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The number of all three digit even numbers such that if 5 is one of the digits then next digit is 7 is
- a)360
- b)370
- c)365
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The number of all three digit even numbers such that if 5 is one of th...
Correct Answer :- c
Explanation : As given condition is , 5 must be followed by 7. So only possible way is 57X where X denotes 0,2,4,6 and 8.
So,total no. of ways=1×1×5=5
Hence, total ways in which we can make a 3-digit even no. without violating given condition are:
360+5=365
Most Upvoted Answer
The number of all three digit even numbers such that if 5 is one of th...
Solution:
To form a three digit even number, we have two choices for the units digit: 0 or 8.
Case 1: Units digit is 0
In this case, we cannot use 5 as the hundreds digit. So, we have 8 choices for the hundreds digit (excluding 5) and 9 choices for the tens digit (any digit except 0 and 5). Therefore, the total number of such numbers is 8 × 9 = 72.
Case 2: Units digit is 8
In this case, we can use 5 as the hundreds digit. So, we have 1 choice for the hundreds digit (which is 5), and 9 choices for the tens digit (any digit except 0 and 7). Therefore, the total number of such numbers is 1 × 9 = 9.
Total number of three digit even numbers satisfying the given conditions = 72 + 9 = 81
Therefore, the correct answer is option C (365 is incorrect).
To form a three digit even number, we have two choices for the units digit: 0 or 8.
Case 1: Units digit is 0
In this case, we cannot use 5 as the hundreds digit. So, we have 8 choices for the hundreds digit (excluding 5) and 9 choices for the tens digit (any digit except 0 and 5). Therefore, the total number of such numbers is 8 × 9 = 72.
Case 2: Units digit is 8
In this case, we can use 5 as the hundreds digit. So, we have 1 choice for the hundreds digit (which is 5), and 9 choices for the tens digit (any digit except 0 and 7). Therefore, the total number of such numbers is 1 × 9 = 9.
Total number of three digit even numbers satisfying the given conditions = 72 + 9 = 81
Therefore, the correct answer is option C (365 is incorrect).
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The number of all three digit even numbers such that if 5 is one of the digits then next digit is 7 isa)360b)370c)365d)none of theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of all three digit even numbers such that if 5 is one of the digits then next digit is 7 isa)360b)370c)365d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of all three digit even numbers such that if 5 is one of the digits then next digit is 7 isa)360b)370c)365d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
The number of all three digit even numbers such that if 5 is one of the digits then next digit is 7 isa)360b)370c)365d)none of theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of all three digit even numbers such that if 5 is one of the digits then next digit is 7 isa)360b)370c)365d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of all three digit even numbers such that if 5 is one of the digits then next digit is 7 isa)360b)370c)365d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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