Permutations and Combinations · Mathematics · NDA
MCQ (Single Correct Answer)
What is the sum of all four-digit numbers formed by using all digits 0, 1, 4, 5 without repetition of digits?
A man has 7 relatives (4 women and 3 men). His wife also has 7 relatives (3 women and 4 men). In how many ways can they invite 3 women and 3 men so that 3 of them are man's relatives and 3 of them are his wife's relatives?
A triangle $PQR$ is such that 3 points lie on the side $PQ$, 4 points on $QR$ and 5 points on $RP$ respectively. Triangles are constructed using these points as vertices. What is the number of triangles so formed?
If $26! = n8^k$, where $k$ and $n$ are positive integers, then what is the maximum value of $k$?
How many four-digit natural numbers are there such that all of the digits are even?
Four digit numbers are formed by using the digits 1, 2, 3, 5 without repetition of digits. How many of them are divisible by 4?
What is the number of different matrices, each having 4 entries that can be formed using 1, 2, 3, 4 (repetition is allowed)?
Consider the following statements :
1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above statements is/are correct ?
How many 4-letter words each of two vowels and two consonants with or without meaning, can be formed ?
How many 8-letter words with or without meaning, can be formed such that consonants and vowels occupy alternate positions?
How many 8-letter words with or without meaning, can be formed so that all consonants are together?
Consider the following statements:
1. $\frac{n!}{3!}$ is divisible by 6, where n > 3
2. $\frac{n!}{3!}+3 $ is divisible by 7, where n > 3
Which of the above statements is/are correct?