{5})-\frac{125}{15}\)
\(=\frac{50}{3}-\frac{125}{15}=\frac{25}{3}\)
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
- A line \(4 x+y=1\) passes through the point \(\mathrm{A}(2,-7)\) meets the line BC whose equation is \(3 x-4 y+1=0\) at the point B . The equation of the line \(A C\) so that \(A B=A C\) isMHT CET 2024 Hard
- \(\sqrt{2+\sqrt{2+2 \cos 4 \theta}}=\)MHT CET 2020 Easy
- In a meeting \(60 \%\) of the members favour and \(40 \%\) oppose a certain proposal. A member is selected at random and we take \(\mathrm{X}=0\) if the opposed and \(\mathrm{X}=1\) if he is in favour, then Var \(\mathrm{X}=\)MHT CET 2021 Easy
- If the volume of the parallelopiped whose conterminus edges are along the vectors \(\bar{a}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) is 12, then the volume of the tetrahedron whose conterminus edges are \(\bar{a}+\overline{\mathrm{b}}, \overline{\mathrm{b}}+\overline{\mathrm{c}}\) and \(\overline{\mathrm{c}}+\overline{\mathrm{a}}\) isMHT CET 2020 Easy
- The discrete random variable \(\mathrm{X}\) can take all possible integer values from 1 to \(\mathrm{k}\), each with a probability \(\frac{1}{\mathrm{k}}\), then its variance isMHT CET 2023 Easy
- Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold isMHT CET 2020 Easy
More PYQs from MHT CET
- The equation of the plane containing the line \(\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}\) and the point \((0,7,-7)\) isMHT CET 2021 Medium
- A sphere of mass \(m\) moving with velocity \(v\) collides head-on another sphere of same mass which is at rest. The ratio of final velocity of the second sphere to the initial velocity of the first sphere is ( \(e\) is the coefficient of restitution and collision is inelastic)MHT CET 2018 Medium
- Nitrates of soil are also leached deep into the earth by ________.MHT CET 2025 Medium
- Which of the following statements is correct about zero order reaction?MHT CET 2024 Medium
- A wire of length 'L' and radius ' \(\mathrm{r}\) ' is loaded with a weight ' \(\mathrm{Mg}\) '. If ' \(\mathrm{Y}\) ' and ' \(\sigma\) ' denote the Young's modulus and poisson's ratio of the material of the wire respectively, then the decrease in the radius of the wire \((\Delta \mathrm{r})\) is given byMHT CET 2020 Medium
- A body of mass ' \(\mathrm{m}\) ' attached at the end of a string is just completing the loop in a vertical circle. The apparent weight of the body at the lowest point in its path is ( \(\mathrm{g}=\) gravitational acceleration)MHT CET 2023 Medium