Question 1 :
Let $A=\left\{ u,v,w,z \right\} ;B=\left\{ 3,5 \right\} $, then the number of relations from $A$ to $B$ is
Question 2 :
Consider two sets $A=\{a, b, c\}, B=\{e, f\}$. If maximum numbers of total relations from A to B; symmetric relation from A to A and from B to B are $l, m, n$ respectively, then the value of $2l+m-n$ is
Question 4 :
If $\{ (x, 2), (4, y) \}$ represents an identity function, then $( x, y)$ is :
Question 5 :
Let $R$ be a relation from a set $A$ to a set $B$, then:
Question 6 :
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a function such that for any irrational number $r,$ and any real number $x$ we have $f(x)=f(x+r)$. Then, $f$ is
Question 7 :
If A = (a, b, c, d), B= (p, q, r, s). then which of the following are relations from A to B? Give reasons for your answer:
Question 8 :
If $\displaystyle \left[ x \right] $ is the greatest integer less than or equal to $x$, what is the value of $\displaystyle \left[ -1.6 \right] +\left[ 3.4 \right] +\left[ 2.7 \right] $?
Question 9 :
We want to find a polynomial f(x) of degree n such that f(1) = $\sqrt2$ and f(3) =$\pi$. Which of the following is true?
Question 10 :
$f(x)=\begin{cases} 2-|{ x }^{ 2 }+5x+6|,\quad \quad \quad x\neq -2 \\ a^{ 2 }+1,\quad \quad \quad \quad \quad \quad \quad \quad \quad x=-2 \end{cases}$. then the range of $a$, so that $f(x)$ has maxima at $x=-2$, is
Question 12 :
Evaluate $\displaystyle \left ( 4a + 3b \right )^{2} - \left ( 4a - 3b \right )^{2} + 48ab$
Question 13 :
If ordered pair $(a, b)$ is given as $(-2, 0)$, then $a =$
Question 15 :
$f:\left( 0,\infty \right) \rightarrow R$ is continuous. If $F\left(x\right)$ is a differentiable function such that $F\left(x\right)= f\left(x\right), \forall x>0$ and $ f\left( { x }^{ 2 } \right) ={ x }^{ 2 }+{ x }^{ 3 }$, then $f\left(4\right)$ equals
Question 16 :
If f is even function and g is an odd function, then $f_og$ is ............function.
Question 18 :
State whether the following statement is True or False.<br/>The inverse of an identity function is the identity function itself.<br/>
Question 19 :
If $x$ and $y$ co-ordinate of a point is $(3, 10)$, then $y$ co-ordinate is
Question 20 :
If $2\leq a < 3$, then the value of $\cos^{-1} \cos [a] + \text{cosec}^{-1} \text{cosec }[a] + \cot^{-1} \cot [a]$. where [.] denotes greater integer less then equal to $x$) is equal to:
Question 22 :
If $x$ co-ordinate of a point is $2$ and $y$ co-ordinate is $0$, then ordered pair for its coordinate on $XY$ plane is
Question 23 :
Let $R$ be a relation on the set $N$ given by $R=\left\{ \left( a,b \right) :a=b-2,b>6 \right\}$. Then
Question 24 :
Let R be the relation in the set N given by = {(a, b): a = b - 2, b > 6}. Choose the correct answer
Question 25 :
Define $f(x)=\cfrac { 1 }{ 2 } \left[ \left| \sin { x } \right| +\sin { x } \right] ,0<x<2\pi \quad $<br>Then, $f$ is
Question 26 :
If $p(x) = \dfrac{1 + x^2 + x^4 + ... + x^{2n - 2}}{1 + x + x^2 + ... + x^{n - 1}}$ is a polynomial in $x$, then  $n$ can be
Question 27 :
Let $A = \left \{x, y, z\right \}$ and $B = \left \{p, q, r, s\right \}$. What is the number of distinct relations from $B$ to $A$?
