Fundamental Principle of Counting

Q.

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

1. 36
2. 144
3. 151
4. 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 ?

1. $100$

2. $600$

3. $300$

4. $400$

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?

1. $12$

2. $16$

3. $4$

4. $8$

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

1. 9
2. 11
3. 19
4. 10

Q. Number of ordered triplets of natural number (a, b, c) for which $abc\le 11$ is

1. 53
2. 52
3. 55
4. 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

1. $24$

2. $18$

3. $12$

4. $30$

Q. Let $n_1<n_2<n_3<n_4<n_5$ be positive integers such that $n_1+n_2+n_3+n_4+n_5=20.$ The number of such distinct arrangements $(n_1,n_2,n_3,n_4,n_5)$ is ?

1. 7
2. 6
3. 8
4. 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 _____ .

1. 10
2. 20
3. 9
4. 15

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

1. $125$
2. $625$
3. $1024$
4. 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 _____ .

1. 10
2. 9
3. 15
4. 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.

1. $315$
2. $256$
3. $300$
4. $275$

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

1. $5\times 8^3$
2. $5\times 9^2$
3. $5\times 7^3$
4. $5\times 9^3$

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

1. 64
2. 72
3. 900
4. 81

Q. Reciprocal of $\frac{7}{5}$ is

1. $1\frac{2}{5}$
2. $\frac{5}{7}$
3. $5\frac{2}{3}$
4. $\frac{12}{5}$

Q. The first twenty natural numbers from $1to20$ are written next to each other to form a $31-$digit number $N=1234567891011121314151617181920$. What is the remainder when this number is divided by $16$

1. $0$
2. $4$
3. $7$
4. $9$

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

1. $720$
2. $1024$
3. $120$
4. $180$

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?

1. $25$
2. $35$
3. $45$
4. $55$

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

1. $120$
2. $96$
3. $32$
4. $24$

Q.

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

1. 7

2. 9

3. 12

4. 14

Q. Find the positive natural number for which $n^2=n^3=n$.

1. $1$
2. $-1$
3. $0$
4. Cannot be determined

Q. Product of the numbers $\frac{12}{24}$ and $\frac{36}{72}$ is

1. $\frac{16}{24}$
2. $\frac{3}{5}$
3. $4$
4. $\frac{1}{4}$

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

1. 36
2. 28
3. 23
4. 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 $\frac{3}{14}$th of a certain number. By mistake, he found $\frac{3}{4}$ of it. His answer was $150$ more than the correct answer. The number given him is:

1. $290$
2. $280$
3. $240$
4. $180$

Q.

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

$m+10=16$

$\begin{array}{cccccccccccccc}m& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10& \cdots & \cdots & \cdots \\ m+10& \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \end{array}$

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-

1. ${1800}^{\text{th}}$ number in the list 3142567
2. ${1897}^{\text{th}}$ number in the list is 4231567
3. ${1994}^{\text{th}}$ number in the list is 4321567
4. ${2004}^{\text{th}}$ number in the list is 4316527