Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let  be the maximum value of the product of two positive integers when their sum is 66 . Let the sample space <img a

Let M be the maximum value of the product of two positive integers when their sum is 66 . Let the sample space \mathrm{S}=\left\{x \in \mathbb{Z}: x(66-x) \geq \frac{5}{9} M\right\}and the event \mathrm{A}=\{x \in \mathrm{S}: x  is a multiple of 3 \}. Then \mathrm{P}(\mathrm{A}) is equal to

Option: 1

\frac{7}{22}


Option: 2

\frac{1}{5}


Option: 3

\frac{15}{44}


Option: 4

\frac{1}{3}


Answers (1)

best_answer

Let \mathrm{a}, \mathrm{b} \rightarrow 2 positive number
\frac{\mathrm{a}+\mathrm{b}}{2} \geq \sqrt{a b}

\sqrt{\mathrm{ab}} \leq 33
\mathrm{ab} \leq(33)^{2} \quad \mathrm{M}=(33)^{2}

x(66-x) \geq \frac{5}{9}(33)^{2}
66 \mathrm{x}-\mathrm{x}^{2} \geq 605
0 \geq x^{2}-66 x+605
(\mathrm{x}-11)(\mathrm{x}-55) \leq 0
\mathrm{x} \in[11,55]
A=\{12,15,18 \ldots .54\}

\text { Total number in } \mathrm{A}=15
\mathrm{P}(\mathrm{A})=\frac{15}{45}=\frac{1}{3} \text { Ans. }

Posted by

Devendra Khairwa

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Mains 2026 April 8 LIVE: Day 6 exam for BTech from 3 pm today; guidelines, question paper analysis
anam-khan

JEE Main 2026 April 6 shift 2 exam ‘easy to moderate’; Maths toughest, Physics easier
anam-khan

JEE Main 2026 April 6 Shift 1: Students find Maths tough, chemistry slightly tough, physics calculation heavy

Latest Question