Question 1 :
Number of odd numbers of five distinct digits can be formed by the digits $0,1,2,3,4,$ is 
Question 2 :
Arrange the given words in the sequence in which they occur in the dictionary and then choose the correct sequence.<br/>1. Page 2. Pagan 3. Palisade 4. Pageant 5. Palate
Question 3 :
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 4 :
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 5 :
$15$ 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 6 :
The number of nine digit numbers that can be formed with different digits is
Question 7 :
$3$ letters are posted in $5$ letters boxes. If all the letters are not posted in the same box, then number of ways of posting is
Question 8 :
Two persons entered a Railway compartment in which 7 seats were vacant.The number of ways in which they can be seated is
Question 9 :
A bag contains Rs. $112$ in the form of $1$-rupee, $50$-paise and $10$-paise coins in the ratio $3 : 8 : 10$. What is the number of $50$-paise coins?
Question 10 :
 An automobile dealer provides motor cycles and scooters in three body patterns and $4$ different colours each. The number of choices open to a customer is
Question 11 :
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 12 :
In the series given below. count the number of 9s, each of which Is not immediately preceded by 5 but is immediately followed by either 2 or 3. How many such 9s are there?<br>1 9 2 6 5 9 3 8 3 9 3 2 5 9 2 9 3 4 8 2 6 9 8<br>
Question 13 :
How many ways can $4$ prizes be given away to $3$ boys, if each boy is eligible for all the prizes?
Question 14 :
If the letters of word ' IMPORTANCE ' are arranged from left to right in alphabetic order , then which letter will be the fifth from left <br>
Question 15 :
The greatest number that can be formed by the digits $7,0,9,8,6,3$
Question 16 :
The number of unsuccessful attempts that can be made by a thief to open a number lock having $3$ rings in which each rings contains $6$ numbers is
Question 17 :
There are $5$ roads leading to a town from a village. The number of different ways in which a villager can go to the town and return back, is
Question 18 :
There are 44 candidates for a Natural science scholarship, 22 for a Classical and 66 for a Mathematical scholarship,then find the no. of ways one of these scholarship can be awarded is,
Question 19 :
Re. 1 and Rs. 5 coins are available (as many required). Find the smallest payment which cannot be made by these coins, if not more than 5 coins are allowed.
Question 20 : 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 21 :
Using the  digits $0,  2, 4, 6,  8$ not  more than once in any number, the number of $5$ digited numbers that can be formed is<br/>
Question 23 :
In a class there are 18 boys who are over 160 cm tall If these constitute three-fourths of the boys and the total number of boys is tow-third of the total number of students in the class what is the number of girls in the class?
Question 24 :
Five persons A, B, C, D and E occupy seats in a row such that A and B sit next to each other. In how many possible ways can these five people sit?
Question 25 :
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 26 :
A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is:
Question 27 :
A pod of $6$ dolphins always swims single file, with $3$ females at the front and $3$ males in the rear. In how many different arrangements can the dolphins swim?
Question 28 :
On the eve of Diwali festival, a group of 12 friends greeted every other friend by sending greeting cards. Find the number of cards purchased by the group.
Question 29 :
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 30 :
State following are True or False<br/>If m=n=p and the groups have identical qualitative characterstic then the number of groups $=\dfrac { (3n)! }{ n!n!n!3! } $<br/>Note : If 3n different things are to be distributed equally three people then the number of ways$=\dfrac { (3n)! }{ { (n!) }^{ 3 } } $
Question 31 :
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 32 :
A shelf contains $15$ books, of which $4$ are single volume and the others are $8$ and $3$ volumes respectively. In how many ways can these books be arranged on the shelf so that order of the volumes of same work is maintained $?$
Question 33 :
Out of 100 students 50 fail in English and 30 in Maths. If 12 students fail in both English and Maths, then the number of students passing both the subjects is
Question 34 :
There are $4$ boys and $4$ girls. In how many ways they can sit in a row.
Question 35 :
There  are 'mn' letters and n post boxes. The number of ways in which these letters can be posted is:
Question 36 :
A batsman can score $0,1,2,3,4$ or $6$ runs from a ball. The number of different sequences in which he can score exactly $30$ runs in an over of six balls is:
Question 37 :
A garrison of '$n$' men had enough food to last for $30$ days. After $10$ days, $50$ more men joined them. If the food now lasted for $16$ days, what is the value of $n$?
