Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 7

MEDIUM

JEE Main

IMPORTANT

Earn 100

Product of all the even divisors of $N = 1000$ is

100% studentsanswered this correctly

Important Questions on Permutation and Combination

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 8

How many combinations can be made up of three hens, four ducks and two geese, so that each combination has hens, ducks and geese?

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 9

A positive integer

n

is of the form

n = 2^{α} 3^{β}

, where

α \geq 1

,

β \geq 1

. If

n

has

12

positive divisors and

2 n

has

15

positive divisors, then the number of positive divisors of

3 n

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 10

The number of permutations of $1, 2, 3, 4, 5, 6, 7, 8$ and $9$ taken all at a time, such that digit $1$ appears some where to the left of digit $2$ and digit $3$ appears to the left of digit $4$ and digit $5$ appears some where to the left of digit $6$ , is (e.g. $815723946$ would be one such permutation)

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 6 - Permutation and Combination>DPP>Q 11

The number of arrangements of all the digits of

12345

, such that at least three digits will not come in their position, is

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JEE Main

IMPORTANT

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

A contest consists of ranking

10

songs of which

6

are Indian classics and

4

are western songs. The number of ways of ranking the songs, such that

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JEE Main

IMPORTANT

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

P = n (n^{2} - 1) (n^{2} - 4) (n^{2} - 9) \dots (n^{2} - 100)

,

n \in I

is always divisible by

HARD

JEE Main

IMPORTANT

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

How many permutations of six

0'

s, five

1'

s and four

2'

s have the first

0

preceding the first

1

have?

HARD

JEE Main

IMPORTANT

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

In how many permutations of six

0'

s, five

1'

s and four

2'

s, does the first

0

precede the first

1

and the first

1

precede the first

2

?