Import Question JSON

Current Question (ID: 18939)

Question:

$\text{Match the following quantities in List I with their dimensions in List II:}$ $\begin{array}{|c|c|} \hline \text{List I} & \text{List II} \\ \hline \text{(P) Young's modulus} & \text{(A) } [ML^2T^{-1}] \\ \text{(Q) Planck's constant} & \text{(B) } [ML^{-1}T^{-2}] \\ \text{(R) Work function} & \text{(C) } [ML^{-1}T^{-1}] \\ \text{(S) Coefficient of viscosity} & \text{(D) } [ML^2T^{-2}] \\ \hline \end{array}$ $\text{Codes:}$ $\begin{array}{l} 1. \ P \rightarrow A, \ Q \rightarrow B, \ R \rightarrow C, \ S \rightarrow D \\ 2. \ P \rightarrow B, \ Q \rightarrow A, \ R \rightarrow D, \ S \rightarrow C \\ 3. \ P \rightarrow D, \ Q \rightarrow A, \ R \rightarrow C, \ S \rightarrow B \\ 4. \ P \rightarrow D, \ Q \rightarrow A, \ R \rightarrow B, \ S \rightarrow C \end{array}$

Options:

1. $P \rightarrow A, \ Q \rightarrow B, \ R \rightarrow C, \ S \rightarrow D$
2. $P \rightarrow B, \ Q \rightarrow A, \ R \rightarrow D, \ S \rightarrow C$
3. $P \rightarrow D, \ Q \rightarrow A, \ R \rightarrow C, \ S \rightarrow B$
4. $P \rightarrow D, \ Q \rightarrow A, \ R \rightarrow B, \ S \rightarrow C$

Solution:

$\text{Hint: } Y = \frac{FL}{A \Delta L}$ $\text{Step: Identify the correct match.}$ $\text{The dimensions of Young's modulus are given by:}$ $\Rightarrow [Y] = \left[ \frac{F}{A} \right] = [ML^{-1}T^{-2}]$ $\text{The dimensions of the Planck's constant are given by:}$ $\Rightarrow [h] = \left[ \frac{E}{\nu} \right] = [ML^2T^{-1}]$ $\text{The dimensions of the work function are given by:}$ $\Rightarrow [\phi] = [h\nu_0] = [ML^2T^{-2}]$ $\text{The dimensions of the coefficient of the viscosity are given by:}$ $\Rightarrow [\eta] = \left[ \frac{F}{6\pi rv} \right] = \left[ \frac{F}{L[LT^{-1}]} \right] = [ML^{-1}T^{-1}]$ $\text{Therefore, the correct match is } P \rightarrow B; \ Q \rightarrow A; \ R \rightarrow D; \ S \rightarrow C.$ $\text{Hence, option (2) is the correct answer.}$

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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
}