JEE Mains · Maths · STD 12 - 8. Application and integration
Let the area of the region \(\left\{(x, y):|2 x-1| \leq y \leq\left|x^2-x\right|, 0 \leq x \leq 1\right\}\) be \(A\). Then \((6 A +11)^2\) is equal to \(.......\).
- A \(124\)
- B \(123\)
- C \(198\)
- D \(125\)
Answer & Solution
Correct Answer
(D) \(125\)
Step-by-step Solution
Detailed explanation
\(y \geq|2 x -1|, y \leq\left| x ^2- x \right|\) Both curve are symmetric about \(x =\frac{1}{2}\) Hence \(A=2 \int \limits_{\frac{3-\sqrt{5}}{2}}^{\frac{1}{2}}\left(\left(x-x^2\right)-(1-2 x)\right) d x\)…
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
- The common difference of the \(A.P.:a_{1},a_{2},....,a_{m}\) is 13 more than the common difference of the \(A.P.: b_{1}, b_{2},...,b_{n}.\) If \(b_{31}=-277, b_{43}=-385\) and \(a_{78}=327,\) then \(a_{1}\) is equal toJEE Mains 2026 Hard
- If \(f(x)\, = {x^2} - x + 5,\,\,x > \frac{1}{2},\) and \(g(x)\) is its inverse function, then \(g'(7)\) equalsJEE Mains 2014 Hard
- Let \(\vec{a}=6 \hat{i}+9 \hat{j}+12 \hat{k}, \vec{b}=\alpha \hat{i}+11 \hat{j}-2 \hat{k}\) and \(\vec{c}\) be vectors such that \(\vec{a} \times \vec{c}=\vec{a} \times \vec{b}\). If \(\vec{a} \cdot \vec{c}=-12\), \(\vec{c} .(\hat{i}-2 \hat{j}+\hat{k})=5\), then \(\vec{c} \cdot(\hat{i}+\hat{j}+\hat{k})\) is equal to \(.............\).JEE Mains 2023 Hard
- Let \(x_1, x_2, \ldots, x_{10}\) be ten observations such that \(\sum_{i=1}^{10}\left(x_i-2\right)=30, \sum_{i=1}^{10}\left(x_i-\beta\right)^2=98, \beta\gt2\), and their variance is \(\frac{4}{5}\). If \(\mu\) and \(\sigma^2\) are respectively the mean and the variance of \(2\left(x_1-1\right)+4 \beta\), \(2\left(x_2-1\right)+4 \beta, \ldots ., 2\left(x_{10}-1\right)+4 \beta\), then \(\frac{\beta \mu}{\sigma^2}\) is equal to :JEE Mains 2025 Medium
- Let \(N\) be the set of natural numbers and a relation \(R\) on \(N\) be defined by \(R=\left\{(x, y) \in N \times N: x^{3}-3 x^{2} y-x y^{2}+3 y^{3}=0\right\} .\) Then the relation \(R\) is:JEE Mains 2021 Hard
- Let \(f\left( x \right) = x\left| x \right|\,,\,g\left( x \right) = \sin \,x\) and \(h\left( x \right) = \left( {gof} \right)\left( x \right)\). ThenJEE Mains 2014 Hard
More PYQs from JEE Mains
- Let \(B _{i}(i=1,2,3)\) be three independent events in a sample space. The probability that only \(B _{1}\) occur is \(\alpha,\) only \(B _{2}\) occurs is \(\beta\) and only \(B _{3}\) occurs is \(\gamma\). Let \(p\) be the probability that none of the events \(B _{i}\) occurs and these \(4\) probabilities satisfy the equations \((\alpha-2 \beta) p =\alpha \beta\) and \((\beta-3 \gamma) p =2 \beta \gamma\) (All the probabilities are assumed to lie in the interval \((0,1))\). Then \(\frac{ P \left( B _{1}\right)}{ P \left( B _{3}\right)}\) is equal to ..........JEE Mains 2021 Hard
- Let \(A = \begin{bmatrix} 1 & 1 & 2 \\ -2 & 0 & 1 \\ 1 & 3 & 5 \end{bmatrix}\). Then the sum of all elements of the matrix \(\text{adj}(\text{adj}(2(\text{adj}A)^{-1}))\) is equal to:JEE Mains 2026 Hard
- A bag contains \(8\) balls, whose colours are either white or black. \(4\) balls are drawn at random without replacement and it was found that \(2\) balls are white and other \(2\) balls are black. The probability that the bag contains equal number of white and black balls is :JEE Mains 2024 Medium
- Let the normals at all the points on a given curve pass through a fixed point \((a, b) .\) If the curve passes through \((3,-3)\) and \((4,-2 \sqrt{2}),\) and given that \(a-2 \sqrt{2} b=3,\) then \(\left(a^{2}+b^{2}+a b\right)\) is equal to ..... .JEE Mains 2021 Hard
- A random variable \(X\) has the following probability distribution
Then \(\mathrm{P}(\mathrm{X}> 2)\) is equal to\(X\) \(1\) \(2\) \(3\) \(4\) \(5\) \(P(X)\) \(K^2\) \(2K\) \(K\) \(2K\) \(5K^2\) JEE Mains 2020 Hard - Let \(\mathrm{P}\) be the plane passing through the point \((1,2,3)\) and the line of intersection of the planes \(\vec{r} \cdot(\hat{i}+\hat{j}+4 \hat{k})=16\) and \(\vec{r} \cdot(-\hat{i}+\hat{j}+\hat{k})=6\). Then which of the following points does NOT lie on \(\mathrm{P}\) ?JEE Mains 2021 Medium