Question 28 :
In $[0, 1]$ Lagranges Mean Value theorem is NOT applicable to<br>
Question 29 :
If $\displaystyle a + \frac{1}{a} = 6$ and $\displaystyle a \neq 0$; find $\displaystyle a - \frac{1}{a}$ .
Question 30 :
The minimum value of $f\left( x \right) ={ x }^{ 2 }+2x+3 ,x\in R$ is equal to 
Question 31 :
If $\displaystyle f\left( { x }_{ 1 } \right) -f\left( { x }_{ 2 } \right) =f\left( \frac { { x }_{ 1 }-{ x }_{ 2 } }{ 1-{ x }_{ 1 }{ x }_{ 2 } }  \right) $ for $\displaystyle { x }_{ 1 },{ x }_{ 2 }\in \left[ -1,1 \right] $ then $f\left( x \right) $ is 
Question 32 :
If $A=\left \{x:x^2-3x+2=0\right \}$ and $B=\left \{x:x^2+4x-5=0\right \}$ then the value of A-B is
Question 33 :
$A$ and $B$ are two sets having $3$ and $4$ elements respectively and having $2$ elements in common. The number of relations which can be defined from $A$ to $B$ is:
Question 34 :
Let R be the set of real numbers and the mapping $f:R\rightarrow R$ and $g:R\rightarrow R$ be defined by $f(x)=5-x^2$ and $g(x)=3\lambda-4$, then the value of $(fog)(-1)$ is
Question 36 :
If $\displaystyle a - b = 4$ and $\displaystyle a + b = 6$, find $\displaystyle ab$
Question 37 :
If $X \in R,$ then sgn $\left( {{X^2} + 1} \right)$ is equal to
Question 38 :
If $A = \{1, 2 \}$ and $B = \{3, 4\}$ then find $A \times B$<br/>
Question 39 :
If $x$ and $y$ coordinate of a point is $(3, 10)$, then the $x$ co-ordinate is
Question 41 :
Find the range of$\displaystylef\left( x \right)=\dfrac { \sin { \left( \pi \left[ { x }^{ 2 }+1 \right] \right) } }{ { x }^{ 4 }+1 } $ where $[.]$ is greatest integer function
Question 44 :
The value of$\displaystyle 16-\left | -7 \right |-\left | 11-22 \right |$ is equal to
Question 45 :
If $\displaystyle a + \frac{1}{a} = 6$ and $\displaystyle a \neq 0$; find $\displaystyle a^{2} - \frac{1}{a^{2}}$ .
Question 46 :
Let $R$ be a relation on $N$ defined by $x+2y=8$. The domain of $R$ is
Question 47 :
If $\displaystyle a - \frac{1}{a} = 8$ and $\displaystyle a \neq 0$; find :$\displaystyle a + \frac{1}{a}$.
Question 48 :
State the whether given statement is true or falseIf $f\left( x \right) = \dfrac{{x + 1}}{{x - 1}},$ then $f\left( x \right) + f\left( {\dfrac{1}{x}} \right) = 0$
Question 49 :
Cartesian product of sets $A$ and $B$ is denoted by _______.<br/>
Question 51 :
A group consists of 4 couples in which each of the 4 persons have one wife each. In howmany ways could they be arranged in a straight line such that the men and womenoccupy alternate positions?
Question 52 :
How many numbers consisting of $5$ digits can be formed in which the digits $3,4$ and $7$ are used only once and the digit $5$ is used twice<br>
Question 54 :
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 55 :
A total of $324$ coins of $20$ paise and $25$ paise make a sum of $Rs.71$, the number of $25$ paise coins is
Question 56 :
The number of ways in which ten candidates $A_1, A_2,......A_{10}$ can be ranked such that $A_1$ is always above $A_{10}$ is
Question 57 :
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 58 : 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 59 :
Number of ways in which $15$ different books can be arranged on a shelf so that two particular books shall not be together is<br>
Question 60 :
Find the number of permutations that can be made with the letters of the word $'MOUSE'$
Question 61 :
Find the number of permutations that can be made with the letters of the word $'REAR'$?
