# JEE Main > Permutations and Combinations

Explore popular questions from Permutations and Combinations for JEE Main. This collection covers Permutations and Combinations previous year JEE Main questions hand picked by popular teachers.

Physics
Chemistry
Maths

Q 1.

Correct4

Incorrect-1

Number greater than {tex}1000{/tex} but less than {tex}4000{/tex} is formed using the digits {tex} 0,2,3,4 {/tex} repetition allowed is

A

125

B

105

128

D

625

##### Explanation

Q 2.

Correct4

Incorrect-1

Five digit number divisible by 3 is formed using {tex} 0,1,2,3,4,6 {/tex} and {tex} 7{/tex} without repetition. Total number of such numbers are

A

312

B

3125

C

120

216

##### Explanation

Q 3.

Correct4

Incorrect-1

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

A

3000

3050

C

3600

D

3250

##### Explanation

Q 4.

Correct4

Incorrect-1

Total number of four digit odd numbers that can be formed using {tex} 0,1,2,3,5,7 {/tex} are

A

216

B

375

C

400

720

##### Explanation

Q 5.

Correct4

Incorrect-1

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

A

30

B

{tex} 5 ! \times 4 ! {/tex}

C

{tex} 7 ! \times 5 ! {/tex}

{tex} 6 ! \times 5 ! {/tex}

##### Explanation

Q 6.

Correct4

Incorrect-1

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

196

B

280

C

346

D

140

##### Explanation

Q 7.

Correct4

Incorrect-1

If {tex} ^ { n } C _ { r } {/tex} denotes the number of combinations of {tex} n {/tex} things taken {tex} r {/tex} at a time, then the expression {tex} ^ { n } C _ { r + 1 } + ^ { n } C _ { r - 1 } + 2 \times ^ { n } C _ { r } {/tex} equals

{tex} ^{n + 2} C _ { r + 1 } {/tex}

B

{tex} ^{n + 1} C _ { r } {/tex}

C

{tex} ^{n + 1} C _ { r + 1 } {/tex}

D

{tex} ^{n + 2} C _ { r } {/tex}

##### Explanation

Q 8.

Correct4

Incorrect-1

How many ways are there to arrange the letters in the word {tex}GARDEN{/tex} with the vowels in alphabetical order?

360

B

240

C

120

D

480

##### Explanation

Q 9.

Correct4

Incorrect-1

Then number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

A

{tex} 3 ^ { 8 } {/tex}

{tex}21{/tex}

C

{tex}5{/tex}

D

{tex} ^ { 8 } C _ { 3 } {/tex}

##### Explanation

Q 10.

Correct4

Incorrect-1

If the letters of the word {tex}SACHIN{/tex} are arranged in all possible ways and these words are written out as in dictionary, then the word {tex}SACHIN{/tex} appears at serial number

A

602

B

603

C

600

601

##### Explanation

Q 11.

Correct4

Incorrect-1

The value of {tex}\mathrm{^{50}C_{4}+\sum\limits_{r=1}^6 {^{56-r}C_{3}}}{/tex} =

{tex} ^ { 56 } C _ { 4 } {/tex}

B

{tex} ^ { 56 } C _ { 3 } {/tex}

C

{tex} ^ { 55 } C _ { 3 } {/tex}

D

{tex} ^ { 55 } C _ { 4 } {/tex}

##### Explanation

Q 12.

Correct4

Incorrect-1

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is

5040

B

6210

C

385

D

1110

##### Explanation

Q 13.

Correct4

Incorrect-1

The sum of the series {tex}^{20} C _ { 0 } - ^ { 20 } C _ { 1 } + ^ { 20 } C _ { 2 } - ^ { 20 } C _ { 3 } + \ldots . . + ^ { 20 } C _ { 10 } {/tex} is

A

0

B

{tex} ^{20} C _ { 10 } {/tex}

C

{tex} - ^ { 20 } C _ { 10 } {/tex}

{tex} \frac { 1 } { 2 } ^ { 20 } C _ { 10 } {/tex}

##### Explanation

Q 14.

Correct4

Incorrect-1

The question contains two statements :
{tex}Statement-1:{/tex} (Assertion) and {tex}Statement-2{/tex} : (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.
In a shop there are five types of ice-creams available. A child buys six ice-creams.
{tex}Statement-1:{/tex} The number of different ways the child can buy the six ice-creams is {tex} ^{10}C_5.{/tex}
{tex}Statement-2:{/tex} The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging {tex} 6\, A ^ { \prime }s {/tex} and {tex} 4\, B ^ { \prime }s {/tex} in a row.