Question 38 :
Ten different letter of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is:
Question 39 :
Find the number of permutations that can be made with the letters of the word $'MOUSE'$
Question 40 :
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 41 :
The number of permutations of letters of the word "PARALLAL" atken four at a time must be,
Question 42 :
Let $y$ be an element of the set $A=\left\{1,2,3,5,6,10,15,30\right\}$ and $x_1,x_2,x_3$ be integers such that $x_1x_2x_3=y,$ then the number of positive integral solutions of $x_1x_2x_3=y$ is
Question 43 :
The number of different signals that can be formed by using any number of flags from $4$ flags of different colours is
Question 44 :
There are $4$ candidates for a Natural science scholarship, $2$ for a Classical and $6$ for a Mathematical scholarship,then find No. of ways these scholarships can be awarded is,
Question 45 :
Let the eleven letters, $A, B, ....K$ denote an artbitrary permutation of the integers $(1,2,....11)$, then $(A-1)(B-2)(C-3)...(K-11)$ is
Question 46 :
Let $\boxed { n }$ be defined as $\frac{(n+2)!}{(n-1)!}$, what is the value of $\frac{\boxed{7}}{\boxed {3}}$ ?
Question 47 :
$4$ buses runs between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by another bus, then the total possible ways are
Question 48 :
How many four letter words with or without meaning, can be formed out of the letters of the word $'LOGARITHMS'$, if repetition of letters is not allowed
Question 49 :
The digits $4,5,6,7$ and $8$ written in every possible order. The number of numbers greater than $56,000$ is
Question 50 :
$n-$digit number is a positive number with exactly $n$ digits. Nine hundred distinct $n-$digit numbers are to be formed using only the three digits $2,5$ and $7$. The smallest value of $n$ for which this is possible, is
Question 51 :
There are $n$ different books and $p$ copies of each in a library. The number of ways in which one or more than one book can be selected is:
Question 52 :
The number of even numbers with three digits such that if 3 is one of the digit then 5 is the next digit are <br/>
Question 53 :
How many different words can be formed by taking four letters out of the letters of the word 'AGAIN' if each word has to start with A ?
Question 54 :
Let $A=(x|x$ is a prime number and $x<300$ > the number of different rational numbers, whose numerator and denominator belong to $A$ is:
Question 55 :
Let x.y.z$=$105 where $ x, y, z \in N $. Then number of ordered triplets (x, y, z) satisfying the given equation is
Question 56 :
The number of different ways in which $5$ 'dashes' and $8$ 'dots' can be arranged, using only $7$ of these 'dashes' and 'dots', is
Question 57 :
How many five-digit multiples of 11 are there, if the five digits are 3, 4, 5, 6 and 7?<br/>
Question 58 :
The sum of the digits at the ten's place of all the all the numbers formed with the digits $3, 4, 5, 6$ taken all at a time is
Question 59 :
The number of ways in which $6$ rings can be worn on the four fingers of one hand is
Question 60 :
Assertion: The number of different codes formed by three letters of English alphabet followed by a three digit number is $\displaystyle (26)^{3}\times900 $ (if repetitions are allowed)
Reason: The number of permutations of $n$ different things taken $r$ at a time when each thing may be repeated.any number of times is $\displaystyle n^{r}$
Question 61 :
Mario's Pizza has 2 choices of crust: deep dish and thin-and-crispy. The restaurant also has a choice of 5 toppings: tomatoes, sausage, peppers, onions, and pepperoni. Finally, Mario's offers every pizza in extra cheese as well as regular. If Linda's volleyball team decides to order a pizza with 4 toppings, how many different choices do the teammates have at Mario's Pizza?
Question 62 :
The number of numbers of 9 different nonzero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than that in the middle is
Question 63 : <p>The total number of different combinations of one<br/>or more letters which can be made from the letter of the word MISSISSIPPI is,</p>
Question 64 :
All the numbers that can be formed using the digits of $12345$ are arranged in the decreasing order of magnitude. The rank of $32415$ is:
Question 65 :
The number of words that can be formed using any number of letters of the word "KANPUR" without repeating any letter is
Question 66 :
A vehicle registration number consists of $2$ letters of English alphabet followed by $4$ digits, where the first digit is not zero. Then, the total number of vehicles with distinct registration numbers is
Question 67 :
In an examination there are three multiple choice questions and each question has $4$ choices. Number of ways in which a student can fail to get all answer correct is?
