more acticity questions for week 3 mathematics

Author: aryan

content/notes/iit-madras/data-science-and-application/foundational-level/mathematics/week 2/aq2.1.md

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+**Question 1 (Multiple Choice)**
 
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+**1**. Choose the correct option with respect to the points P(5, -3), Q(-3, 3), R(0, -100), and S(-2.5, 0) on the rectangular coordinate system.
 
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+Options:
 
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+Point R does not lie in any quadrant
 
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+Points P and R lie in Quadrant III
 
+Points S and Q lie in Quadrant II
 
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- 
+Points R and S cannot be represented on the rectangular coordinate system
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+**Question 2 (Multiple Select Questions - MSQ)**
 
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+2) Which of the following is/are correct with respect to the rectangular coordinate system?
+
+Options:
+
+The horizontal line is called Y-axis
+
+The point of intersection of the X and Y axes is called the origin
+
+The vertical line is called X-axis
 
+Any point on the coordinate plane can be represented as an ordered pair (x, y)
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+**Question 3 (Multiple Select)**
 
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+3) Identify the incorrect options for the representation of a point on the coordinate plane.
 
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+Options:
 
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+Quadrant I: (+, +)
 
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+Quadrant IV: (-, +)
 
+Quadrant II: (-, -)
 
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+Quadrant III: (-, +)
 
+On X-axis: (0, ±)
+
+On Y-axis: (±, 0)
+
+Origin (0,0)
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-
+These three questions cover topics related to the rectangular coordinate system, including point locations in quadrants, coordinate system terminology, and proper representation of points in different quadrants and on axes.

content/notes/iit-madras/data-science-and-application/foundational-level/mathematics/week 2/aq2.10.md

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+---
+title: Activity Questions 2.10
+date: 2025-05-08
+tags:
+  - Notes 
+  - IIT Madras
+excludeSearch: false
+weight: 30.1
+---
+
+**Multiple Select Question**
+
+{{< border >}}
+
+**Question 1**: Which of the following statements are true?
+
+Options:
+
+Lines 2x + 3y - 8 = 0 and 3x - y - 2 = 0 are parallel lines
+
+Lines 3x + 5y - 10 = 0 and 6x + 10y - 26 = 0 are parallel lines
+
+Lines 6x + 8y - 20 = 0 and 4x - 3y = 0 are perpendicular to each other
+
+Lines 2x - 3y + 8 = 0 and 3x + 2y - 18 = 0 are not perpendicular to each other
+
+Lines 4x + 5y + 10 = 0 and 10x - 8y - 16 = 0 are perpendicular to each other
+{{< /border >}}
+
+{{< border type="tip" title="Solution" >}}
+
+{{< /border >}}
+
+**Numerical Answer Type**
+
+{{< border >}}
+**Question 2**: Given lines 4x + 2ky + 5 = 0 and 12x + 6y + 15 = 0 are parallel, find the value of k.
+{{< /border >}}
+
+{{< border type="tip" title="Solution" >}}
+
+{{< /border >}}

content/notes/iit-madras/data-science-and-application/foundational-level/mathematics/week 2/aq2.11.md

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+---
+title: Activity Questions 2.11
+date: 2025-05-08
+tags:
+  - Notes 
+  - IIT Madras
+excludeSearch: false
+weight: 30.2
+---
+
+**Multiple Choice Question**
+
+{{< border >}}
+Question 1: The equation of a line passing through the point (3, 4) and perpendicular to the line 3x + 4y - 8 = 0 is
+
+Options:
+
+8x - 6y = 0
+
+2x + 8y = 38
+
+8x + 4y = 5
+
+x + y = 1
+{{< /border >}}
+
+{{< border type="tip" title="Solution" >}}
+
+{{< /border >}}
+
+**Numerical Answer Type**
+
+{{< border >}}
+Question 2: Given lines 18x - 8y + 30 = 0 and 4x + ky + 5 = 0 are perpendicular to each other, find the value of k.
+{{< /border >}}
+
+{{< border type="tip" title="Solution" >}}
+
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+{{< border type="tip" title="Solution" >}}
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+{{< border type="tip" title="Solution" >}}
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+{{< border type="tip" title="Solution" >}}
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content/notes/iit-madras/data-science-and-application/foundational-level/mathematics/week 2/aq2.12.md