Question 62 :
How many numbers amongst the numbers 9 to 54 are there which are exactly divisible by 9 but not by 3?
Question 63 :
Find the number of three letter words that can be formed by using the letters of the word $'MASTER'$
Question 65 :
When we realize a specific implementation of a pancake algorithm, every move when we find the greatest of the sized array and flipping can be modeled through ____________.<br/>
Question 66 :
Ten different letter of an alphabet are given. Words with five letters are formed fromthese given letters. Then the number of words which have at least one letter repeated is:
Question 67 :
If $^{13}C_x=^{13}C_y$ and $x\neq y$, then the value of $x+y$ is ?
Question 68 :
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 69 :
How many ways can $4$ prizes be given away to $3$ boys, if each boy is eligible for all the prizes?
Question 70 :
 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 71 :
From a well shuffled pack of $52$ playing cards two cards drawn at random. The probability that either both are red or both are kings is:
Question 72 :
$3$ 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 73 :
How many different signals can be transmitted by arranging 3 red, 2 yellow and 2 greenflags on a pole? [Assume that all the 7 flags are used to transmit a signal].
Question 74 :
At the end of a business conference, the ten people present all shake hands with each other once. How many handshakes will there be altogether?
Question 75 :
In how many ways can $6$ boys and $5$ girls can be seated in a row such that no two girls are together?
Question 76 :
The number of ways in which $5$ beads, chosen from $8$ different beads be threaded on to a ring, is:
Question 77 :
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 78 :
How many different words can be formed by jumbling the letter in the word MISSISSIPPI in which no two S are adjacent?
Question 79 :
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 80 :
If chocolates of a particular brand are all identical then the number of ways in which we can choose $6$chocolates out of $8$different brands available in the market is :
Question 81 :
In a chess tournament each of six players will play every other player exactly once. How many matches will be played during the tournament?
Question 82 :
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 83 :
$15$ 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 84 :
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 85 :
The greatest number that can be formed by the digits $7,0,9,8,6,3$
Question 86 :
The number of ordered triplets of positive integers which are solutions of the equation $x+y+z=100$ is 
Question 87 :
The number of ways in which all the letters of the word 'MESSI' be arranged is
Question 88 :
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 89 :
A person tries to form as many different parties as he can, out of his $20$ friends. Each party should consist of the same number. How many friends should be invited at a time? In how many of these parties would the same friends be found?
Question 90 :
What is the probability of selecting two spade cards from a pack of 52 cards?
Question 91 :
The no of ways of selecting $3$ people from $10$ is
Question 92 :
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 93 :
The number of nine digit numbers that can be formed with different digits is
Question 94 :
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 95 :
In how many different ways can the letters in the word "LEVEL" be arranged?
Question 96 :
Two persons entered a Railway compartmentin which 7 seats were vacant.The number ofways in which they can be seated is
Question 97 :
The number of numbers between 300 and 700that can be formed using the digits 1,2,3,4,5,and 6 without repetition is
Question 98 :
In how many ways can we select two vowels and three consonants from the letters of the word ARTICLE ?
Question 99 :
Let the coefficient of $10^{th}$ term of an expansion be $a$ and $b$ be the power.<br/>Expansion:$\left (2x^2+ \dfrac 1x\right)^{12}$<br/>Find $a \times b$.<br/>
Question 101 :
The number of signals that can be formed using 6 flags of different colours taking $1$ or more flags at a time is ?
Question 103 :
If $\displaystyle \sum_{r = 1}^{10} r(r - 1) ^{10}C_{r} = k.2^{9}$, then $k$ is equal to
Question 105 :
The number of three digit numbers having only two consecutive digits identical is:
Question 106 :
There are 13 players of cricket out of which 4 are bowlers. In how many ways a team of eleven selected from them so as to include at least two bowlers-
Question 107 :
A question paper on mathmatics consists of twelve question divided into three parts . A,B and C, each containing four questions . In how many ways can an examinee answer five questions , selecting atleast one from each part.