Question 68 :
Consider all permutations of the letters of the word MORADABAD.<br/>The number of permutations which contain the word BAD is:
Question 69 :
The sum of all the four digit numbers which can be formed using the digits $6, 7, 8, 9$(repetition is allowed).
Question 70 :
In how many ways is it possible to choose a white square and a black square on a chessboards, so that the squares must not lie in the same row or column?
Question 71 :
Two series of a question booklet for an aptitude test are to be given to twelve students. In how many ways can the students be placed in two rows of six each so that there should be no identical series side by side and that the students sitting one behind the other should have the same series?
Question 72 :
There are 8 types of pant pieces and $9$ types of shirt pieces with a man. The number of ways in which a pair ($1$ pant, $1$ shirt) can be stitched by the tailor is
Question 73 :
There are twelve bulbs in a hall, each one of them can be switched independently. The number of ways in which the hall can be illuminated is
Question 74 :
The number of rational numbers $ \dfrac {p}{q}$, where $p,q$ $ \in $ ${1, 2, 3, 4, 5, 6}$ is
Question 75 :
Let $ S= \left\{1,2,3,.......n\right\} $ and $ A =\left\{(a, b) \left. \right | 1 \geq a, b \geq n\right\} = S \times S\: $. A subset $ B$ of $A $ is said to be a good subset if $ (x, x) \in B$ for every $x \in S.$ Then the number of good subsets of $A$ is<br/>
Question 76 :
The number of words that can be formed by using all the letters of the word PROBLEM only one is
Question 77 :
Find the number of four letter words, with meaning or without meaning, that can be formed by using the letters of the word $'CHEMISTRY'$
Question 78 :
The number of ways in which one or more letters be selected from the letters $AAAABBCCCDEF$ is
Question 80 :
The number of quadratic expressions with the coefficients drawn from the set $( 0, 1, 2, 3 )$ is:
Question 81 :
The different six digit numbers whose 3 digits are even and 3 digits are odd is<br><br>
Question 82 :
The number of six-digit numbers that can be formed from the digits $1, 2, 3, 4, 5, 6$ and $7$ so that digits do not repeat and the terminal digits are even is
Question 83 :
A five digit number divisible by $3$ is to be formed using the numerals $0, 1, 2, 3, 4$ and $5$ without repetition. The total number of ways in which this can be done is:
Question 84 :
Assertion: If the postman delivers 1332 card to the students then number of students are 36.
Reason: If there are n students then total number of cards are n (n-1).
Question 85 :
If it is possible to make only one meaningful word from the second, the sixth, the seventh, the eighth and the tenth letters of the word PERFORMANCE using each letter only once, then first letter of the word is your answer. If no such word can be formed your answer is X and if more than one such word can be formed your answer is Y.
Question 86 :
The number of such numbers which are divisible by two and five (all digits are not different) is
Question 87 :
The number of $5$ digit telephone numbers having least one of their digits repeated is
Question 88 :
Number plates of cars have to made. The first two digits should be alphabets and the next three digits should be numbers. How many number plates can be made such that the number $2$ can only be appeared in the middle of the three digits ( repetition of alphabets and numbers is not allowed)
Question 89 :
The number of six-digit numbers which have sum of their digits as an odd integer, is
Question 90 :
Three players play a total of $9$ games. In each game, one person wins and the other two lose; the winner gets $2$ points and the losers lose $1$ each. The number of ways in which they can play all the $9$ games and finish each with a zero score is
Question 91 :
The number of factors (excluding $1$ and the expression itself) of the product of $a^7b^4c^3def$ where $a,b,c,d,e,f$ are all prime numbers is
Question 92 :
Let E denote the set of letters of the English alphabet, $V = \{a, e, i, o , u\}$ and C be the complement of V in E. Then, the number of four letter words (where repetitions of letters are allowed) having at least one letter from V and at least one letter from C is
Question 93 :
Let $ (a_1, a_2, a_3, . . . , a_{2011}) $ be a permutation (that is a rearrangement) of the numbers 1, 2, 3, . . . , 2011. Show that there exist two numbers $ j, k $ such that $ 1 \le j < k \le 2011 $ and $ |a_j - j| = |a_k - k|$
Question 94 :
The rank of the word $NUMBER$ obtained, if the letters of the word $NUMBER$ are written in all possible orders and these words are written out as in a dictionary is<br/><br/>
Question 95 :
The letters of word $OUGHT$ are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word $TOUGH$ in this dictionary.
