One non-zero digit, one vowel and one consonant from English alphabet (in capital) are to be used in forming passwords, such that each password has to start with a vowel and end with a consonant. How many such passwords can be generated?
- A105
- B525
- C945Correct
- D1050
Explanation
The password consists of three characters: one non-zero digit, one vowel, and one consonant. The constraints are:
- The password must start with a vowel.
- The password must end with a consonant.
Let's determine the number of choices for each type of character:
- Number of non-zero digits: Digits are 1, 2, 3, 4, 5, 6, 7, 8, 9. So, there are 9 choices.
- Number of vowels (capital): A, E, I, O, U. So, there are 5 choices.
- Number of consonants (capital): Total letters = 26. Vowels = 5. Consonants = 26 - 5 = 21 choices.
Now, let's place these characters according to the given rules:
- The first position must be a vowel. Number of choices for the first position = 5 (any of A, E, I, O, U).
- The third (last) position must be a consonant. Number of choices for the third position = 21 (any of the 21 consonants).
- The remaining character is the non-zero digit, which must occupy the middle (second) position. Number of choices for the second position = 9 (any of the 9 non-zero digits).
To find the total number of such passwords, we multiply the number of choices for each position: Total passwords = (Choices for 1st position) * (Choices for 2nd position) * (Choices for 3rd position) Total passwords = 5 * 9 * 21 Total passwords = 45 * 21 Total passwords = 945
Therefore, 945 such passwords can be generated.
The final answer is C) 945.

Related questions
More UPSC Prelims practice from the same subject and topic.
- Prelims 2024CSATQuantitative Aptitude
There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many ways can they be arranged so that each row should…
- Prelims 2024CSATQuantitative Aptitude
There are two containers X and Y. X contains 100 ml of milk and Y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back t…
- Prelims 2024CSATQuantitative Aptitude
There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in t…
- Prelims 2024CSATQuantitative Aptitude
There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider t…
- Prelims 2024CSATQuantitative Aptitude
In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots?
- Prelims 2024CSATQuantitative Aptitude
Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what…