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Current Question (ID: 18940)

Question:

$\text{If the dimensional formula of the pressure gradient is } X, \text{ the electric field has } Y, \text{ energy density has } W \text{ and latent heat has } Z. \text{ Then the dimensional formula of } \frac{[X][Y]}{[Z][W]} \text{ is:}$

Options:

1. $[ML^{-2}T^{-1}A]$
2. $[ML^{-2}T^{-1}A^{-1}]$
3. $[M^{-1}L^2T^{-1}A]$
4. $[ML^2T^{-1}A^{-1}]$

Solution:

$\text{Hint: Use dimension analysis.}$ $[X] = \left[ \frac{\Delta P}{\Delta X} \right] = \left[ \frac{MLT^{-2}}{L^3} \right] = [ML^{-2}T^{-2}]$ $[Y] = [E] = [MLT^{-3}A^{-1}]$ $[W] = \left[ \frac{MLT^{-2}}{L^2} \right] = [ML^{-1}T^{-2}]$ $[Z] = \left[ \frac{ML^2T^{-2}}{M} \right] = [L^2T^{-2}]$ $\frac{[X][Y]}{[Z][W]} = \left[ \frac{[ML^{-2}T^{-2}][MLT^{-3}A^{-1}]}{[L^2T^{-2}][ML^{-1}T^{-2}]} \right] = [ML^{-2}T^{-1}A^{-1}]$

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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
}