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+---
+title: Activity Questions 2.12
+date: 2025-05-08
+tags:
+  - Notes 
+  - IIT Madras
+excludeSearch: false
+weight: 30.3
+---
+
+Multiple Select Questions
+
+{{< border >}}
+Question 1: If the general form of a line is 3x + 2y - 5 = 0, then choose the correct set of options.
+
+Options:
+
+The slope of the given line is -3/2
+
+The x-intercept is 3
+
+The point where the given line cuts the X-axis is (5/3, 0)
+
+The y-intercept is 2
+
+The point where the given line cuts the Y-axis is (0, 5/2)
+{{< /border >}}
+
+{{< border type="tip" title="Solution" >}}
+
+{{< /border >}}
+
+
+{{< border >}}
+Question 2: Given the point (-2, 1) and the line -3x + 4y - 7 = 0, choose the correct set of options.
+
+Options:
+
+The distance between (-2, 1) and the line -3x + 4y - 7 = 0 is 2
+
+The slope of the given line is 5
+
+The distance between (-2, 1) and the line -3x + 4y - 7 = 0 is 3/5
+
+The y-intercept of the given line is 7/4
+{{< /border >}}
+
+{{< border type="tip" title="Solution" >}}
+
+{{< /border >}}
+
+Numerical Answer Type
+
+{{< border >}}
+Question 3: Find the distance between the two parallel lines 4x + 3y + 5 = 0 and 8x + 6y - 30 = 0
+{{< /border >}}
+
+{{< border type="tip" title="Solution" >}}
+
+{{< /border >}}
+
+
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+Question 4: If the distance between the point (-1, 3) and the line 4x + c = 0 is 3/2, then find the value of c where c is a positive number.
+{{< /border >}}
+
+{{< border type="tip" title="Solution" >}}
+
+{{< /border >}}
+
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+Question 5: The coordinates of the vertices of a triangle are (0, 3), (0, 0), (2, 0). Find the area of the triangle.
+{{< /border >}}
+
+{{< border type="tip" title="Solution" >}}
+
+{{< /border >}}
+

content/notes/iit-madras/data-science-and-application/foundational-level/mathematics/week 2/aq2.13.md

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+---
+title: Activity Questions 2.13
+date: 2025-05-08
+tags:
+  - Notes 
+  - IIT Madras
+excludeSearch: false
+weight: 30.5
+---
+
+### Numerical Answer Type
+
+{{< border >}}
+
+**Question 1:** If a line fit y = x + 1 is given for the data as shown in Table AQ-3.1, then compute the Sum Squares Error (SSE).
+
+**Table AQ-3.1:**
+
+
+| x | 1 | 2 | 3 | 4 | 6 |
+| :-- | :-- | :-- | :-- | :-- | :-- |
+| y | 1 | 1 | 2 | 5 | 7 |
+{{< /border >}}
+
+{{< border type="tip" title="Solution" >}}
+
+{{< /border >}}
+
+### Multiple Choice Question
+
+{{< border >}}
+
+**Question 2:** If the relation between x and y is as shown in Table AQ-3.2, then which among the following lines is the best fit?
+
+**Table AQ-3.2:**
+
+
+| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
+| :-- | :-- | :-- | :-- | :-- | :-- | :-- | :-- |
+| y | 1 | 3 | 4 | 2 | 5 | 0 | 8 |
+
+Options:
+
+- y = 2x with SSE=143
+- y = x with SSE=40
+- y = 3x with SSE=428
+- y = 4x with SSE=895
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+
+{{< border type="tip" title="Solution" >}}
+
+{{< /border >}}