Import Question JSON

Current Question (ID: 16791)

Question:

$\text{A particle having a mass of } 10^{-2} \text{ kg carries a charge of } 5 \times 10^{-8} \text{ C.}$ $\text{The particle is given an initial horizontal velocity of } 10^5 \text{ ms}^{-1} \text{ in the presence of an}$ $\text{electric field } \vec{E} \text{ and magnetic field } \vec{B}. \text{ How can we keep the particles moving in a horizontal direction?}$

Options:

1. $\vec{B} \text{ should be perpendicular to the direction of velocity and } \vec{E} \text{ should be along the direction of velocity.}$
2. $\text{Both } \vec{B} \text{ and } \vec{E} \text{ should be along the direction of velocity.}$
3. $\text{Both } \vec{B} \text{ and } \vec{E} \text{ are mutually perpendicular and perpendicular to the direction of velocity.}$
4. $\vec{B} \text{ should be along the direction of velocity and } \vec{E} \text{ should be perpendicular to the direction of velocity.}$

Solution:

$\text{Both } \vec{B} \text{ and } \vec{E} \text{ should be along the direction of velocity and both } \vec{B} \text{ and } \vec{E}$ $\text{are mutually perpendicular and perpendicular to the direction of velocity.}$

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
}