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IMPORTANT

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Number of ways in which $7$ green bottles and $8$ blue bottles can be arranged in a row if exactly $1$ pair of green bottles is side by side is (assume all bottles to be alike except for the colour)

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Important Questions on Permutation and Combination

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 12

Which of the following is not the number of ways of selecting

n

objects from

2 n

objects of which

n

objects are identical?

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 13

A seven-digit number is in the form of

a b c d e f g

(

g, f, e \dots

etc.,, are digits at the units, tens, hundred place, and so on), where

a < b < c < d > e > f > g

and

a, b, c, e, f, g

are different digits. The number of such numbers is

HARD

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 14

The number of all six-digit numbers using digits

1, 2, 3, 4, 5

, such that any digit that appears in the number appears at least twice is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 15

All the five-digit numbers

N = a b c d e

having the property

a < b < c < d < e

are arranged in the increasing order of their magnitude. The

97^{th}

number in the list does not contain the digit

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 1

Find the number of

n

digit numbers formed by using digits

\{1, 2, 3\}

, such that if

1

appears, it appears even number of times.

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 2

A, B, C

and

D

develop

18

items. That is, five items jointly by

A

and

C

, four items by

A

and

D

, four items by

B

and

C

and five items by

B

and

D

. The number of ways of selecting eight items out of

18

, so that the selected ones belong equally to

A, B, C

and

D

, is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 3

The number of pairs of the diagonals of a regular polygon of

10

sides that are parallel is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 4

Four letters, two

a

and two

b

are filled into

16

cells of a matrix as shown in the given figure. It is required that each cell contains at most one letter and each row or column cannot contain the same letters. Then the number of ways the matrix can be filled is

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Number of ways in which 7 green bottles and 8 blue bottles can be arranged in a row if exactly 1 pair of green bottles is side by side is (assume all bottles to be alike except for the colour)

Important Questions on Permutation and Combination

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Number of ways in which $7$ green bottles and $8$ blue bottles can be arranged in a row if exactly $1$ pair of green bottles is side by side is (assume all bottles to be alike except for the colour)