NCERT Solutions for Class 11 Maths Chapter 7: Permutations and Combinations

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NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations are provided in the article. Permutation and Combination are used to determine the number of ways in which a number can be arranged and selected without listing them out. NCERT Solutions Class 11 Maths Chapter 7 Permutations and Combinations cover following key concepts in detail:

Fundamental Principle of Counting
Permutations
Combinations

Download: NCERT Solutions for Class 11 Mathematics Chapter 7 pdf

Class 11 Maths NCERT Solutions Chapter 7 Permutations and Combinations

Class 11 Maths NCERT Solutions Chapter 7 Permutations and Combinations are provided below:

Also check: Permutations and Combinations

Important Topics for Class 11 Maths NCERT Solutions Chapter 7 Permutations & Combinations

Important Topics for Class 11 Maths NCERT Solutions Chapter 7 Permutations & Combinations are as follows:

Fundamental Principle of Counting

Fundamental Principle of Counting is a rule used to count total number of possible outcomes in a situation. This rule states that if there are n ways of doing something, and m ways of doing another thing after that, then there are n × m ways to perform both of these actions.

Example: A restaurant has 5 appetizers, 7 beverages, 9 entrees, and 5 desserts on the menu. If you have a beverage and a dessert, there are 7*5 = 35 different meals consisting of a beverage and dessert.

Permutations

Permutation is an arrangement of objects in a definite order. Members or elements of sets are arranged here in a sequence or linear order.

Example: Permutation of Set A = {1,6} is 2, such as {1,6}, {6,1}

Combinations

Combination is a mathematical technique that determines number of possible arrangements in a collection of items where order of the selection does not matter. In combinations, you can select the items in any order.

Combination Formula

NCERT Solutions For Class 11 Maths Chapter 7 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 7 Permutations and Combinations under different exercises are as follows:

Also check:

Chapter Related Topics
Permutations and Combinations Formulas	Factorial Formula	Stirling Formula
Combinatorics	Involute	Difference between Permutation and Combination

Also check:

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CBSE CLASS XII Related Questions

1.
Find the value of \(x\) if \(A = B\), where
\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]
View Solution
2.
For the given Linear Programming Problem, shade the feasible region on the graph and write the coordinates of the corner points.
Minimize \(Z = 5x + 7y\)
subject to constraints
\[ 2x + y \geq 8 \]
\[ x + 2y \geq 10 \]
\[ x,\ y \geq 0. \]
View Solution
3.
For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :
Minimize \(Z = 18x + 10y\)
subject to constraints
\[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]
View Solution
4.
Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).
View Solution
5.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).
View Solution
6.
\( \int e^{x}\left( \frac{2+\sin 2x}{1+\cos 2x} \right) dx \) is equal to :
- \( \log \cos 2x + C \)
- \( \sec^{2} 2x + C \)
- \( e^{x}\tan x + C \)
- \( e^{x}\cot x + C \)
View Solution

View All

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Important Questions For Class 11 Maths Chapter 7: Permutations and Combinations

NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.1

NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.2

NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.3

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NCERT Solutions for Class 11 Maths Chapter 7: Permutations and Combinations

Class 11 Maths NCERT Solutions Chapter 7 Permutations and Combinations

Important Topics for Class 11 Maths NCERT Solutions Chapter 7 Permutations & Combinations

NCERT Solutions For Class 11 Maths Chapter 7 Exercises:

CBSE CLASS XII Related Questions

1.
Find the value of \(x\) if \(A = B\), where
\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]

2.
For the given Linear Programming Problem, shade the feasible region on the graph and write the coordinates of the corner points.
Minimize \(Z = 5x + 7y\)
subject to constraints
\[ 2x + y \geq 8 \]
\[ x + 2y \geq 10 \]
\[ x,\ y \geq 0. \]

3.
For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :
Minimize \(Z = 18x + 10y\)
subject to constraints
\[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]

4.
Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).

5.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

6.
\( \int e^{x}\left( \frac{2+\sin 2x}{1+\cos 2x} \right) dx \) is equal to :

Similar Mathematics Concepts

Comments

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NCERT Solutions for Class 11 Maths Chapter 7: Permutations and Combinations

Class 11 Maths NCERT Solutions Chapter 7 Permutations and Combinations

Important Topics for Class 11 Maths NCERT Solutions Chapter 7 Permutations & Combinations

NCERT Solutions For Class 11 Maths Chapter 7 Exercises:

CBSE CLASS XII Related Questions

1.Find the value of \(x\) if \(A = B\), where\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]

2.For the given Linear Programming Problem, shade the feasible region on the graph and write the coordinates of the corner points.Minimize \(Z = 5x + 7y\)subject to constraints\[ 2x + y \geq 8 \]\[ x + 2y \geq 10 \]\[ x,\ y \geq 0. \]

3.For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :Minimize \(Z = 18x + 10y\)subject to constraints\[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]

4.Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).

5.Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

6.\( \int e^{x}\left( \frac{2+\sin 2x}{1+\cos 2x} \right) dx \) is equal to :

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Find the value of \(x\) if \(A = B\), where
\[ A = \begin{bmatrix} 6 & 3x \\ 8 & -6 \end{bmatrix} \text{ and } B = \begin{bmatrix} 6 & x^2+2 \\ 8 & x^2-5x \end{bmatrix}. \]

2.
For the given Linear Programming Problem, shade the feasible region on the graph and write the coordinates of the corner points.
Minimize \(Z = 5x + 7y\)
subject to constraints
\[ 2x + y \geq 8 \]
\[ x + 2y \geq 10 \]
\[ x,\ y \geq 0. \]

3.
For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :
Minimize \(Z = 18x + 10y\)
subject to constraints
\[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]

4.
Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).

5.
Find the sum of maximum and minimum values of \(f(x) = \sin x\,(1 + \cos x)\) in the interval \([0, \pi]\).

6.
\( \int e^{x}\left( \frac{2+\sin 2x}{1+\cos 2x} \right) dx \) is equal to :