Question 1 :
How many chords can be drawn through 21 points on a circle ?

Question 2 :
There are $'m'$ copies each of $'n'$ different books in a university library. The number of ways in which one or more than one book can be selected is

Question 3 :
There are $5\ mangoes$ and $4\ apples$. In how many different ways can a selection of fruits be made if fruits of same kind are different?(if minimum $1$ fruit is selected)

Question 4 :
The number of the words that can be formed using all the letters of the word BRAIN such that it starts with R and but does not end with A.<br/>

Question 5 :
There are 'mn' letters and n post boxes. The number of ways in which these letters can be posted is:

Question 6 :
Number of odd numbers of five distinct digits can be formed by the digits $0,1,2,3,4,$ is

Question 7 :
Ten different letters of alphabet are given. Words with four letters are formed from these letters, then the number of words which have at least one letter repeated is - <br><br>

Question 8 :
The no .of ways of selecting $3$ men and $2$ women from $6$ men and $6$ women.

Question 9 :
How many zeroes are there in $1 \times 2 \times 3 \times 4 ........... 49 \times 50 $:

Question 10 :
The number of arrangements of these letters of the word 'CALCUTTA'

Question 11 :
The given table shows the possible food choices for lunch. How many different types of lunch can be made each including $1$ type of soup, $1$ type of sandwich and $1$ type of salad?<table class="wysiwyg-table"><tbody><tr><td colspan="3"> Lunch Choices</td></tr><tr><td>Soup</td><td>Sandwich</td><td>Salad</td></tr><tr><td>Chicken</td><td>Cheese</td><td>Vegetable</td></tr><tr><td>Tomato</td><td>Paneer</td><td>Fruit</td></tr></tbody></table>

Question 12 :
10 different letters of a alphabet are given. Words with 5 Letters are formed from these given letters, then the numbers of words which have at least one letter repeated is

Question 13 :
In a crossword puzzle, $20$ words are to be guessed of which $8$ words have each an alternative solution also. The number of possible solutions will be

Question 14 :
The total number of natural numbers lying between $20,000$ and $60,000$ including $60000,$ whose sum of digits is even is

Question 15 :
Words of $4$ letters are to be formed from $10$ different letters. How many words are formed in which at least one letter is repeated?

Question 16 :
Find the number of three letter words that can be formed by using the letters of the word $'MASTER'$

Question 17 :
How many different signals can be transmitted by arranging 3 red, 2 yellow and 2 green flags on a pole? [Assume that all the 7 flags are used to transmit a signal].

Question 18 :
A group consists of 4 couples in which each of the 4 persons have one wife each. In how many ways could they be arranged in a straight line such that the men and women occupy alternate positions?

Question 19 :
Three boys and three girls are to be seated around a table in a circle. Among them the boy X does not want any girl neighbour and the girl Y does not want any boy neighbour. How many such arrangements are possible?

Question 20 :
How many combinations of two-digit numbers having 8 can be made from the following numbers?<br>8, 5, 2, 1, 7, 6

Question 21 :
There are $5$ doors to a lecture hall. The number of ways that a student can enter the hall and leave it by a different door is

Question 22 :
Consider the following statements:<br/>1. If $18$ men can earn Rs. $1,440$ in $5$ days, then $10$ men can earn Rs. $ 1,280$ in $6$ days.<br/>2. If $16$ men can earn Rs. $ 1,120$ in $7$ days, then $21$ men can earn Rs. $ 800$ in $4$ days.<br/>Which of the above statements is/are correct?

Question 23 :
If $\left( {n + 1} \right)! = 12 \times (n - 1)!\;then\;n = $

Question 25 :
If $^{13}C_x=^{13}C_y$ and $x\neq y$, then the value of $x+y$ is ?

Question 26 :
Find the coefficient of the middle term of the expansion $\left (x-\dfrac{1}{2y}\right)^{10}$:<br/>

Question 27 :
If the letter of the word $LATE$ be permuted and the words so formed be arranged as in a dictionary . Then the rank of $LATE$ is :

Question 28 :
In there are 12 persons in a party, and if each two of them shake hands with each other, how many handshakes happen in the party ?

Question 29 :
How many 3-letter words with or without meaning, can be formed out of the letters of the word $LOGARITHMS$ if repitition of letters is not allowed ?

Question 31 :
<div>There are <span class="MathJax_Preview"></span><span class="MathJax"><span class="math"><span><span class="mrow"><span class="mn">4</span></span></span></span><span class="MJX_Assistive_MathML">4</span></span> candidates for a Natural science scholarship, <span class="MathJax_Preview"></span><span class="MathJax"><span class="math"><span><span class="mrow"><span class="mn">2</span></span></span></span><span class="MJX_Assistive_MathML">2</span></span> for a Classical and <span class="MathJax_Preview"></span><span class="MathJax"><span class="math"><span><span class="mrow"><span class="mn">6</span></span></span></span><span class="MJX_Assistive_MathML">6</span></span> for a Mathematical scholarship,then find the no. of ways one of these scholarship can be awarded is,</div>

Question 32 :
If $^nP_r = 30240$ and $^nC_r = 252, $ then the ordered pair $(n,r) $ is equal to :

Question 33 :
In a party, there are 10 married couples. Each person shakes hands with every person other than her or his spouse. The total number of handshakes exchanged in that party is

Question 34 :
In how many ways can 5 persons A,B,C,D and E sit around a circular table.

Question 35 :
Five - digit numbers divisible by 3 are formed using 0, 1, 2, 3, 4, 5 without repetition. The total number of such numbers is :

Question 36 :
Two persons entered a Railway compartment in which 7 seats were vacant.The number of ways in which they can be seated is

Question 37 :
Given 12 points in a plane no three of which are collinear, the number of lines they determine is:

Question 38 :
Ten different letters of an alphabet are given. Words with 5 letters are formed from these given letters. Then the number of words which have at least one letter repeated is

Question 39 :
$15$ buses operate between Hyderabad and Tirupathi.The number of ways can a man go to Tirupathi from Hyderabad by a bus and return by a different bus is

Question 40 :
Find the number of ways in which $5$ persons $A,B,C,D,E$ can be seated round a table such that A and B always sit together?