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JEE Advanced > Permutations and Combinations

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

Q 1.

Correct4

Incorrect-1

{tex} ^ n C _ { r - 1 } = 36 , ^ { n } C _ { r } = 84 {/tex} and {tex} ^ { n } C _ { r + 1 } = 126 , {/tex} then {tex} r {/tex} is

A

1

B

2

3

D

None of these

Explanation

Q 2.

Correct4

Incorrect-1

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are

69760

B

30240

C

99748

D

none of these

Explanation

Q 3.

Correct4

Incorrect-1

The value of the expression {tex} ^ { 47 } C _ { 4 } + \sum _ { j = 1 } ^ { 5 }{^{ 52 - j }C _ { 3 }} {/tex} is equal to

A

{tex} ^ { 47 } C _ { 5 } {/tex}

B

{tex} ^ { 52 } C _ { 5 } {/tex}

{tex} ^ { 52 } C _ { 4 } {/tex}

D

none of these

Explanation

Q 4.

Correct4

Incorrect-1

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

A

{tex}\mathrm { ^ { 6 } C _ { 3 } \times ^ { 4 } C _ { 2 }} {/tex}

B

{tex}\mathrm { ^ { 4 } P _ { 2 } \times ^ { 4 } P _ { 3 }} {/tex}

C

{tex}\mathrm { ^ { 4 } C _ { 2 } + ^ { 4 } P _ { 3 } }{/tex}

none of these

Explanation

Q 5.

Correct4

Incorrect-1

A five-digit numbers divisible by {tex}3{/tex} is to be formed using the numerals {tex} 0,1,2,3,4 {/tex} and {tex} 5 , {/tex} without repetition. The total number of ways this can be done is

216

B

240

C

600

D

3125

Explanation


Q 6.

Correct4

Incorrect-1

How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?

A

16

B

36

60

D

180

Explanation

Q 7.

Correct4

Incorrect-1

Let {tex} T _ { n } {/tex} denote the number of triangles which can be formed using the vertices of a regular polygon of {tex} n {/tex} sides. If {tex} T _ { n + 1 } - T _ { n } = 21 , {/tex} then {tex} n {/tex} equals

A

5

7

C

6

D

4

Explanation

Q 8.

Correct4

Incorrect-1

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is

40

B

60

C

80

D

100

Explanation

Q 9.

Correct4

Incorrect-1

A rectangle with sides of length {tex} ( 2 m - 1 ) {/tex} and {tex} ( 2 n - 1 ) {/tex} units is divided into squares of unit length by drawing parallel lines as shown in the diagram, then the number of rectangles possible with odd side lengths is

A

{tex} ( m + n - 1 ) ^ { 2 } {/tex}

B

{tex} 4 ^ { m + n - 1 } {/tex}

{tex} m ^ { 2 } n ^ { 2 } {/tex}

D

{tex} m ( m + 1 ) n ( n + 1 ) {/tex}

Explanation


Q 10.

Correct4

Incorrect-1

If the LCM of {tex} p , q {/tex} is {tex} r ^ { 2 } t ^ { 4 } s ^ { 2 } , {/tex} where {tex} r , s , t {/tex} are prime numbers and {tex} p , q {/tex} are the positive integers then the number of ordered pair {tex} ( p , q ) {/tex} is

A

252

B

254

225

D

224

Explanation

Q 11.

Correct4

Incorrect-1

The letters of the word {tex} \mathrm {COCHIN}{/tex} are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word {tex} \mathrm {COCHIN}{/tex} is

A

360

B

192

96

D

48

Explanation

Q 12.

Correct4

Incorrect-1

The number of seven digit integers, with sum of the digits equal to {tex}10{/tex} and formed by using the digits {tex} 1,2 {/tex} and {tex}3{/tex} only, is

A

55

B

66

77

D

88

Explanation

Q 13.

Correct4

Incorrect-1

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

A

75

150

C

210

D

243

Explanation



Q 14.

Correct4

Incorrect-1

Six cards and six envelopes are numbered {tex} 1,2,3,4,5,6 {/tex} and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered {tex}1{/tex} is always placed in envelope numbered {tex} 2 . {/tex} Then the number of ways it can be done is

A

264

B

265

53

D

67

Explanation

Q 15.

Correct4

Incorrect-1

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 memoers) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

380

B

320

C

260

D

95

Explanation

Q 16.

Correct4

Incorrect-1

The number of 4-digit natural numbers in which digit at {tex} 1000 ^ { \text {th } } {/tex} places are 1 and exactly one of the digit comes twice are

A

108

B

216

432

D

864

Explanation


Q 17.

Correct4

Incorrect-1

Consider 26 tangent lines to an ellipse. The lines separate the plane into several regions, some enclosed and others unbounded. Then the number of unbounded regions is

A

50

52

C

{tex} ^ { 26 } C _ { 2 } {/tex}

D

None of these

Explanation

Q 18.

Correct4

Incorrect-1

Given 6 different toys of green colour, 5 different toys of blue colour and 4 different toys of red colour. Combination of toys that can be chosen taking at least one green and one blue toys are

A

31258

31248

C

31

D

63

Explanation


Q 19.

Correct4

Incorrect-1

Given distinct lines {tex} L _ { 1 } , L _ { 2 } , \ldots , L _ { 1000 } {/tex} in which all lines of the form {tex} L _ { 4 n ^ { \prime } } {/tex} where {tex} n {/tex} is a positive integer, are parallel to each other. All lines {tex} L _ { 4 n - 3 ^ { \prime } } {/tex} are concurrent at a point. The maximum number of the points of intersection of pairs of line from the complete set {tex} \left( L _ { 1 } , L _ { 2 } , \cdots , L _ { 1000 } \right) {/tex} is

437251

B

437250

C

437252

D

437200

Explanation

Q 20.

Correct4

Incorrect-1

The number of integral points on the hyperbola {tex} x ^ { 2 } - y ^ { 2 } = ( 2000 ) ^ { 2 } {/tex} is (an integral point is a point both of whose co-ordinates are integer)

98

B

96

C

48

D

24

Explanation