The sum of the digits in the unit's place of all the 4-digit numbers formed by using the numbers $3,4,5$ and $6$, without repetition is:
(1) 18
(2) 36
(3) 108
(4) 432

The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:
(1) 216
(2) 192
(3) 120
(4) 72

The number of integers greater than 6000 that can be formed, using the digits $3,5,6,7$ and 8 , without repetition is
(1) 72
(2) 216
(3) 192
(4) 120

The number of numbers between 2,000 and 5,000 that can be formed with the digits $0,1,2,3,4$ (repetition of digits is not allowed) and are multiple of 3 is
(1) 36
(2) 30
(3) 24
(4) 48

$n$-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