NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1

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Class 11 Maths NCERT Solutions Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.1 is based on the following concepts:

Coordinate Axes and Coordinate Planes in Three Dimensional Space
Coordinates of a Point in Space

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Chapter Related Topics
Angle Between Two Plane	Angle between two lines	Angle between line and plane

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CBSE CLASS XII Related Questions

1.
Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is:
- $x^3 + 3x^2 + \frac{2}{x^2} + 5x + 11$
- $x^3 + 3x^2 + \frac{2}{x^2} + 5x - 11$
- $x^3 + 3x^2 - \frac{2}{x^2} + 5x - 11$
- $x^3 - 3x^2 - \frac{2}{x^2} + 5x - 11$
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2.
The diagonals of a parallelogram are given by $ \mathbf{a} = 2 \hat{i} - \hat{j} + \hat{k} $ and $ \mathbf{b} = \hat{i} + 3 \hat{j} - \hat{k}$ . Find the area of the parallelogram.
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3.
The integrating factor of the differential equation $ \frac{dy}{dx} + y = \frac{1 + y}{x} $ is:
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4.
Let $f(x) = |x|$, $x \in \mathbb{R}$. Then, which of the following statements is incorrect?
- $f$ has a minimum value at $x = 0$
- $f$ has no maximum value in $\mathbb{R}$
- $f$ is continuous at $x = 0$
- $f$ is differentiable at $x = 0$
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5.
The probability that a student buys a colouring book is 0.7, and a box of colours is 0.2. The probability that she buys a colouring book, given that she buys a box of colours, is 0.3. Find:
(i) The probability that she buys both the colouring book and the box of colours.
(ii) The probability that she buys a box of colours given she buys the colouring book.
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6.
A furniture workshop produces three types of furniture: chairs, tables, and beds each day. On a particular day, the total number of furniture pieces produced is 45. It was also found that the production of beds exceeds that of chairs by 8, while the total production of beds and chairs together is twice the production of tables. Determine the units produced of each type of furniture, using the matrix method.
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