NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.1 Solutions

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Class 12 Maths NCERT Solutions Chapter 12 Linear Programming Exercise 12.1 is provided in the article. Class 12 Chapter 12 Linear Programming Exercises include questions on Mathematical formulation of the problem and Graphical method of solving linear programming problems.

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Chapter 12 Linear Programming Important Topics
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Class 12 Mathematics Notes	Math MCQs	Trigonometry
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CBSE CLASS XII Related Questions

1.
If \( \vec{a} \), \( \vec{b} \) and \( \vec{c} \) are unit vectors, then prove that \( |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 \leq 9 \).

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2.
Sketch the graph defined by \( \left\{ (x, y) : \frac{x^2{25} + \frac{y^2}{25} = 1 \right\} \). Find the area of the region of minor segment cut off by the line \( x = \frac{5}{2} \), using integration.}

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3.
Find the value of \( p \) if the shortest distance between the lines \( \vec{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} - \hat{j} + \hat{k}) \) and \( \vec{r} = (p\hat{i} - \hat{j} - \hat{k}) + \mu(2\hat{i} + \hat{j} + 2\hat{k}) \) is \( \frac{3}{\sqrt{2}} \) units.

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4.
Evaluate : \( \int_0^2 \frac{1}{\sqrt{x^2 + 2x + 3}} \, dx \).

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5.
Three students A, B and C go to a book-store to buy art books, story books and puzzle solving books. A buys one of each type of book for a total of RS 21. B buys 4 art books, 3 story books and 2 puzzle solving books for RS 60. C buys 6 art books, 2 story books and 3 puzzle solving books and pays RS 10 more than B. Use matrix method to find the cost of each type of book.

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6.
A box contains 6 cards numbered 1 to 6. A student is asked to pick up two cards, one by one after replacement and note down the numbers on the cards. Let A be the event of getting sum of the numbers on two cards as 10, and B, the event of a number other than 4 on the first card selected. Find \( P(A \text{ and } B) \) and find whether the events A and B are independent events or not.

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NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.1 Solutions

CBSE CLASS XII Related Questions

1.
If \( \vec{a} \), \( \vec{b} \) and \( \vec{c} \) are unit vectors, then prove that \( |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 \leq 9 \).

2.
Sketch the graph defined by \( \left\{ (x, y) : \frac{x^2{25} + \frac{y^2}{25} = 1 \right\} \). Find the area of the region of minor segment cut off by the line \( x = \frac{5}{2} \), using integration.}

3.
Find the value of \( p \) if the shortest distance between the lines \( \vec{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} - \hat{j} + \hat{k}) \) and \( \vec{r} = (p\hat{i} - \hat{j} - \hat{k}) + \mu(2\hat{i} + \hat{j} + 2\hat{k}) \) is \( \frac{3}{\sqrt{2}} \) units.

4.
Evaluate : \( \int_0^2 \frac{1}{\sqrt{x^2 + 2x + 3}} \, dx \).

Similar Mathematics Concepts

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NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.1 Solutions

CBSE CLASS XII Related Questions

1.If \( \vec{a} \), \( \vec{b} \) and \( \vec{c} \) are unit vectors, then prove that \( |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 \leq 9 \).

2.Sketch the graph defined by \( \left\{ (x, y) : \frac{x^2{25} + \frac{y^2}{25} = 1 \right\} \). Find the area of the region of minor segment cut off by the line \( x = \frac{5}{2} \), using integration.}

3.Find the value of \( p \) if the shortest distance between the lines \( \vec{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} - \hat{j} + \hat{k}) \) and \( \vec{r} = (p\hat{i} - \hat{j} - \hat{k}) + \mu(2\hat{i} + \hat{j} + 2\hat{k}) \) is \( \frac{3}{\sqrt{2}} \) units.

4.Evaluate : \( \int_0^2 \frac{1}{\sqrt{x^2 + 2x + 3}} \, dx \).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
If \( \vec{a} \), \( \vec{b} \) and \( \vec{c} \) are unit vectors, then prove that \( |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 \leq 9 \).

2.
Sketch the graph defined by \( \left\{ (x, y) : \frac{x^2{25} + \frac{y^2}{25} = 1 \right\} \). Find the area of the region of minor segment cut off by the line \( x = \frac{5}{2} \), using integration.}

3.
Find the value of \( p \) if the shortest distance between the lines \( \vec{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} - \hat{j} + \hat{k}) \) and \( \vec{r} = (p\hat{i} - \hat{j} - \hat{k}) + \mu(2\hat{i} + \hat{j} + 2\hat{k}) \) is \( \frac{3}{\sqrt{2}} \) units.

4.
Evaluate : \( \int_0^2 \frac{1}{\sqrt{x^2 + 2x + 3}} \, dx \).