JEE Mains · Maths · STD 11 - 9. straight line
Let the point \((p, p+1)\) lie inside the region \(E=\left\{(x, y): 3-x \leq y \leq \sqrt{9-x^2}, 0 \leq x \leq 3\right\}\) If the set of all values of \(p\) is the interval \((a, b)\). then \(b^2+b-a^2\) is equal to \(.................\).
- A \(2\)
- B \(1\)
- C \(4\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\(3-x \leq y \leq \sqrt{9-x^2}\) Points \(( p , p +1)\) lies on \(y = x +1\) So point of intersection between \(y = x +1 y =3- x \text { is } x =1, y =2\) and point of intersection between \(x+1=\sqrt{9-x^2}\) is \(x=\frac{-1+\sqrt{17}}{2}\) Hence…
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 \( a_{1}=1 \) and for \( n\ge1 \), \( a_{n+1}\)
= \(\frac{1}{2}a_{n}+\frac{n^{2}-2n-1}{n^{2}(n+1)^{2}} \). Then \( |\sum_{n=1}^{\infty}(a_{n}-\frac{2}{n^{2}})| \) is equal to ........... .JEE Mains 2026 Easy - Let \(I\) be an identity matrix of order \(2 \times 2\) and \(P=\left[\begin{array}{cc}2 & -1 \\ 5 & -3\end{array}\right] .\) Then the value of \(n \in N\) for which \(P^n =5 I -8 P\) is equal to ..... .JEE Mains 2021 Medium
- If \(f(x)\) and \(g(x)\) are two polynomials such that the polynomial \(P ( x )=f\left( x ^{3}\right)+ xg \left( x ^{3}\right)\) is divisible by \(x^{2}+x+1,\) then \(P(1)\) is equal to ....... .JEE Mains 2021 Hard
- An unbiased coin is tossed \(5\) times. Suppose that a variable \(\mathrm{X}\) is assigned the value \(\mathrm{k}\) when \(\mathrm{k}\) consecutive heads are obtained for \(\mathrm{k}=3,4,5\) otherwise \(X\) takes the value \(-1 .\) Then the expected value of \(X,\) isJEE Mains 2020 Hard
- If \(\mathrm{e}_{1}\) and \(\mathrm{e}_{2}\) are the eccentricities of the ellipse, \(\frac{\mathrm{x}^{2}}{18}+\frac{\mathrm{y}^{2}}{4}=1\) and the hyperbola, \(\frac{\mathrm{x}^{2}}{9}-\frac{\mathrm{y}^{2}}{4}=1\) respectively and \(\left(\mathrm{e}_{1}, \mathrm{e}_{2}\right)\) is a point on the ellipse, \(15 \mathrm{x}^{2}+3 \mathrm{y}^{2}=\mathrm{k},\) then \(\mathrm{k}\) is equal toJEE Mains 2020 Hard
- One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two faces marked 2 , two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are thrown together, isJEE Mains 2025 Medium
More PYQs from JEE Mains
- Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}=1+x e^{y-x},-\sqrt{2}\,<\,x\,<\,\sqrt{2}, y (0)=0\) then, the minimum value of \(y(x)\) , \(\mathrm{x} \in(-\sqrt{2}, \sqrt{2})\) is equal to:JEE Mains 2021 Hard
- The mean and variance of \(n\) observations are \(8\) and \(16\), respectively. If the sum of the first \((n-1)\) observations is \(48\) and the sum of squares of the first \((n-1)\) observations is \(496\), then the value of \(n\) is:JEE Mains 2026 Medium
- Let \(E ^{ C }\) denote the complement of an event \(E\). Let \(E _{1}, E _{2}\) and \(E _{3}\) be any pairwise independent events with \(P \left( E _{1}\right) > 0\) and \(P \left( E _{1} \cap E _{2} \cap E _{3}\right)=0\) Then \(P \left( E _{2}^{ C } \cap E _{3}^{ C } / E _{1}\right)\) is equal toJEE Mains 2020 Hard
- Let the line \(\mathrm{L}\) be the projection of the line \(\frac{x-1}{2}=\frac{y-3}{1}=\frac{z-4}{2}\) in the plane \(x-2 y-z=3 .\) If \(d\) is the distance of the point \((0,0,6)\) from \(\mathrm{L}\), then \(\mathrm{d}^{2}\) is equal to .... .JEE Mains 2021 Hard
- If \(f : R \rightarrow R\) be a continuous function satisfying \(\int \limits_0^{\pi / 2} f(\sin 2 x) \cdot \sin x d x+\alpha \int \limits_0^{\pi / 4} f(\cos 2 x) \cdot \cos x d x=0\)then \(\alpha\) is equal toJEE Mains 2023 Hard
- Let \(m\) and \(n\) be the number of points at which the function \(f(\mathrm{x})=\max \left\{\mathrm{x}, \mathrm{x}^3, \mathrm{x}^5, \ldots ., \mathrm{x}^{21}\right\}, \mathrm{x} \in \mathbb{R}\), is not differentiable and not continuous, respectively. Then \(\mathrm{m}+\mathrm{n}\) is equal to ________ .JEE Mains 2025 Easy