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A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated $(P)$ by the metal. The sensor has a scale that displays $\log _{2}\left(P / P_{0}\right)$, where $P_{0}$ is a constant. When the metal surface is at a temperature of $487^{\circ} \mathrm{C}$, the sensor shows a val... | Okay, so I have this problem where a metal is heated in a furnace, and there's a sensor above it that measures the power radiated by the metal. The sensor displays the value of log base 2 of (P/P₀), where P is the power radiated and P₀ is a constant. When the metal is at 487°C, the sensor shows 1. Now, I need to find t... | 9 | 14 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Llama-8B |
The isotope ${ }_{5}^{12} \mathrm{~B}$ having a mass 12.014 u undergoes $\beta$-decay to ${ }_{6}^{12} \mathrm{C}$. ${ }_{6}^{12} \mathrm{C}$ has an excited state of the nucleus $\left({ }_{6}^{12} \mathrm{C}^{*}\right)$ at $4.041 \mathrm{MeV}$ above its ground state. If ${ }_{5}^{12} \mathrm{~B}$ decays to ${ }_{6}^{1... | Okay, so I have this problem about beta decay, and I need to find the maximum kinetic energy of the beta-particle. Let me try to figure this out step by step.
First, the problem says that the isotope Boron-12, which is written as _{5}^{12}B, has a mass of 12.014 u. It undergoes beta decay to become Carbon-12 in an exc... | 9 | 15 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Llama-8B |
A hydrogen atom in its ground state is irradiated by light of wavelength 970 A. Taking $h c / e=1.237 \times 10^{-6} \mathrm{eV} \mathrm{m}$ and the ground state energy of hydrogen atom as $-13.6 \mathrm{eV}$, what is the number of lines present in the emission spectrum?
Please reason step by step, and put your final ... | Okay, so I have this problem here where a hydrogen atom in its ground state is irradiated by light with a wavelength of 970 Å, and I need to find the number of lines present in its emission spectrum. The given constants are \( h c / e = 1.237 \times 10^{-6} \) eV·m and the ground state energy of the hydrogen atom is -1... | 6 | 16 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Llama-8B |
Consider two solid spheres $\mathrm{P}$ and $\mathrm{Q}$ each of density $8 \mathrm{gm} \mathrm{cm}^{-3}$ and diameters $1 \mathrm{~cm}$ and $0.5 \mathrm{~cm}$, respectively. Sphere $P$ is dropped into a liquid of density $0.8 \mathrm{gm} \mathrm{cm}^{-3}$ and viscosity $\eta=3$ poiseulles. Sphere $Q$ is dropped into a... | Okay, so I have this physics problem here about two solid spheres, P and Q, being dropped into different liquids, and I need to find the ratio of their terminal velocities. Hmm, terminal velocity is the maximum velocity a falling object reaches when the forces balance out, right? So, I remember that terminal velocity d... | 3 | 17 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Llama-8B |
Two inductors $L_{1}$ (inductance $1 \mathrm{mH}$, internal resistance $3 \Omega$ ) and $L_{2}$ (inductance $2 \mathrm{mH}$, internal resistance $4 \Omega$ ), and a resistor $R$ (resistance $12 \Omega$ ) are all connected in parallel across a $5 \mathrm{~V}$ battery. The circuit is switched on at time $t=0$. What is th... | Okay, so I have this problem where two inductors, L₁ and L₂, with inductances 1 mH and 2 mH respectively, and internal resistances 3 Ω and 4 Ω, are connected in parallel with a resistor R of 12 Ω, all across a 5 V battery. The circuit is switched on at time t=0, and I need to find the ratio of the maximum to the minimu... | 8 | 18 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Llama-8B |
The mole fraction of a solute in a solution is 0.1 . At $298 \mathrm{~K}$, molarity of this solution is the same as its molality. Density of this solution at $298 \mathrm{~K}$ is $2.0 \mathrm{~g} \mathrm{~cm}^{-3}$. What is the ratio of the molecular weights of the solute and solvent, $\left(\frac{M W_{\text {solute }}... | Okay, so I have this problem here where I need to find the ratio of the molecular weights of the solute and solvent. Let me try to figure this out step by step.
First, the problem says that the mole fraction of the solute is 0.1 at 298 K. Molarity and molality are given to be the same for this solution at that tempera... | 9 | 32 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Llama-8B |
The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases $x$ times. What is the value of $x$?
Please reason step by st... | Okay, so I have this problem about the diffusion coefficient of an ideal gas. Hmm, I remember that the diffusion coefficient depends on a few factors, but I need to recall exactly which ones. The problem says it's proportional to the mean free path and the mean speed. Let me jot that down.
So, if I denote the diffusio... | 4 | 33 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Llama-8B |
"In neutral or faintly alkaline solution, 8 moles of permanganate anion quantitatively oxidize thios(...TRUNCATED) | "Okay, so I have this chemistry problem here: In a neutral or faintly alkaline solution, 8 moles of (...TRUNCATED) | 6 | 34 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Llama-8B |
"What is the total number of distinct $x \\in \\mathbb{R}$ for which $\\left|\\begin{array}{ccc}x & (...TRUNCATED) | "Alright, so I have this determinant problem to solve. It says:\n\nFind the total number of distinct(...TRUNCATED) | 2 | 50 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Llama-8B |
"Let $m$ be the smallest positive integer such that the coefficient of $x^{2}$ in the expansion of $(...TRUNCATED) | "Okay, so I have this problem here where I need to find the smallest positive integer \\( m \\) such(...TRUNCATED) | 5 | 51 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Llama-8B |
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