Combination

Q.

How many ways 10 identical chocolates can be distributed to three people?

1. 

2. 

3. 

4. 

Q.

The number of $4$ letter words (with or without meaning) that can be made from the eleven letters of the word “EXAMINATION” is

Q. Showing the man receiving the prize, Saroj said, "He is the brother of my uncle's daughter." Who is the man to Saroj?

1. Brother-in-law
2. Nephew
3. Son
4. Cousin

Q. Seven people leave their bags outside a temple and returning after worshiping picked one bag each at random. In how many ways at least one and at most three of them get their correct bag?

1. $2\cdot 7\cdot 13\cdot 17$
2. $4\cdot 7\cdot 13\cdot 17$
3. $7\cdot 13\cdot 17$
4. $3\cdot 7\cdot 13\cdot 17$

Q.

The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?

Q. $\sum _{k=0}^{20}{\left({}^{20}{C}_k\right)}^2$ is equal to

1. ${}^{41}{C}_{20}$
2. ${}^{40}{C}_{19}$
3. ${}^{40}{C}_{21}$
4. ${}^{40}{C}_{20}$

Q.

What is the greatest $3$digit even number?

Q.

If $\frac{(a^{n+1}+b^{n+1})}{(a^n+b^n)}$ be the A.M of $a$ and $b$, then $n=$

1. $1$

2. $-1$

3. $0$

4. None of these

Q. The total number of triangles and squares in the given figure is

1. $21$ triangles, $7$ squares
2. $21$ triangles, $8$ squares
3. $22$ triangles, $7$ squares
4. $22$ triangles, $8$ squares

Q.

In a party, there are 10 married couples. Each person shake hands with every persion other than her or his spouce. The total numberof hand shakes exchanged in that party is ______?

Q.

If $AandB$are square matrices of size $n\times n$ such that $A^2–B^2=(A–B)(A+B)$, then which of the following will be always correct?

1. $AB=BA$

2. either $AorB$ is a zero matrix

3. either $AorB$ is an identity matrix

4. $A=B$

Q. In a certain code, $REQUEST$ is written as $S2R52TU.$ How is $ACID$ written in that code?

1. $1394$
2. $IC94$
3. $BDJE$
4. $1D3E$

Q. How many ways we can select four letters from the word mathematics?

Q. Number of positive integral solutions of the equation $xyz=90$ is

1. $54$
2. $108$
3. $120$
4. $60$

Q.

In how many ways 4 persons can occupy 10 chairs in a row , if no two sit on adjacent chairs.

Q.

Write the smallest $8$-digit odd number using all odd digits.

Q. In a train five seats are vacant, then how many ways can three passengers sit

1. 20
2. 30
3. 10
4. 60

Q. There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84$, then the value of $m$ is :

1. $7$
2. $9$
3. $11$
4. $12$

Q.

Coefficient of $x^6$ in $\left(\right(1+x\left)\right(1+x^2{)}^2(1+x^3{)}^3....(1+x^n{)}^n)$ is

1. 26
2. 35
3. 28
4. 30

Q.

In how many ways can $5$ boys and $5$ girls stand in a row so that no two girls maybe together?

1. $\left(5!\right)2$

2. $5!\times 4!$

3. $5!\times 6!$

4. $6\times 5!$

Q. Seven people leave their bags outside a temple and returning after worshiping picked one bag each at random.In how many ways atleast one and atmost three of them get their correct bags?

1. $3094$
2. $3095$
3. $3096$
4. $3093$

Q. How many words comprising of any three letters of the word UNIVERSAL can be formed

1. 504
2. 450
3. 540
4. 405

Q.

A question paper is divided into two parts A and B and each part contains $5$ questions. The number of ways in which a candidate can answer $6$ questions selecting at least two questions from each part is?

1. $80$

2. $100$

3. $200$

4. None of these

Q. In a chess tournment, where the participants were to play one game with another. Two chess players fell ill, having played three games each. If the total number of games played is $84$, the number of participants at the beginning was:

1. $16$
2. $20$
3. $21$
4. $15$

Q.

By a reduction of Rs. $1$ per kg in the price of sugar, Mohan can buy one kg more for Rs. $56$. Find the original price of sugar per kg.

Q. There are five students $S_1,S_2,S_3,S_4$ and $S_5$ in a music class and for them there are five seats $R_1,R_2,R_3,R_4$ and $R_5$ arranged in a row, where initially the seat $R_i$ is allotted to the student $S_i,i=1,2,3,4,5$. But, on the examination day, the five students are randomly allotted the five seats.

For $i=1,2,3,4,$ let $T_i$ denote the event that the students $S_i$ and $S_{i+1}$ do $NOT$ sit adjacent to each other on the day of the examination. Then, the probability of the event $T_1\cap T_2\cap T_3\cap T_4$ is

1. $\frac{1}{15}$
2. $\frac{1}{5}$
3. $\frac{7}{60}$
4. $\frac{1}{10}$

Q.

The eccentricity of the hyperbola $9x^2-16y^2-18x-64y-199=0$ is

1. $\frac{16}{9}$

2. $\frac{5}{4}$

3. $\frac{25}{16}$

4. $0$

Q. Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is

1. 9
2. 10
3. 5
4. 15

Q.

Let a complex number $z$, $\left|z\right|\ne 1$, satisfy ${\log }_{\frac{1}{\sqrt{2}}}\left(\frac{\left|z\right|+11}{{\left(\left|z\right|-1\right)}^2}\right)\le 2$. Then the largest value of $\left|z\right|$ is equal to ______

1. $5$

2. $8$

3. $6$

4. $7$

Q.

The value of $i^{\left(1+3+5+.....+(2n+1)\right)}$ is

1. $i$ if $n$ is even, $-i$ if $n$ is odd

2. $1$ if $n$ is even, $-1$ if $n$ is odd

3. $1$ if $n$ is odd, $-1$ if $n$ is even

4. None of these