Fundamental Principle of Counting

Q. How many numbers can be formed from 1, 2, 3, 4, 5 (without repeating), where the digit at the unit’s place must be greater than that in the ten’s place?(CAT 1998)

1. 
2. 2×4!
3. 54
4. 60

Q. A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees? (CAT 1996)

1. 80
2. 200
3. 320
4. 160

Q.

$12$ persons are to be arranged at a round table . If two particular persons among them are not to be side by side, the total number of arrangements is?

1. $9(10!)$

2. $2(10!)$

3. $45(8!)$

4. $10!$

Q.

How many numbers greater than a hundred and divisible by $5$can be made from the digits $3,4,5,6,$ if no digit is repeated?

1. $6$

2. $12$

3. $24$

4. $30$

Q.

Find the largest four-digit number divisible by $16$.

Q.

What is the place value of $6$ in $64$?

1. $6$

2. $60$

3. $64$

4. $10$

Q. In how many ways can 10 people line up at a ticket window of a cinema hall?

1. 3482800
2. 3328800
3. 3628800
4. 344800
5. None of these

Q.

In how many of the distinct permutations of the letters in “MISSISSIPPI” do the four I’s not come together?

Q. In which year was the difference between the basic model and the premium model of cars produced by company E the second highest?

1. 2008
2. 2009
3. 2010
4. 2006
5. 2007

Q. A basket has 5 oranges and 4 apples. In how many ways can you make a selection if you have to take at least 1 orange and 1 apple?

1. 465
2. 20
3. 345
4. 365
5. 22

Q. Out of 6 green balls, 4 blue balls, in how many ways can we select one or more balls ?

1. 42
2. 34
3. 31
4. 22
5. None of these

Q. How many numbers greater than a million can be formed with the digits $2,3,0,3,4,2,3$?

Q.

There are $5$ways leading to a town from a village. the number of different ways in which a villager can go to the town and return back is

1. $20$

2. $25$

3. $5$

4. $10$

Q. How many seven letter words can be formed without repetition out of the letters of the word ${}^{\prime }MISTAK{E}^{\prime }$ such that the vowels go only into the odd places

1. $786$
2. $480$
3. $625$
4. $576$

Q.

It was a sunday on 9${}^{th}$ Nov, 2006. What day of the week was it on 9${}^{th}$ Nov, 2005?

1. Sunday

2. Thursday

3. Friday

4. Saturday

5. Tuesday

Q.

If farmer Q sells 14 kg of wheat, farmer S sells 21 kg of jowar and farmer R sells 30 kgs of sugarcane, what will be their combined earning?

1. Rs. 779

2. Rs. 650

3. Rs. 786

4. Rs. 699

5. None of these

Q.

On 23${}^{rd}$ Apr, 2001 it was Monday. What was the day of the week on 23${}^{rd}$ Apr, 2000?

1. Tuesday

2. Monday

3. Thursday

4. Sunday

Q. For numbering the pages of an encyclopedia the printer used 2989 digits. How many pages did the book contain?

1. 924
2. 996
3. 1024
4. 1009

Q. Find the digits at the tens place of $6^{24}$.

1. $3$
2. $1$
3. $9$
4. $5$

Q. What is the difference between the number of CDs produced by Company B and the number of Computers produced by Company A?

1. 200
2. None of these
3. 300
4. 250
5. 350

Q.

If $p:Theearthisround,q:3+4=7$ then $\left(~p\right)\vee \left(~q\right)$ is

1. It is not that the earth is round or $3+4=7$

2. The earth is round and $3+4=7$

3. It is not that the earth is round or it is not that $3+4=7$

4. The earth is round or $3+4=7$

5. The earth is round or it is not that $3+4=7$

Q. Given 5 different green dyes, four different blue dyes and three different red dyes, how many combinations of dyes can be chosen taking at least one green and one blue dye?

Q. The HCF and LCM of 36 and 15 are 'p' and 'q'. Find 'pxq'.

Q. None of the digits are repeated?

1. 216
2. 240
3. 360
4. 120
5. 412

Q. The integers P, Q, R and S shown on the number line above are all equally spaced. If R and S are equal to $7^{12}$ and $7^{13}$, respectively, what is the value of P?

1. 7¹⁰
2. 7¹¹
3. -7¹³
4. 7⁹
5. none of these

Q. Assuming that no two consecutive digits are same, the number of n is

1. $n!$
2. $9!$
3. $9^n$
4. $n^9$

Q. You are Pramod Sharma residing at $80$, Saket Nagar, Jabalpur. Your younger brother lives in a hostel. Write a letter of advice to your brother to set a goal in life and try to achieve it.

Q.

On 23${}^{rd}$ Apr, 2001 it was Monday. What was the day of the week on 23${}^{rd}$ Apr, 2000?

1. Monday

2. Sunday

3. Wednesday

4. Thursday

5. Tuesday

Q. Pupils of ${10}^{th}$ standard of a school had arranged a function at a total cost of Rs. $1,000$ which was to be shared equally among them. Since $10$ of them failed to join the function each of them had to pay Rs. $5$ more. Find the number of pupils in the class.

Q. 4 7 11 18 29 ? 76 123

1. 53
2. None of these
3. 59
4. 38
5. 46