Combination

Q. How many 3-digit odd numbers can be formed from the digits 1, 2, 3, 4, 5, 6 when (i) repetition of digits is not allowed
(ii) repetition of digits is allowed?

1. None of these
2. (i) 60, (ii) 108
3. (i) 50, (ii) 98
4. (i) 70, (ii) 118
5. (i) 80, (ii) 128

Q. If there are 6 periods in each working day of a school, in how many ways can 1 arrange 5 subjects such that each subject is allowed at least 1 period?

1. None of these
2. 3500
3. 3600
4. 3550
5. 3650

Q.

In a party, everyone gave a gift to everyone else. The total number of gifts exchanged in the party was 600.
How many persons were present in the party?

1. 25

2. 30

3. 10

4. 20

5. 15

Q.

If p = x ${}^{1/3}$ + x ${}^{-1/3}$ , then p${}^3$ - 3p is equal to

1. 3

2. (x + x^-1)/2

3. x + x^-1

4. -2

5. 2(x + x^-1)

Q.

How many $3$-digit natural numbers are completely divisible by $3$?

Q. In how many different ways can the letters of the word 'DESIGN' be arranged so that the vowels are at the two ends?

1. 48
2. 72
3. 36
4. 24
5. None of these

Q.

In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman?

1. $186$

2. $246$

3. $252$

4. None of these

Q. A committee of 3 members is to be formed out of 3 men and 4 women. In how many different ways can it be done so that atleast one member is woman?

1. 34
2. 12
3. 30
4. None of these
5. 36

Q.

There are $15$ persons in a party and each person shakes hand with another, then total number of handshakes is?

1. ${}^{15}{\mathrm{P}}_2$

2. ${}^{15}{C}_2$

3. $15!$

4. $2\left(15!\right)$

Q. A code word is to consist of 2 English alphabets followed by 2 distinct numbers between 1 and 9. For example, CA23 is a code word. How many such code words are there?

1. 410800
2. 615800
3. 46800
4. 719500
5. None of these

Q. In how many ways, the letters of the word 'SACRED' can be arranged so that vowels come together?

1. 240
2. 320
3. 120
4. 720
5. None of these

Q.

A college has 12 basketball players. A 5 member team and a captain are to be selected out of these 12 players. How many different selections can be made?

1. none

2. ¹²C₆*⁶C₁

3. ¹²C₅*5

4. ¹²C₆

5. ¹²C₅

Q. There are four married couples in a club. The number of ways of choosing a committee of three members so that no complete couple appears in the committee is

1. 4
2. 32
3. 8
4. 16
5. none of these

Q.

The decimal equivalent of the binary number $11010101$is ?

Q. Two persons move down on an escalator. A takes 50 steps and B takes 75 steps while the escalator is moving down. The time taken by A to take 1 step is equal to time taken by B to take 3 steps.
What is the number of steps on the escalator when it is stationary?

1. 125 steps
2. 150 steps
3. 100 steps
4. 25 steps
5. None of these

Q. 45 46 70 141 ? 1061.5

1. 353
2. 353.5
3. 352
4. 352.5
5. None of these

Q.

Explain the process of finding the orthocenter of a triangle and also mention the formula.

Q. Fresh grapes contain $90\%$ water by weight and dry grapes contain $20\%$ water by weight. What is the weight of dry grapes obtained from 20 kg of fresh grapes ?

1. 2 kg
2. 3 kg
3. 2.5 kg
4. 2.4 kg

Q.

A student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first five questions. The number of choices available to him is equal to?

1. $140$

2. $196$

3. $280$

4. $346$

Q. 25 29 67 217 ? 4501

1. 885
2. 887
3. 889
4. 891
5. None of these

Q.

10 chairs are arranged in a row and are numbered 1 to 10. 4 men have to be seated in these chairs so that the ending chairs in the row can never be empty. In how many ways can this be done?

1. 336

2. 112

3. 168

4. 672

Q. In a college a committee of 7 people has to be selected from a group of 8 fourth year and 6 third year students. In how many ways can this committee be selected if in the committee, majority of fourth year students is required?

1. 2320
2. 1960
3. 1530
4. 2216
5. 2416

Q. What is the number of distinct terms in the expansion of $(p+q+r+s{)}^{10}$?

1. none of these
2. 245
3. 105
4. 98
5. 378

Q. Find the value of x such that: ${}^7$C${}_{x-1}$+ ${}^7$C${}_x$ = ${}^8$C${}_{x+2}$

1. 4
2. 3
3. 5
4. 6
5. 2

Q. Number of players participating in three different sports

In which school is the number of players participating in Hockey and Basketball together the second highest?

1. School 3
2. School 1
3. School 5
4. School 2
5. School 4

Q. In a class of 120 students numbered 1 to 120, there are 3 extracurricular activities to choose from. All even numbered students opt for Dance, whose numbers are divisible by 5 opt for Music and those whose numbers are divisible by 7 opt for Debate. How many opt for none of the three subjects?

1. 52
2. 19
3. 41
4. 20
5. 31

Q. In which PG course, is the number of girls the highest and in which course is the number of boys is the lowest?

1. Botany and Mathematics
2. Mathematics and Physics
3. Botany and Zoology
4. Botany and Physics
5. Statistics and Physics

Q.

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

1. 4:5

2. 5:4

3. 2:5

4. 5:2

5. none

Q.

There are 4 Rock songs, 5 Carnatic songs and 2 Indi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song and 1 Carnatic song?

1. None of these

2. 110

3. 100

4. 90

5. 130

Q.

The number of natural numbers less than $1000$, in which no two digits are repeated, is equal to:

1. $738$

2. $792$

3. $837$

4. $720$