Import Question JSON

Current Question (ID: 15971)

Question:

$\text{A person standing between two parallel hills fires a gun and hears the first echo after } t_1 \text{ sec and the second echo after } t_2 \text{ sec. The distance between the two hills is: [Given: Speed of sound } = v]$

Options:

1. $\frac{v(t_1 - t_2)}{2}$
2. $\frac{v(t_1 t_2)}{2(t_1 + t_2)}$
3. $v(t_1 + t_2)$
4. $\frac{v(t_1 + t_2)}{2}$

Solution:

$\text{Hint: Use distance = speed } \times \text{ time}$ $\text{Step 1: Find the distance from the first hill.}$ $\text{For the first echo, } t_1 = \frac{2d_1}{v} \Rightarrow d_1 = \frac{vt_1}{2}$ $\text{Step 2: Find the distance from the second hill.}$ $\text{For the second echo, } t_2 = \frac{2d_2}{v} \Rightarrow d_2 = \frac{vt_2}{2}$ $\text{Step 3: Find the distance between the hills.}$ $\text{The distance between hills is given by; } d = d_1 + d_2 = \frac{vt_1 + vt_2}{2} = \frac{v(t_1 + t_2)}{2}.$ $\text{Hence, option (4) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}