Import Question JSON

Current Question (ID: 8873)

Question:

$\text{If a freely falling body travels in the last second a distance equal to the distance travelled by it in the first three seconds, the time of the travel is:}$

Options:

1. $6 \text{ sec}$
2. $5 \text{ sec}$
3. $4 \text{ sec}$
4. $3 \text{ sec}$

Solution:

$\text{Hint: } S_t = u + \frac{g}{2}(2t - 1)$ $\text{Step: Find the time taken in the travel.}$ $\text{The distance travelled in the last second,}$ $s_{\text{last}} = u + \frac{g}{2}(2t - 1) = \frac{1}{2} \times 9.8(2t - 1) = 4.9(2t - 1)$ $\text{and, the distance travelled in the first three seconds,}$ $s_{\text{three}} = 0 + \frac{1}{2} \times 9.8 \times 9 = 44.1 \text{ m}$ $\text{According to the problem, } s_{\text{last}} = s_{\text{three}}$ $\Rightarrow 4.9(2t - 1) = 44.1 \Rightarrow 2t - 1 = 9 \Rightarrow t = 5 \text{ sec}$ $\text{Hence, option (2) is the correct answer.}$

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
}