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made changes in modular calculator - Show result on window load & input variable change, Other changes
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‎content/exercises/graded-assignments/mathematics-1/W1GA1.md‎

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title: Mathematics for Data Science 1
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description: Q1. Which of the following are irrational numbers❓ (a) $3^{1/3}$ (b) $(\sqrt{8}+\sqrt{2})(\sqrt{12}-\sqrt{3})$ (c) $\frac{\sqrt{18}-3}{\sqrt{2}-1}$ (d) $\frac{\sqrt{8}+\sqrt{2}}{\sqrt{8}-\sqrt{2}}$
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weight: 1
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subject: programming
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subtitle: Graded Assignment
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label: Week 1
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categories:
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- Mathematics Graded Assignment

‎content/exercises/graded-assignments/mathematics-1/_index.md‎

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cascade:
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title: Mathematics I
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subtitle: Graded Assignment
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label: Week 1
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label: Assignments
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subject: math
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avatar: "https://upload.wikimedia.org/wikipedia/en/6/69/IIT_Madras_Logo.svg"
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keywords: ["Mathematics for Data Science 1","Graded Assignment","IIT Madras"]

‎content/exercises/graded-assignments/mathematics-1/mathematic-questions.md‎

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---
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title: Mathematics for Data Science 1
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weight: 1
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subtitle: All Questions
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label: Questions
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categories:
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- Mathematics Graded Assignment
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---
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{{< qna/question >}}
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**Q:** If the slope of parabola y = ax² + bx + c, where a, b, c ∈ ℝ\{0} at points (3, 2) and (2, 3) are 31 and 14 respectively, then find the value of a.
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---
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### Solution Step by Step 📝
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**Step 1: Find the derivative** 🔍
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For parabola y = ax² + bx + c, the slope at any point is:
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\$ \frac{dy}{dx} = 2ax + b \$
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**Step 2: Set up equations using given conditions** 📐
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At point (3, 2), slope = 31:
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\$ 2a(3) + b = 31 \$
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\$ 6a + b = 31 \quad ...(equation 1) \$
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At point (2, 3), slope = 14:
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\$ 2a(2) + b = 14 \$
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\$ 4a + b = 14 \quad ...(equation 2) \$
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**Step 3: Solve the system** ⚡
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From equation 1: \$ b = 31 - 6a \$
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Substitute into equation 2:
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\$ 4a + (31 - 6a) = 14 \$
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\$ 4a + 31 - 6a = 14 \$
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\$ -2a = 14 - 31 \$
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\$ -2a = -17 \$
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\$ a = \frac{17}{2} = 8.5 \$
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**Step 4: Verify** ✅
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If a = 8.5, then b = 31 - 6(8.5) = -20
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Check equation 2: 4(8.5) + (-20) = 34 - 20 = 14 ✓
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**Answer:** \$ a = \frac{17}{2} or 8.5 \$ 🎯
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{{</ qna/question >}}
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{{< qna/question >}}
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**Q:** If the slope of parabola y = ax² + bx + c, where a, b, c ∈ ℝ\{0} at points ({{< qna/variable name="a" value="3" >}}, {{< qna/variable name="b" value="2" >}}) and ({{< qna/variable name="c" value="2" >}}, {{< qna/variable name="d" value="3" >}}) are {{< qna/variable name="x" value="31" >}} and {{< qna/variable name="y" value="14" >}} respectively, then find the value of a.
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---
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**Solution Step by Step** 📝
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**Step 1: Find the derivative** 🔍
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For parabola y = ax² + bx + c, the slope at any point is:
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\$ \frac{dy}{dx} = 2ax + b \$
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**Step 2: Set up equations using given conditions** 📐
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At point (3, 2), slope = 31:
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\$ 2a(3) + b = 31 \$
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\$ 6a + b = 31 \quad ...(equation 1) \$
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At point (2, 3), slope = 14:
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\$ 2a(2) + b = 14 \$
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\$ 4a + b = 14 \quad ...(equation 2) \$
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**Step 3: Solve the system** ⚡
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From equation 1: \$ b = 31 - 6a \$
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Substitute into equation 2:
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\$ 4a + (31 - 6a) = 14 \$
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\$ 4a + 31 - 6a = 14 \$
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\$ -2a = 14 - 31 \$
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\$ -2a = -17 \$
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\$ a = \frac{17}{2} = 8.5 \$
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**Step 4: Verify** ✅
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If a = 8.5, then b = 31 - 6(8.5) = -20
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Check equation 2: 4(8.5) + (-20) = 34 - 20 = 14 ✓
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**Answer:** \$ a = \frac{17}{2} or 8.5 \$ 🎯
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{{</ qna/question >}}

