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.


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

Explanation