Question 108 :
In how many ways can four people, each throwing a dice once, make a sum of $6$?
Question 109 :
A polygon has $44$ diagonals, then the number of its sides is:
Question 110 :
A lady gives a dinner party for six guests. The number of ways in which they may be selected from  ten friends, if two of the friends will not attend the party together, is?
Question 111 :
Given that C(n, r) : C ( n, r + 1)=1 : 2 and C (n, r + 1) : C (n, r + 2) = 2 : 3. <br/>Find $n.$
Question 113 :
If $\displaystyle^nC_4,^nC_5 $ and $ ^nC_6$ are in AP then n is
Question 114 :
Number of $5$ digited numbers using $0,1,2,3,4,5$ divisible by $5$ repetition is allowed
Question 115 :
State true or false. $C _ { 0 } + C _ { 1 } + C _ { 2 } + \ldots + C _ { n } = 2 ^ { n }$
Question 116 :
Assertion: A student is allowed to select at most $n$ books from a collection of $(2n+1)$ books. If the total number of ways in which he can select at least one book is $255$ then $n=3$, because
Reason: $^{ 2n+1 }{ { C }_{ 0 } }+^{ 2n+1 }{ { C }_{ 1 } }+...+^{ 2n+1 }{ { C }_{ n } }=4^n$
Question 117 :
Every body in a room shakes hands with every body else. The total number of hand shakes is $66$. The total number of persons in the room is
Question 118 :
There are $10$ seats in the first row of a theatre of which 4 are to be occupied. The number of ways of arranging 4 persons so that no two person sit side by side is :
Question 119 :
The sum $\sum_{i=0}^{m}\binom{10}{i}\binom{20}{m-i}$ where $\binom{p}{q} = 0$; If (p<q) is maximum when m is
Question 120 :
Out of $10$ white, $9$ black and $7$ red balls, the number of ways in which selection of one or more balls can be made, is:
Question 121 :
If $P(n,r)=2520$ and $C(n,r)=21$, then what is the value of $C(n+1,r+1)?$
Question 122 :
Consider the letters of the word $EQUATION$. What is the number of the arrangements of the letters in this wordso that the vowel appear, not necessarily successively, in the dictionary order?
Question 123 :
In a examination, a student has to answer $8$ questions out of $10$ questions. If questions $1$ and $10$ are compulsory, in how many ways can a student choose the questions? 
Question 126 :
In how many  ways can $5$ rings of differents type can be worn in $4$ fingers ?
Question 128 :
If $n<p<2n$ and $p$ is prime and $N=^{ 2n }{ { C }_{ n } }$, then
Question 129 :
The greatest possible number of points of intersection of $8$straight lines and $4$circles is
Question 130 :
Assertion: The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $^9C_3$.
Reason: The number of ways of choosing any $3$ places from $9$ different places is $^9C_3$.
Question 131 :
If $p> q$, the number of ways of $p$ men and $q$ women can be seated in a row so that no two women sit together is
Question 132 :
Everybody in a room shakes hand with everybody else.The total number of handshakes is $66 .$ The total number of persons in the room is ..
Question 133 :
The number of five-letter words that are formed out of the letters of the word INFINITESIMAL
Question 135 :
If $2\times$ $^nC_5 = 9\times$ $^{n-2}C_5$, then the value of n will be:<br/>
Question 136 :
The $9$ horizontal and $9$ vertical lines on an $8 \times 8$ chessboard from 'r' rectangles and 's' squares. The ratio $\dfrac{s}{r}$ in its lowest term,is
Question 137 :
The number of values of r satisfying the equation $^{39}C_{3r-1}-\ ^{39}C_{r^2}=\ ^{39}C_{r^2-1}-\ ^{39}C_{3r}$ is<br/>
Question 138 :
If $ {^2}{^n}C_3 : ^nC_2  = 44 :3$, then $n =$
Question 139 :
The letters of the word $'CLIFTON'$ are arranged randomly in a row. What is the chance that two vowels come together? 
