Total number of 6-digit numbers in which only and all the five digits $1, 3, 5, 7$ and 9 appears, is
(1) $\frac { 1 } { 2 } (6!)$
(2) $6!$
(3) $5 ^ { 6 }$
(4) $\frac { 5 } { 2 } (6!)$

If the number of five digit numbers with distinct digits and 2 at the $10 ^ { \text {th} }$ place is $336 k$, then $k$ is equal to:
(1) 4
(2) 6
(3) 7
(4) 8

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated ?
(1) $2 ! 3 ! 4$ !
(2) $( 3 ! ) ^ { 3 } \cdot ( 4 ! )$
(3) $( 3 ! ) 2 . ( 4 ! )$
(4) $3 ! ( 4 ! ) ^ { 3 }$

The value of $\left( 2 \cdot { } ^ { 1 } P _ { 0 } - 3 \cdot { } ^ { 2 } P _ { 1 } + 4 \cdot { } ^ { 3 } P _ { 2 } - \right.$ up to $51 ^ { \text {th} }$ term $) + ( 1 ! - 2 ! + 3 ! -$ up to $51 ^ { \text {th} }$ term) is equal to
(1) $1 - 51 ( 51 )$ !
(2) $1 + ( 51 )$ !
(3) $1 + ( 52 )$ !
(4) 1

Let $A = \{a, b, c\}$ and $B = \{1, 2, 3, 4\}$. Then the number of elements in the set $C = \{f: A \rightarrow B \mid 2 \in f(A)$ and $f$ is not one-one$\}$ is ...

Team '$A$' consists of 7 boys and $n$ girls and Team '$B$' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then $n$ is equal to:
(1) 5
(2) 2
(3) 4
(4) 6

The sum of all the 4-digit distinct numbers that can be formed with the digits $1, 2, 2$ and 3 is:
(1) 26664
(2) 122664
(3) 122234
(4) 22264

The total number of positive integral solutions $( x , y , z )$ such that $x y z = 24$ is :
(1) 45
(2) 30
(3) 36
(4) 24

Let $A = \{ 2,3,4,5 , \ldots , 30 \}$ and $\sim$ be an equivalence relation on $A \times A$, defined by $( a , b ) \simeq ( c , d )$, if and only if $ad = bc$. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $( 4,3 )$ is equal to :
(1) 5
(2) 6
(3) 8
(4) 7

Let $x$ denote the total number of one-one functions from a set $A$ with 3 elements to a set $B$ with 5 elements and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then:
(1) $y = 273 x$
(2) $2 y = 273 x$
(3) $2 y = 91 x$
(4) $y = 91 x$

The total number of numbers, lying between 100 and 1000 that can be formed with the digits $1,2,3,4,5$, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is

The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is

The number of seven digit integers with sum of digits equal to 10 and formed by using the digits 1, 2 and 3 only is

The total number of 5-digit numbers, formed by using the digits $1,2,3,5,6,7$ without repetition, which are multiple of 6, is
(1) 72
(2) 48
(3) 24
(4) 60

The total number of functions, $f : \{1,2,3,4\} \rightarrow \{1,2,3,4,5,6\}$ such that $f(1) + f(2) = f(3)$, is equal to
(1) 60
(2) 90
(3) 108
(4) 126

The number of 7-digit numbers which are multiples of 11 and are formed using all the digits $1,2,3,4,5,7$ and 9 is $\_\_\_\_$.

The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is $\_\_\_\_$.

The number of 5-digit natural numbers, such that the product of their digits is 36, is $\_\_\_\_$.

Let $A$ be a matrix of order $2 \times 2$, whose entries are from the set $\{ 0,1,2,3,4,5 \}$. If the sum of all the entries of $A$ is a prime number $p , 2 < p < 8$, then the number of such matrices $A$ is

The number of functions $f$, from the set $A = \left\{ x \in N : x ^ { 2 } - 10 x + 9 \leq 0 \right\}$ to the set $B = \left\{ n ^ { 2 } : n \in N \right\}$ such that $f ( x ) \leq ( x - 3 ) ^ { 2 } + 1$, for every $x \in A$, is $\_\_\_\_$ .

The number of integers, greater than 7000 that can be formed, using the digits $3,5,6,7,8$ without repetition is
(1) 120
(2) 168
(3) 220
(4) 48

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is
(1) 576
(2) 578
(3) 580
(4) 582

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which $C$ and $S$ do not come together, is $( 6 ! ) k$ then $k$ is equal to
(1) 2835
(2) 5670
(3) 1890
(4) 945

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is
(1) 327
(2) 328
(3) 324
(4) 326

The total number of three-digit numbers, divisible by 3, which can be formed using the digits $1,3,5,8$, if repetition of digits is allowed, is
(1) 21
(2) 20
(3) 22
(4) 18