Question 96 :
There are $6$ red, $6$ brown, $6$ yellow, and $6$ gray scarves packaged in $24$ identical, unmarked boxes, $1$ scarf per box. What is the least number of boxes that must be selected in order to be sure that among the boxes selected $3$ or more contain scarves of the same color?
Question 97 :
Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.<br>
Question 98 :
When two coins are tossed and a cubical dice is rolled, then the total outcomes for the compound event is
Question 99 :
After every get-together every person present shakes the hand of every other person. If there were 105 handshakes in all, how many persons were present in the party?
Question 100 :
A password for a computer system requires exactly $6$ characters. Each character can be either one of the $26$ letters from A to Z or one of the ten digits from $0$ to $9$. The first character must be a letter and the last character must be a digit. How many different possible passwords are there?
Question 101 :
lf $\displaystyle x,y\in(0,30)$ such that $ [ \dfrac{x}{3}]+[\dfrac{3x}{2}]+[\dfrac{y}{2}]+[\dfrac{3y}{4}]=\dfrac{11x}{6}+\dfrac{5y}{4} $ (where [x] denote greatest integer $ \le x $) then the number of ordered pairs $(x, y)$ is
Question 102 :
The  number of signals that can be given using any number of flags of 5 different colors, is 
Question 103 :
There are three copies of Harry Potter,four copies of The Last Symbol and five copies of The Secret of the Unicorn. In how many ways can you arrange these books in a shelf?
Question 104 :
How many $3$ digit numbers can we make using the digits $4,5,7$ and $9$ and where repetition is allowed?
Question 105 :
The number of permutations of the letters of the word AGAlN taken three at a time is<br>
Question 106 :
Suppose a lot of n objects having $\displaystyle n_{1} $ objects of one kind, $\displaystyle n_{2} $ objects are of second kind, $\displaystyle n_{3} $ objects of third kind, .... , $\displaystyle n_{k} $ objects of $\displaystyle k^{th} $ kind satisfying the condition $\displaystyle n_{1} + n_{2}.... + n_{k}=n,$ then the number of possible arrangements/permutation of m objects out of this lot is the coefficient of $\displaystyle x ^{m}$ in the expansion of $\displaystyle m!\prod \left \{ \sum_{\lambda=0}^{a_{1}}\frac{x^\lambda}{\lambda!} \right \}$<br/><br/>The number of permutations of the letters of the word SURITI taken 4 at a time is<br/>
Question 107 :
The number of ways of dividing $2n$ people into $n$ couples is
Question 108 :
Two classrooms A and B having capacity of $25$ and $(n-25)$ seats respectively. $A_n$ denotes the number of possible seating arrangements of room $'A'$, when 'n' students are to be seated in these rooms, starting from room $'A'$ which is to be filled up to its capacity. If $A_n-A_{n-1}=25!(^{49}C_{25})$ then 'n' equals:
Question 109 :
$8064$ is resolved into all possible product of two factors. Find the number of ways in which this can be done?
Question 110 :
How many ways are there to invite one of three friends for dinner on $6$ successive nights such that to friend is invited more than three times ?
Question 111 :
If $r, s$ and $t$ are prime numbers and $p, q$ are positive integers such that the LCM of $p,q$ is $\displaystyle r^{2}t^{4}s^{2}$ then the number of ordered pair $(p, q)$ is
Question 112 :
Ten different letters of alphabet are given, words with five letters are formed with these given letters. Then the number of words which have at least one letter repeated
Question 113 :
Three persons entered a railway compartment in which $5$ seats were vacant. Find the number of ways in which they can be seated
Question 114 :
A person always prefers to eat parantha and vegetable dish in his meal. How many ways can he make his plate in a marriage party if there are three types of paranthas, four types of vegetable dishes, three types of salads, and two types of sauces?<br>
Question 115 :
The number of permutations or the letters of the word EXAMINATION taken 4 at a time is<br>
Question 116 :
Find the number of four digit numbers that are divisible by $15$ and formed with the digits $0,1,2,3,4,5$ when repetition is not allowed.