Question 140 :
A man wears socks of two colours - Black and brown. He has altogether $20$ black socks and $20$ brown socks in a drawer. Supposing he has to take out of the socks in the dark, how many must he take out to be sure that he has a matching pair?
Question 141 :
The value of $\displaystyle \sum _{ r=1 }^{ 10 }{ r.\dfrac { _{ }^{ n }{ C }_{ r }^{ } }{ ^{ n }{ C }_{ r-1 }^{ } } } $ is equal to
Question 142 :
The number of ways which any four letters can be selected from the word 'CORGOO' is _____________.
Question 143 :
How many words of 4 consonants and 3 vowels can be formed from 6 consonants and 5 vowels
Question 144 :
If $^{2n}{C_r}{:^n}{C_2} = 44:3$, then for which of the following values of $r$ the value of $^n{C_r}$ will be $15$
Question 145 :
The number of solutions of $ ^{61}C_{n + 1} =^{61}C_{2n - 1} $is
Question 146 :
A student has to answer 6 questions out of 10 questions. In how many ways he can choose the questions.
Question 148 :
How many parallelograms will be formed, if $7$ parallel horizontal lines intersect $6$ parallel vertical lines?
Question 150 :
A village has $10$ players. A team of $6$ players is to be formed. $5$ members are chosen first out of these $10$ players and then the captain from the remaining players. Then the total number of ways of choosing such teams is
Question 152 :
$ABCD $ is a convex quadrilateral and $ 3, 4, 5 $ and 6 points are marked on the sides $ AB, BC, CD $ and $ DA,$ respectively. The number of triangles with vertices on different sides is (none of them is $ A,B,C$ or$ D)$
Question 153 :
The number of different nine digit numbers that can be formed from $22, 33, 55, 888$ by rearranging the digits, so that odd digits occupy even places and even digits occupy odd position, is
Question 154 :
The number of words of four letters containing equal number of vowels and consonants, repetition being allowed, is
Question 155 :
A box contained 2 white balls , 3 black $ 4 red balls . In how many ways can three balls be drawn from the box if atleast one black ball is to be included in draw (the balls of the same colour are different).
Question 157 :
Different words are being formed by arranging the letters of the word ARRANGE. All the words obtained are written in the form of a dictionary<br/>Number of ways (words) in which neither two A's nor two R's comes together<br/><br/>
Question 158 :
If $_{ }^{ n+1 }{ { C }_{ r+1 } }$: $_{ }^{ n }{ { C }_{ r } }$: $_{ }^{ n-1 }{ { C }_{ r-1 } }=$ 11: 6: 3 , then $r=$<br>
Question 159 :
The number of ways of dividing $2n$ people into $n$ couples is
Question 160 :
A word has 4 identical letters andothers different. If the total number of words that can be made with the letters of the word be 210 then the number of different letters in the word is
Question 161 :
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 163 :
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 164 :
Let $\mathrm{S}=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $\mathrm{S}$ is equal to<br/>
Question 165 :
In a conference there are $11$ mechanical engineers and $7$ metallurgical engineers. In how many ways can they be seated in a row such that all the metallurgical engineers do not sit together?
Question 166 :
How many different words can be formed using all the letters of the word $'\text{ALLAHABAD}' $ when both $L's$ are not together
Question 167 :
A sports team of $11$ students is to be constituted, choosing at least $5$ from class $XI$ and at least $5$ from class $XII$. If there are $20$ students in each of these classes, in how many ways can the teams be constituted?
Question 168 :
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 169 :
How many four-digit numbers divisible by $10$ can be formed using $1,5,0,6,7$ without repetition of digits?
