JEE Exam > JEE Questions > If the integers m and n are chosen at random ...
Start Learning for Free
If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)
- a)1/4
- b)1/7
- c)1/8
- d)1/49
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If the integers m and n are chosen at random from 1 to 100, then the p...
We know that, 71= 7, 72 = 49, 73 = 343, 74 = 2401, 75 = 16807
∴ 7k (where k ∈ Z), results in a number whose unit’ss digit is 7 or 9 or 3 or 1.
Now, 7m + 7n will be divisible by 5 if unit’s place digit of resulting number is 5 or 0 clearly it can never be 5.
But it can be 0 if we consider values of m and n such that the sum of unit’s place digits become 0. And this can be done by choosing
∴ 7k (where k ∈ Z), results in a number whose unit’ss digit is 7 or 9 or 3 or 1.
Now, 7m + 7n will be divisible by 5 if unit’s place digit of resulting number is 5 or 0 clearly it can never be 5.
But it can be 0 if we consider values of m and n such that the sum of unit’s place digits become 0. And this can be done by choosing
(25 options each) [7 + 3 = 10]
(25 options each) [9 + 1= 10]Case I : Thus m can be chosen in 25 ways and n can be chosen in 25 ways
Case II : m can be chosen in 25 ways and n can be chosen in 25 ways
∴ Total no. of selections of m, n so that 7m + 7n is divisible by 5 = (25 × 25 + 25 × 25 ) × 2
Note we can interchange values of m and n.
Also no. of total possible selections of m and n out of 100 = 100 × 100
Also no. of total possible selections of m and n out of 100 = 100 × 100
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer?
Question Description
If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer?.
If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer?.
Solutions for If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals (1999 - 2 Marks)a)1/4b)1/7c)1/8d)1/49Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup