Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 5

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The number less than $1000$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ when repetition is not allowed 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 6

Number greater than

1000

but not greater than

4000

which can be formed with the digits

0, 1, 2, 3, 4

(

repetition of digits is allowed

)

are

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

The total number not more than

20

digits that are formed by using the digits

0, 1, 2, 3

and

4

is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 8

Two teams are to play a series of five matches between them. A match ends in a win, loss, or draw for a team. A number of people forecast the result of each match and no two people make the same forecast for the series of matches. The smallest group of people in which one person forecasts correctly for all the matches will contain

n

people, where

n

is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 9

n

is selected from the set

\{1, 2, 3, . . ., 100\}

and the number

2^{n} + 3^{n} + 5^{n}

is formed. Total number of ways of selecting

n

so that the formed number is divisible by

4

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 10

The last digit of

{(1! + 2! + . . . + 2005!)}^{500}

is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 11

Let

A

be a set of

n, (\geq 3)

distinct elements. The number of triplets

(x, y, z)

of the

A

elements in which atleast two coordinates is equal to

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 12

The number of four-digit numbers that can be made with the digits

1, 2, 3, 4

and

5

in which at least two digits are identical is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 7 - Permutation and Combination>Exercises>Q 13

The total number of five-digit numbers of different digits in which the digit in the middle is the largest is