# Fundamental Principle of Counting

## Trending Questions

**Q.**

Find the least number which when divided by 12, 16 , 24 and 36 leaves a remainder 7 in each case.

- 36
- 144
- 151
- 137

**Q.**

The total number of $4$-digit numbers whose greatest common divisor with $18$ is $3$, is

**Q.**The abacus classes chosen by 20 students is given below. Find the probability of choosing Level-3 classes.

**Q.**

How many numbers lying between $999$ and $10000$ can be formed with the help of the digit $0$, $2$, $3$, $6$, $7$, $8$ when the digits are not to be repeated ?

$100$

$600$

$300$

$400$

**Q.**

We already know the rule for the pattern of letter L, C and F. Give us the same rule as that given by L. Which are these? Why does this happen?

**Q.**

$4$**buses run between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by bus and comes back to Gwalior by another bus, then the total possible ways are?**

$12$

$16$

$4$

$8$

**Q.**How many times does the digit 7 appear when you write from 11 to 100?

- 9
- 11
- 19
- 10

**Q.**Number of ordered triplets of natural number (a, b, c) for which abc≤11 is

- 53
- 52
- 55
- 56

**Q.**

The number of numbers that can be formed with the help of the digits $1,2,3,4,3,2,1$ so that odd digits always occupy odd places, is

$24$

$18$

$12$

$30$

**Q.**Let n1<n2<n3<n4<n5 be positive integers such that n1+n2+n3+n4+n5=20. The number of such distinct arrangements (n1, n2, n3, n4, n5) is ?

- 7
- 6
- 8
- 4

**Q.**Alex was asked to multiply a number by 23. He instead multiplied the number by 32 and got the result 135 more than the correct answer. The number to be multiplied is _____ .

- 10
- 20
- 9
- 15

**Q.**How many 4 digit numbers can be formed with digits 1, 2, 3, 4, 5 when digit may be repeated?

- 125
- 625
- 1024
- None of these

**Q.**Alex was asked to multiply a number by 23. He instead multiplied the number by 32 and got the result 135 more than the correct answer. The number to be multiplied is _____ .

- 10
- 9
- 15
- 20

**Q.**Let 15 toys be distributed among three children such that any child can take any number of toys.Find the required number of ways to do this if toys are identical.

- 315
- 256
- 300
- 275

**Q.**

Give the first four multiples of $12$

______________________________

**Q.**The number of four digit odd numbers that can be formed using 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition of digits is allowed ) are

- 5×83
- 5×92
- 5×73
- 5×93

**Q.**A three digit number ‘n’ is such that the last two digits of it are equal and different from the first. The number of such ‘n’s is

- 64
- 72
- 900
- 81

**Q.**Reciprocal of 75 is

- 125
- 57
- 523
- 125

**Q.**The first twenty natural numbers from 1 to 20 are written next to each other to form a 31−digit number N=1234567891011121314151617181920. What is the remainder when this number is divided by 16

- 0
- 4
- 7
- 9

**Q.**How many numbers can be formed by using all the given digits 1, 2, 8, 9, 3, 5 when repetition is not allowed

- 720
- 1024
- 120
- 180

**Q.**In a quiz, positive marks were given for correct answers and negative marks for incorrect answers. If Guru's scores in five successive rounds were 35, −10, −15, 20, and 5, what is his total score at the end?

- 25
- 35
- 45
- 55

**Q.**The number of 5 digit numbers which are not divisible by 5 and contains 5 odd digits {repetition of digits are not allowed} is

- 120
- 96
- 32
- 24

**Q.**

If there are 36 gems on a necklace and out of them 1/3 are red, then the number of red gems is

7

9

12

14

**Q.**Find the positive natural number for which n2=n3=n.

- 1
- −1
- 0
- Cannot be determined

**Q.**Product of the numbers 1224 and 3672 is

- 1624
- 35
- 4
- 14

**Q.**The number of distinct rational numbers of the form p/q, where p, q ϵ {1, 2, 3, 4, 5, 6} is

- 36
- 28
- 23
- 32

**Q.**How many numbers less than 10000 can be made with the eight digits 1, 2, 3, 0, 4, 5, 6, 7?

**Q.**In an examination a student was asked to find 314th of a certain number. By mistake, he found 34 of it. His answer was 150 more than the correct answer. The number given him is:

- 290
- 280
- 240
- 180

**Q.**

Complete the table and by inspection of the table find the solution to the equation.

m+10=16

m12345678910⋯⋯⋯m+10⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯

**Q.**All the 7 digit numbers containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once and not divisible arranged in the increasing oder then-

- 1800th number in the list 3142567
- 1897th number in the list is 4231567
- 1994th number in the list is 4321567
- 2004th number in the list is 4316527