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JEE Main

IMPORTANT

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There are $15$ players in a cricket team, out of which $6$ are bowlers, $7$ are batsmen and $2$ are wicketkeepers. The number of ways, a team of $11$ players be selected from them so as to include at least $4$ bowlers, $5$ batsmen and $1$ wicketkeeper, is

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Important Questions on Permutation and Combination

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 22 July 2021 Shift 1>Q 10

Let

A = {0, 1, 2, 3, 4, 5, 6, 7} .

Then the number of bijective functions

f : A \to A

such that

f (1) + f (2) = 3 - f (3)

is equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 22 July 2021 Shift 1>Q 11

If the digits are not allowed to repeat in any number formed by using the digits

0, 2, 4, 6, 8,

then the number of all numbers greater than

10, 000

is equal to __________.

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JEE Main

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 22 July 2021 Shift 1>Q 12

Let

A = [\begin{array}{l} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array}] .

Then the number of

3 \times 3

matrices

B

with entries from the set

{1, 2, 3, 4, 5}

and satisfying

A B = B A

is ________.

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 25 July 2021 Shift 1>Q 13

There are

5

students in class

10, 6

students in class

11

and

8

students in class

12 .

If the number of ways, in which

10

students can be selected from them so as to include at least

2

students from each class and at most

5

students from the total

11

students of class

10

and

11

100 k,

then

k

is equal to

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JEE Main

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 25 July 2021 Shift 2>Q 14

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

and

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

then the value of

r

is equal to:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main - 27 July 2021 Shift 2>Q 15

Let

n

be a non-negative integer. Then the number of divisors of the form

4 n + 1

of the number

{(10)}^{10} \cdot {(11)}^{11} \cdot {(13)}^{13}

is equal to _____.

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main 16 March 2021 Shift 1>Q 16

The total number of

3 \times 3

matrices

A

having enteries from the set

(0, 1, 2, 3)

such that the sum of all the diagonal entries of

A A^{T}

9

, is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Permutation and Combination>JEE Main 16 March 2021 Shift 2>Q 17

Consider a rectangle

A B C D

having

5, 6, 7, 9

points in the interior of the line segments

A B, B C, C D, D A

respectively. Let

α

be the number of triangles having these points from different sides as vertices and

β

be the number of quadrilaterals having these points from different sides as vertices. Then

(β - α)

is equal to

There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is

Important Questions on Permutation and Combination

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There are $15$ players in a cricket team, out of which $6$ are bowlers, $7$ are batsmen and $2$ are wicketkeepers. The number of ways, a team of $11$ players be selected from them so as to include at least $4$ bowlers, $5$ batsmen and $1$ wicketkeeper, is