Permutations And Combinations - Algebra - Mathematics Previous Year Questions

The remainder obtained when 5¹²⁴ is divided by 124 is

The number of positive divisors of 252 is

Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points?

The value of \(1\,.\,1! + 2\,.\,2! + 3\,.\,3! + \,...\, + \,n\,.\,n!\) is

The number of triangles which can be formed by using the vertices of a regular polygon of \((n+3)\) sides is 220. Then, \(n\) is equal to

If a polygon of n sides has 275 diagonals, then n is equal to

How many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7?

\((2^{3n}-1)\) is divisible by

\(\sum\limits_{n = 1}^m {n\,.\,n!}\) is equal to

If ⁿC₃ = 220, then n = ?

There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?

A regular polygon of n sides has 170 diagonals, then n is equal to

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. The number of ways in which he can choose the 7 question is

In a 12 storey house, 10 people enter a lift cabin. It is known that they will leave the lift in pre-decided groups of 2, 3 & 5 people at different storeys. The number of ways they can do so if the lift does not stop up to the second storey is

How many factors of \(2^5 \times 3^6 \times 5^2\) are perfect squares?

The number of four digit numbers strictly greater than 4321 formed using the digits \(0,1,2,3,4,5\) with repetition of digit is

A student has 3 library cards and 8 books of his interest in the library. Out of these 8 books he does not want to borrow Chemistry part 2 unless he can borrow Chemistry part 1 also. In how many ways can he choose the three books to be borrowed?

For an examination a candidate has to select 7 questions from three different groups \(\mathrm{A}, \mathrm{B}\) and C. The three groups contain 4, 5 and 6 questions respectively. In how many different ways can a candidate make his selection if he has to select atleast 2 questions from each group?

The letters of the word "COCHIN" are permuted and all the permutations are arranged in alphabetical order as in an English dictionary. The number of words that appear before the word "COCHIN" is