Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 15

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IMPORTANT

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If $N$ denotes the number of ways of selecting $r$ objects out of $n$ distinct objects $(r \geq n)$ with unlimited repetition but with each object included at least once in selection, then $N$ is equal to

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Important Questions on Permutation and Combination

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 16

A

is a set containing

n

elements.

A

subset

P_{1}

of

A

is chosen. The set

A

is reconstructed by replacing the elements of

P_{1}

. Next, a subset

P_{2}

of

A

is chosen and again the set is reconstructed by replacing the elements of

P_{2}

. In this way,

m (> 1)

subsets

P_{1}, P_{2}, \dots ., P_{m}

of

A

are chosen. The number of ways of choosing

P_{1}, P_{2}, \dots, P_{m}

is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 17

If

10! = 2^{p} \cdot 3^{q} \cdot 5^{r} \cdot 7^{s}

, then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 18

If

P = 21 (21^{2} - 1^{2}) (21^{2} - 2^{2}) (21^{2} - 3^{2}) \dots (21^{2} - 10^{2})

, then

P

is divisible by

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 19

Let

n

be a four-digit integer in which all the digits are different. If

x

is a number of odd integers and

y

is a number of even integers, then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 1

If

{}^{n}P_{r} =^{n} P_{r - 1}

and

{}^{n}C_{r} =^{n} C_{r - 1}

, then the value of

n + r

is _______.

HARD

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 2

A person has

n

friends. The minimum value of

n

so that a person can invite a different pair of friend every day for four weeks in a row is ______.

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 3

There are

n

distinct white and

n

distinct black balls. If the number of ways of arranging them in a row so that neighboring balls are of different colors is

1152,

then value of

n

is ______.

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 4

Numbers from

1

to

1000

are divisible by

60

but not by

24

is ______.