JEE Mains · Maths · STD 11 - 14. probability
Two integers \(\mathrm{x}\) and \(\mathrm{y}\) are chosen with replacement from the set \(\{0,1,2,3, \ldots ., 10\}\). Then the probability that \(|x-y|>5\) is :
- A \(\frac{30}{121}\)
- B \(\frac{62}{121}\)
- C \(\frac{60}{121}\)
- D \(\frac{31}{121}\)
Answer & Solution
Correct Answer
(A) \(\frac{30}{121}\)
Step-by-step Solution
Detailed explanation
\( \text { If } x=0, y=6,7,8,9,10 \) \( \text { If } x=1, y=7,8,9,10 \) \( \text { If } x=2, y=8,9,10 \) \( \text { If } x=3, y=9,10 \) \( \text { If } x=4, y=10\) If \(x=5, y=\) no possible value Total possible ways \(=(5+4+3+2+1) \times 2\) \( =30 \) Required probability…
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
- From a group of \(10\) men and \(5\) women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, isJEE Mains 2017 Hard
- Let \(S=\left\{x \in[-6,3]-\{-2,2\}: \frac{|x+3|-1}{|x|-2} \geq 0\right\}\) and \(T =\left\{ x \in Z: x ^{2}-7| x |+9 \leq 0\right\}\). Then the number of elements in \(S \cap T\) is \(....\)JEE Mains 2022 Hard
- Let a circle \(\mathrm{C}\) of radius \(1\) and closer to the origin be such that the lines passing through the point \((3,2)\) and parallel to the coordinate axes touch it. Then the shortest distance of the circle \(\mathrm{C}\) from the point \((5,5)\) is :JEE Mains 2024 Hard
- Let a line with direction ratios \(a,-4 a,-7\) be perpendicular to the lines with direction ratios 3, \(-1,2 b\) and \(b, a,-2\). If the point of intersection of the line \(\frac{x+1}{a^{2}+b^{2}}=\frac{y-2}{a^{2}-b^{2}}=\frac{z}{1}\) and the plane \(x - y + z =0\) is \((\alpha, \beta, \gamma)\), then \(\alpha+\beta+\gamma\) is equal to\(.......\)JEE Mains 2022 Hard
- 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
- If the tangent to the curve \(y=x+\sin y\) at a point \((a, b)\) is parallel to the line joining \(\left(0, \frac{3}{2}\right)\) and \(\left(\frac{1}{2}, 2\right),\) thenJEE Mains 2020 Medium
More PYQs from JEE Mains
- Let \(A\) be a \(3 \times 3\) real matrix such that \(A^2(A-2 I)-\) \(4(\mathrm{~A}-\mathrm{I})=\mathrm{O}\), where I and O are the identity and null matrices, respectively. If \(A^5=\alpha A^2+\beta A+\gamma I\), where \(\alpha, \beta\) and \(\gamma\) are real constants, then \(\alpha+\beta+\gamma\) is equal to:JEE Mains 2025 Medium
- Let \(y=y(x)\) be the solution curve of the differential equation secy \(\frac{d y}{d x}+2 x \sin y=x^3 \cos y\), \(y(1)=0\). Then \(y(\sqrt{3})\) is equal to :JEE Mains 2024 Hard
- Let \(f(x)=\int_0^x\left(t+\sin \left(1-e^t\right)\right) d t, x \in \mathbb{R}\). Then \(\lim _{x \rightarrow 0} \frac{f(x)}{x^3}\) is equal toJEE Mains 2024 Hard
- If \((27)^{999}\) is divided by \(7\), then the remainder isJEE Mains 2017 Hard
- Let \(S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }\) If \(T =\sum_{\theta \in S } \cos 2 \theta\), then \(T + n ( S )\) is equalJEE Mains 2022 Hard
- If for the complex numbers \(z\) satisfying \(|z-2-2 i| \leq 1\), the maximum value of \(|3 i z+6|\) is attained at \(\mathrm{a}+i \mathrm{~b}\), then \(\mathrm{a}+\mathrm{b}\) is equal to .... .JEE Mains 2021 Hard