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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?
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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
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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?
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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?.
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