$n$-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of $n$ for which 900 such distinct numbers can be formed is :
(1) 9
(2) 7
(3) 8
(4) 6

$n$ - digit numbers are formed using only three digits 2,5 and 7 . The smallest value of $n$ for which 900 such distinct numbers can be formed, is
(1) 6
(2) 8
(3) 9
(4) 7

The number of natural numbers less than 7000 which can be formed by using the digits $0,1,3,7,9$ (repetition of digits allowed) is equal to:
(1) 375
(2) 250
(3) 374
(4) 372

The number of four-digit numbers strictly greater than 4321 that can be formed using the digit $0,1,2,3,4,5$ (repetition of digits is allowed) is:
(1) 360
(2) 288
(3) 306
(4) 310

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

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 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 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 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 number of 5-digit natural numbers, such that the product of their digits is 36, 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

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

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 total number of 4-digit numbers whose greatest common divisor with 54 is 2 , is $\_\_\_\_$

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 , is (1) 472 (2) 432 (3) 507 (4) 400

The number of ways of selecting two numbers $a$ and $b$, $a \in \{2, 4, 6, \ldots, 100\}$ and $b \in \{1, 3, 5, \ldots, 99\}$ such that 2 is the remainder when $a + b$ is divided by 23 is
(1) 186
(2) 54
(3) 108
(4) 268

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

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 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 $\_\_\_\_$

The number of integers, between 100 and 1000 having the sum of their digits equals to 14, is $\_\_\_\_$

The number of different 5 digit numbers greater than 50000 that can be formed using the digits $0, 1, 2, 3, 4, 5, 6, 7$, such that the sum of their first and last digits should not be more than 8, is
(1) 4608
(2) 5720
(3) 5719
(4) 4607

The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is

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

Q1 Using the five numerals $0,1,2,3,4$, we are to make four-digit integers. (Note that "0123", etc. are not allowed.)
(1) The total possible number of integers where the digits are all different numerals is $\mathbf{AB}$. Among them, the total number of integers that do not use 0 is $\mathbf{CD}$.
(2) If we are allowed to use the same numeral repeatedly, then the total possible number of four-digit integers is $\mathbf{EFG}$. Among them
(i) the total number of integers that use both 1 and 3 twice is $\mathbf{H}$,
(ii) the total number of integers that use both 0 and 4 twice is $\mathbf{I}$,
(iii) the total number of integers that use both of two numerals twice is $\mathbf{JK}$.

A department store holds a Father's Day card drawing promotion with the following rules: The organizer prepares ten cards numbered $1, 2, \ldots, 9$, of which there are two cards numbered 8, and only one card for each other number. Four cards are randomly drawn from these ten cards without replacement and arranged from left to right in order to form a four-digit number. If the four-digit number satisfies any one of the following conditions, a prize is won:
(1) The four-digit number is greater than 6400
(2) The four-digit number contains two digits 8 For example: If the four cards drawn are numbered $5, 8, 2, 8$ in order, then the four-digit number is 5828, and a prize is won. According to the above rules, there are (11-1)(11-2)(11-3)(11-4) four-digit numbers that can win prizes.