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29 changes: 29 additions & 0 deletions 5_sep_maths_hw.md
Original file line number Diff line number Diff line change
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1. If the tangent at the point $(x_1, y_1)$ on the curve $y = x^3 + 3x^2 + 5$ passes through the origin, then $(x_1, y_1)$ does NOT lie on the curve :
* A. $x^2 + \frac{y^2}{81} = 2$
* B. $\frac{y^2}{9} - x^2 = 8$
* C. $y = 4x^2 + 5$
* D. $\frac{x}{3} - y^2 = 2$

2. For the function $f(x) = 4\log_e(x - 1) - 2x^2 + 4x + 5$, $x > 1$, which one of the following is NOT correct?
* A. f is increasing in $(1, 2)$ and decreasing in $(2, \infty)$
* B. $f(x) = -1$ has exactly two solutions
* C. $f'(e) - f''(2) < 0$
* D. $f(x) = 0$ has a root in the interval $(e, e + 1)$

3. If the angle made by the tangent at the point $(x_0, y_0)$ on the curve $x = 12(t + \sin t \cos t)$, $y = 12(1 + \sin t)^2$, $0 < t < \frac{\pi}{2}$, with the positive x-axis is $\frac{\pi}{3}$, then $y_0$ is equal to:
* A. $6(3 + 2\sqrt{2})$
* B. $3(7 + 4\sqrt{3})$
* C. 27
* D. 48

4. Let $f(x) = 2\cos^{-1}x + 4\cot^{-1}x - 3x^2 - 2x + 10, x \in [-1, 1]$. If $[a, b]$ is the range of the function f, then $4a - b$ is equal to :
* A. 11
* B. $11 - \pi$
* C. $11 + \pi$
* D. $15 - \pi$

5. If the maximum value of $a$, for which the function $f_a(x) = \tan^{-1}2x - 3ax + 7$ is non-decreasing in $(-\frac{\pi}{6}, \frac{\pi}{6})$, is $\bar{a}$, then $f_{\bar{a}}(\frac{\pi}{8})$ is equal to :
* A. $8 - \frac{9\pi}{4(9+\pi^2)}$
* B. $8 - \frac{4\pi}{9(4+\pi^2)}$
* C. $8\left(\frac{1+\pi^2}{9+\pi^2}\right)$
* D. $8 - \frac{\pi}{4}$
13 changes: 3 additions & 10 deletions js/client-modules/list-item-controller.js
Original file line number Diff line number Diff line change
Expand Up @@ -175,16 +175,9 @@ class ListItemController {

async copyListContent(element) {
try {
const listIndex = parseInt(element.dataset.listIndex, 10);
const listData = window.__APP_DATA__.listItems;
const isValidIndex = !isNaN(listIndex) && listData && listIndex < listData.length && listData[listIndex];

if (!isValidIndex) {
await this.copyElementText(element);
return;
}

const textToCopy = listData[listIndex].content;
// Copy the full visible text of the list item, including any nested options/sub-lists
const textToCopy = (element.innerText || element.textContent || '').trim();
if (!textToCopy) throw new Error('List item content is empty.');
await this._copyToClipboard(textToCopy);
this.showNotification('List content copied!');
} catch (err) {
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13 changes: 3 additions & 10 deletions js/rendered-page-builder.js
Original file line number Diff line number Diff line change
Expand Up @@ -1147,16 +1147,9 @@ class ListItemController {

async copyListContent(element) {
try {
const listIndex = parseInt(element.dataset.listIndex, 10);
const listData = window.__APP_DATA__.listItems;
const isValidIndex = !isNaN(listIndex) && listData && listIndex < listData.length && listData[listIndex];

if (!isValidIndex) {
await this.copyElementText(element);
return;
}

const textToCopy = listData[listIndex].content;
// Copy the full visible text of the list item, including any nested options/sub-lists
const textToCopy = (element.innerText || element.textContent || '').trim();
if (!textToCopy) throw new Error('List item content is empty.');
await this._copyToClipboard(textToCopy);
this.showNotification('List content copied!');
} catch (err) {
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