The number of numbers, strictly between 5000 and 10000 can be formed using the digits $1,3,5,7,9$ without repetition, is
(1) 6
(2) 12
(3) 120
(4) 72

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is : (1) 89 (2) 84 (3) 86 (4) 79

The number of seven digits odd numbers, that can be formed using all the seven digits $1, 2, 2, 2, 3, 3, 5$ is

The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is
(1) 16800
(2) 33600
(3) 18000
(4) 14800

The number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits $0,1,3,5,7$ and 9 without repetition, is equal to
(1) 132
(2) 120
(3) 72
(4) 96

The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is $\_\_\_\_$.

Five digit numbers are formed using the digits $1,2,3,5,7$ with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1. Then the serial number of 35337 is

If ${}^{2n+1}P_{n-1} : {}^{2n-1}P_n = 11 : 21$, then $n^2 + n + 15$ is equal to $\_\_\_\_$.

The number of 9-digit numbers, that can be formed using all the digits of the number 123456789, such that the even digits occupy only even places, is
(1) 2880
(2) 2520
(3) 2160
(4) 2400

Let $A = \{1, 2, 3, 5, 8, 9\}$. Then the number of possible functions $f: A \rightarrow A$ such that $f(m \cdot n) = f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to

The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is $\_\_\_\_$.

Let 5 digit numbers be constructed using the digits $0, 2, 3, 4, 7, 9$ with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is $\underline{\hspace{1cm}}$.

The number of permutations, of the digits $1, 2, 3, \ldots, 7$ without repetition, which neither contain the string 153 nor the string 2467, is $\_\_\_\_$.

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11, is equal to $\underline{\hspace{1cm}}$.

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to
(1) 18
(2) 16
(3) 12
(4) 15

60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the $50 ^ { \text {th} }$ word is :
(1) JBBOH
(2) OBBJH
(3) OBBHJ
(4) HBBJO

If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at $315 ^ { \text {th} }$ position in this arrangement is:
(1) NRAGUP
(2) NRAPUG
(3) NRAPGU
(4) NRAGPU

Let $[ t ]$ be the greatest integer less than or equal to $t$. Let $A$ be the set of all prime factors of 2310 and $f : A \rightarrow \mathbb { Z }$ be the function $f ( x ) = \left[ \log _ { 2 } \left( x ^ { 2 } + \left[ \frac { x ^ { 3 } } { 5 } \right] \right) \right]$. The number of one-to-one functions from $A$ to the range of $f$ is
(1) 25
(2) 24
(3) 20
(4) 120

The number of 3-digit numbers, formed using the digits $2,3,4,5$ and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is equal to $\_\_\_\_$

All the letters of the word $G T W E N T Y$ are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word $G T W E N T Y$ IS

Let $A = \{ ( x , y ) : 2 x + 3 y = 23 , x , y \in \mathbb { N } \}$ and $B = \{ x : ( x , y ) \in A \}$. Then the number of one-one functions from $A$ to $B$ is equal to $\_\_\_\_$

In a group of 3 girls and 4 boys, there are two boys $B _ { 1 }$ and $B _ { 2 }$. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but $B _ { 1 }$ and $B _ { 2 }$ are not adjacent to each other, is :
(1) 96
(2) 144
(3) 120
(4) 72

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is :
(1) $\frac { 1 } { 2 }$
(2) $\frac { 1 } { 4 }$
(3) $\frac { 2 } { 3 }$
(4) $\frac { 1 } { 3 }$

Let P be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in P are formed by using the digits 1, 2 and 3 only, then the number of elements in the set $P$ is:
(1) 173
(2) 164
(3) 158
(4) 161

If all the words with or without meaning made using all the letters of the word ``KANPUR'' are arranged as in a dictionary, then the word at $440 ^ { \text {th} }$ position in this arrangement, is :
(1) PRNAUK
(2) PRKANU
(3) PRKAUN
(4) PRNAKU