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?

Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct?

1. The number of straight lines that can be drawn by joining any two of these points is 380.

2. The number of triangles that can be drawn by joining any three of these points is 1140.

Select the correct answer using the code given below.