Question 173 :
The value of $x$ in the equation $3 \times^{x+1}C_2 = 2\times ^{x+2}C_2, \space x\space \in N$ is<br>
Question 174 :
How many ordered pairs of (m, n) integers satisfy $\dfrac {m}{12}=\dfrac {12}{n}$?<br/>
Question 175 :
For any positive integer $m,\space n \space(\mbox{ with } n\ge m) = ^nC_m$.<br>$\left(\begin{matrix}n \\ m\end{matrix}\right) +\left(\begin{matrix}n - 1\\ m\end{matrix}\right) +\left(\begin{matrix}n - 2\\ m\end{matrix}\right) + ... +\left(\begin{matrix}m \\ m\end{matrix}\right) = $<br><br>
Question 176 :
If $^{n-1}C_r = (k^2 - 3) ^nC_{r+1} ,$ then k belongs to the interval
Question 178 :
$\displaystyle \sum _{ 0\le i\le  }^{  }{ \sum _{ j\le 10 }^{  }{ ^{ 10 }{ { C }_{ j } }^{ j }{ { C }_{ i } } }  } $ is equal to
Question 179 :
There are three routes; air, rail and road for going from Chennai to Hyderabad. But from Hyderabad to Vikarabad, there are two rotues, rail and road. The number of routes from Chennai to Vikarabad via Hyderabad is
Question 180 :
How many ways the letters of the word $'BANKING'$ can be arranged?
Question 181 :
Word from the letters of the word $ PROBABILITY$ are formed by taking all letters at a time.The probability that both $B's $ are not together and both $I's $ are not together is
Question 182 :
The number of ways in which n books can be arranged can be arranged on a shelf so that two particular books shall not be together is
Question 183 :
A box contains $24$ balls of which $12$ are black and $12$ are white. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw is
Question 185 :
How many $6$ digits odd numbers greater than $60,0000$ can be formed from the digits $5,6,7,8,9,0$ if Repetitions are not allowed:
Question 186 :
Find the number of three digit numbers that are divisible by $2$ but not divisible by $6$ and are formed with the digits $1,2,3,4,6$ when repetition is not allowed
Question 187 :
There are $2n$ things out of which $'n'$ are alike and $'n'$ are different, the number of ways of selecting $'n'$ things is :-<br>
Question 188 :
There are three papers of $100$ marks each in an examination. In how many ways can a student get $150$ marks such that he gets at least $60%$ in two papers?
Question 189 :
How many $6$ digits odd numbers greater than $60,0000$ can be formed from the digits $5,6,7,8,9,0$ if Repetitions are allowed:
Question 190 :
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 193 : $\text{Consider all possible permutations of the letters of the word ENDEANOEL.}$Match the Statements / Expressions in List 1 with the Statements / Expressions in List 2 and indicate your answer<br/><table class="wysiwyg-table"><tbody><tr><td></td><td><b>List I</b></td><td></td><td><b>List II</b></td></tr><tr><td>A.</td><td>The number of permutations containing <br/>the word ENDEA is<br/></td><td>1.</td><td>$5!$<br/></td></tr><tr><td>B.</td><td> The number of permutations in which <br/>the letter E occurs in the first and the <br/>last positions is</td><td>2.</td><td>$2\times 5!$<br/></td></tr><tr><td>C.</td><td>The number of permutations in which <br/>none of the letters D, L, N occurs in the <br/>last five positions is<br/></td><td>3.</td><td>$7\times 5!$<br/></td></tr><tr><td>D.</td><td> The number of permutations in which the <br/>letters A, E, O occur only in odd positions is<br/></td><td>4.</td><td>$21\times 5!$</td></tr></tbody></table><br/>
Question 195 :
If the second term of the expansion $\left[a^{1/13}+\dfrac{a}{\sqrt{a^{-1}}}\right]^n$ is $14a^{5/2}$ then the value of $\dfrac{^{n}C_3}{^{n}C_2}$ is
Question 196 :
The number of permutations of the letters of the word AGAlN taken three at a time is<br>
Question 197 :
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 198 :
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 200 :
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/>