‎content/exercises/graded-assignments/statistics-1/week-4-questions.md‎

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| Dealer's Location | OnePlus | BBK Electronics |
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| :-- | :-- | :-- |
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| Chennai | {{< qna/input name="a" value="2" >}} | {{< qna/input name="b" value="2" >}} |
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| Punjab | {{< qna/input name="c" value="2" >}} | {{< qna/input name="d" value="2" >}} |
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| Chennai | {{< qna/input name="e" value="2" >}} | {{< qna/input name="f" value="2" >}} |
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| Punjab | {{< qna/input name="g" value="2" >}} | {{< qna/input name="h" value="2" >}} |
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| Chennai | {{< qna/input name="i" value="2" >}} | {{< qna/input name="j" value="2" >}} |
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| Punjab | {{< qna/input name="k" value="2" >}} | {{< qna/input name="l" value="2" >}} |
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| Chennai | {{< qna/input name="m" value="2" >}} | {{< qna/input name="n" value="2" >}} |
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| Chennai | {{< qna/variable name="a" value="2" >}} | {{< qna/variable name="b" value="2" >}} |
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| Punjab | {{< qna/variable name="c" value="2" >}} | {{< qna/variable name="d" value="2" >}} |
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| Chennai | {{< qna/variable name="e" value="2" >}} | {{< qna/variable name="f" value="2" >}} |
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| Punjab | {{< qna/variable name="g" value="2" >}} | {{< qna/variable name="h" value="2" >}} |
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| Chennai | {{< qna/variable name="i" value="2" >}} | {{< qna/variable name="j" value="2" >}} |
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| Punjab | {{< qna/variable name="k" value="2" >}} | {{< qna/variable name="l" value="2" >}} |
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| Chennai | {{< qna/variable name="m" value="2" >}} | {{< qna/variable name="n" value="2" >}} |
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#### 1. What is the population standard deviation of sales of OnePlus? (Enter the answer correct to 2 decimal accuracy)
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m_x = \frac{a+c+e+g+i+k+m}{7}
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$$
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{{< qna/formula label="mean" value="((a+b+c+d+e+f+g+h+i+j+k+l+m+n))/7" >}}
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{{< qna/formula label="mean" title="Mean = " value="((a+b+c+d+e+f+g+h+i+j+k+l+m+n))/7" >}}
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$$
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\sigma_x^2 = \frac{(a - m_x)^2 + (c - m_x)^2 + (e - m_x)^2 + (g - m_x)^2 + (i - m_x)^2 + (k - m_x)^2 + (m - m_x)^2}{7}
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{{< qna/question >}}
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{{< qna/input name="a" value="2" >}}
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{{< qna/input name="b" value="3" >}}
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{{< qna/formula label="sum" value="a + b" >}}
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The value of a: {{% qna/variable name="a" value="2" %}} meters.
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b = {{< qna/variable name="b" value="3" >}} meters.
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{{< qna/formula label="sum" title="Sum of " value="a + b" >}}
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The sum is: {{< qna/formula-value label="sum" >}}
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{{< qna/formula label="average" value="sum / 2" >}}
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{{< qna/formula label="average" title="Average of a and b is " value="sum / 2" >}}
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The average is: {{< qna/formula-value label="average" >}}
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{{< qna/result >}}
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{{< /qna/question >}}

‎layouts/shortcodes/qna/formula.html‎

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</div> */}}
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{{ $label := .Get "label" | default (printf "formula_%s" $wrapper) }}
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{{ $title := .Get "title" | default $label }}
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<div>
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<label class="calc-label" for="formula-{{ $wrapper }}">
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{{ $label }}
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{{ $title }}
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</label>
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<span class="calc-formula" id="formula-{{ $wrapper }}" data-calc-formula="{{ .Get "value" | default "a + b" }}" data-calc-label="{{ $label }}">
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{{ .Get "value" | default "a + b" }}<span class="calc-formula-result"></span>

‎layouts/shortcodes/qna/input.html‎

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