A

Statement-1 is true, Statement-2 is false

Statement-1 is false, Statement- 2 is true

C

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

D

Statement-1 is true, Statement- 2 is true; Statement-2 is not a correct explanation for Statement-1

##### Explanation

Q 15.

Correct4

Incorrect-1

How many different words can be formed by jumbling the letters in the word {tex}\mathrm{MISSISSIPPI}{/tex} in which no two S are adjacent?

{tex} 7 \cdot ^ { 6 } C _ { 4 } \cdot ^ { 8 } C _ { 4 } {/tex}

B

{tex} 8 \cdot ^ { 6 } \mathrm { C } _ { 4 } \cdot ^ { 7 } \mathrm { C } _ { 4 } {/tex}

C

{tex} 6 \cdot 7 \cdot ^ { 8 } C _ { 4 } {/tex}

D

{tex} 6 \cdot 8 \cdot ^ { 7 } C _ { 4 } {/tex}

##### Explanation

Q 16.

Correct4

Incorrect-1

The set {tex} S = \{ 1,2,3 , \ldots , 12 \} {/tex} is to be partitioned into three sets {tex} A , B {/tex}
and {tex} C {/tex} of equal size. Thus, {tex} A \cup B \cup C = S , A \cap B = B \cap C = A \cap C = \phi {/tex} The number of ways to partition {tex} S {/tex} is

A

{tex} \frac { 12 ! } { 3 ! ( 4 ! ) ^ { 3 } } {/tex}

B

{tex} \frac { 12 ! } { 3 ! ( 3 ! ) ^ { 4 } } {/tex}

{tex} \frac { 12 ! } { ( 4 ! ) ^ { 3 } } {/tex}

D

{tex} \frac { 12 ! } { ( 3 ! ) ^ { 4 } } {/tex}

##### Explanation

Q 17.

Correct4

Incorrect-1

In a shop there are five types of ice creams available. A child buys six ice creams.
Statement 1: The number of different ways the child can buy the six ice creams is {tex} ^ { 10 } \mathrm { C } _ { 5 } {/tex}.
Statement 2: The number of different ways the child can buy the six ice creams is equal to the number of different ways of arranging 6{tex} A ^ { \prime } s {/tex} and 4{tex} B ^ { \prime } {/tex} in a row.

Statement 1 is false, Statement 2 is true

B

Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1

C

Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1

D

Statement 1 is true, Statement 2 is false

##### Explanation

Q 18.

Correct4

Incorrect-1

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two {tex} S {/tex} are adjacent?

A

8{tex}\,^ { .6 } C _ { 4 } \, ^ { .7 } C _ { 4 } {/tex}

B

6{tex} \cdot 7 \cdot ^ { 8 } C _ { 4 } {/tex}

C

6{tex} \cdot 8 \cdot ^ { 7 } C _ { 4 } {/tex}

7{tex} \cdot ^ { 6 } C _ { 4 } \cdot ^ { 8 } C _ { 4 } {/tex}

##### Explanation

Q 19.

Correct4

Incorrect-1

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is

A

less than 500 .

B

at least 500 but less than 750 .

C

at least 750 but less than 1000 .

at least 1000

##### Explanation

Q 20.

Correct4

Incorrect-1

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

A

36

B

66

108

D

3

##### Explanation

Q 21.

Correct4

Incorrect-1

Statement {tex} 1 : {/tex} The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is {tex} ^ { 9 } \mathrm { C } _ { 3 } {/tex}. Statement 2: The number of ways of choosing any 3 places from 9 different places is {tex} ^ { 9 } \mathrm { C } _ { 3 } {/tex} .

Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1

B

Statement 1 is true, Statement 2 is false

C

Statement 1 is false, Statement 2 is true

D

Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1

##### Explanation

Q 22.

Correct4

Incorrect-1

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

A

880

B

629

C

630

879

##### Explanation

Q 23.

Correct4

Incorrect-1

Let {tex} T _ { n } {/tex} be the number of all possible triangles formed by joining vertices of an {tex} n {/tex} -sided regular polygon. If {tex} T _ { n + 1 } - T _ { n } = 10 {/tex} , then the value of {tex} n {/tex} is

5

B

10

C

8

D

7

##### Explanation

Q 24.

Correct4

Incorrect-1

Let {tex} A {/tex} and {tex} B {/tex} be two sets containing 2 elements and 4 elements, respectively. The number of subsets of {tex} A \times B {/tex} having 3 or more elements is

A

220

219

C

211

D

256

##### Explanation

Q 25.

Correct4

Incorrect-1

The sum of the digits in the unit's place of all the 4 -digit numbers formed by using the numbers {tex} 3,4,5 {/tex} and {tex} 6 , {/tex} without repetition is

A

432

108

C

36

D

18