Arun Sharma Solutions for Exercise 3: Level of Difficulty

How many different $7$-digit numbers are there, the sum of whose digits are odd?

Six white and six black balls of the same size are distributed among ten urns so that there is at least one ball in each urn. What is the number of different distributions of the balls?

Amartya Banerjee has forgotten the telephone number of his best friend Abhijit Roy. All he remembers is that the number had $8$-digits and ended with an odd number and had exactly one $9$. How many possible numbers does Amartya have to try to be sure that he gets the correct number?

There are $100$ articles numbered $n_1$,$n_2$,$n_3$,$n_4$,......$n_{100}$. They are arranged in all possible ways. How many arrangements would be there in which $n_{28}$ will always be before $n_{29}$.

The letters of the word PASTE are written in all possible orders and these words are written out as in a dictionary. Then the rank of the word SPATE is:

The straight lines $S_1$, $S_2$, $S_3$ are in a parallel and lie in the same plane. A total number of $A$ points on $S_1$; $B$ points on $S_2$ and $C$ points on $S_3$ are used to produce triangles. What is the maximum number of triangles formed?

The sides $AB$, $BC,$ $CA$ of a triangle $ABC$ have $3$, $4$ and $5$ interior points respectively on them. The total number of triangles. that can be constructed by using these points as vertices are:

The AMS MOCK CAT test CATALYST $19$ consists of four sections. Each section has a maximum marks of $45$ marks. Find the number of ways in which a student can qualify in the AMS MOCK CAT if the qualifying mark is $90$.