Question 117 :
When listing the integers from $1$ to $1000$, how many times the digit $5$ be written?
Question 118 :
The number of words of four letters containing equal number of vowels and consonants, repetition being allowed, is
Question 119 :
Words with meaning or without meaning are formed in the order opposite to that of in a dictionary, then the rank of the word '$HORROR$' is<br/>
Question 120 :
If $t_{r}$ denotes the number of $1-1$ function from $\left\{x_{1},x_{2}...x_{r}\right\}$ to $\left\{y_{1},y_{2},..y_{r}\right\}$ such that $\displaystyle f(x_{i})\neq y_{i}\forall i=(1,2,3..r)$ then $t_{4}$ equals
Question 121 :
In how many ways can 8 books be distributed among 5 students if each student is eligible for any number of books?
Question 122 :
If the permutation of $a, b, c, d, e$ taken all together be written down in alphabetical order as in dictionary and numbered, then the rank of the permutation $debac$ is:
Question 123 :
How many alphabets need to be there in a language if one were to make $1$ million distinct $3$ digit initials using the alphabets of the language?<br>
Question 124 :
In a game called 'odd man out', $ m (m > 2)$ persons toss a coin to determine who will buy refreshment for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is<br/>
Question 125 :
Number of permutations of 1,2,3,4,5,6,7,8 taken all at a time are such that the digit<br>1 appearing some where to the left of 2<br>3 appearing to the left of 4<br>5 some where to the left of 6<br>(e.g.815723946 would be one such permutation)
Question 126 :
The number of permutations of the letters of the word EXERCISES taken 5 at a time is<br>
Question 127 :
A shopkeeper sells three varieties of perfumes and he has a large number of bottles of the same size of each variety in this stock. There are $5 $ places in a  row in his showcase. Then number of different ways of displaying the three varieties of perfumes in the showcase is :
Question 128 :
If all the permutations of the letters in the word 'OBJECT' are arranged (and numbered serially) in alphabetical order as in a dictionary, then the $717^{th}$ word is<br>
Question 129 :
The number of different matrices that can be formed with elements 0,1,2 or 3, each matrix having 4 elements, is
Question 130 :
In a three-storey building, there are four rooms on the ground floor, two on the first and two on the second floor. If the rooms are to be allotted to six persons, one person occupying one room only, the number of ways in which this can be done so that no floor remains empty is<br>
Question 131 :
If $a$ denotes the number of permutations of $x+2$ things taken all at a time, $b$ the number of permutations of $x$ things taken $11$ at a time and $c$ the number of permutations of $x-11$ things taken all at a time such that $a = 182bc$, then the value of $x$ is
Question 132 :
How many $3$ digit numbers can be formed using the digits $0,1,2,3,4,5,6,7,8$ where digits may be repeated?
Question 133 :
Let $\mathrm{S}=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $\mathrm{S}$ is equal to<br/>
Question 134 :
How many different signals can be made by hoisting $6$ differently coloured flags one above the other, when any number of them may be hoisted at once?
Question 135 :
How many ways the letters of the word $'BANKING'$ can be arranged?
Question 136 :
In a shop there are five types of ice-creams available. A child buys six ice-creams.<br/>Statement-l: The number of different ways the child can buy the six ice-creams is $^{10}{C_{5}}$.<br/>Statement-2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 $\mathrm{A}$'s and 4 $\mathrm{B}$'s in a row. <br/><br/>
Question 137 :
A candidate is required to answer $6$ questions by choosing at least one question from each section, where $1^{st}$ section consists of $4$ questions, $2^{nd}$ section consists of $3$ questions and $3^{rd}$ section consists of $2$ questions. In how many ways can he make up us choice?.
Question 138 :
A college offers $7$ courses in the morning and $5$ in the evening. Find possible number of choices with the student who want to study one course in the morning and one in the evening.
