question string | answer_content string | reference_answer string | id string | metadata dict | model_name string | verifier_score int64 |
|---|---|---|---|---|---|---|
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 need to solve this problem about the sensor reading the power radiated by a metal when its temperature changes. Let me start by understanding the problem again.
The problem says that there's a metal heated in a furnace, and a sensor above the metal's surface measures the power radiated, P. The sensor displ... | 9 | 14 | {
"question_source": "daman1209arora/jeebench"
} | LGAI-EXAONE/EXAONE-Deep-32B | 1 |
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 need to find the maximum kinetic energy of the beta particle when Boron-12 decays into an excited state of Carbon-12. Hmm, let me start by recalling what beta decay involves. Beta decay is when a neutron in the nucleus converts into a proton, emitting an electron (the beta particle) and an antineutrino. The ... | 9 | 15 | {
"question_source": "daman1209arora/jeebench"
} | LGAI-EXAONE/EXAONE-Deep-32B | 1 |
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 need to figure out how many emission lines there will be when a hydrogen atom in its ground state is irradiated by light with a wavelength of 970 angstroms. Hmm, let me start by recalling some basic concepts here.
First, the hydrogen atom's ground state energy is given as -13.6 eV. When it's irradiated by ... | 6 | 16 | {
"question_source": "daman1209arora/jeebench"
} | LGAI-EXAONE/EXAONE-Deep-32B | 1 |
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 need to find the ratio of the terminal velocities of spheres P and Q. Both spheres have the same density, 8 gm/cm3, but different diameters: P is 1 cm and Q is 0.5 cm. They're each dropped into different liquids with different densities and viscosities. Hmm, terminal velocity depends on several factors, righ... | 3 | 17 | {
"question_source": "daman1209arora/jeebench"
} | LGAI-EXAONE/EXAONE-Deep-32B | 1 |
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 need to find the ratio of the maximum to the minimum current drawn from the battery when this parallel circuit is switched on at t=0. The components are two inductors with their own internal resistances and a resistor all in parallel across a 5V battery. Hmm, inductors in parallel with resistors... Since the... | 8 | 18 | {
"question_source": "daman1209arora/jeebench"
} | LGAI-EXAONE/EXAONE-Deep-32B | 1 |
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 need to find the ratio of the molecular weights of the solute and solvent given that the mole fraction of the solute is 0.1, the molarity is equal to the molality at 298 K, and the density of the solution is 2.0 g/cm3. Hmm, let me start by recalling the definitions of mole fraction, molarity, and molality.
... | 9 | 32 | {
"question_source": "daman1209arora/jeebench"
} | LGAI-EXAONE/EXAONE-Deep-32B | 1 |
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 need to figure out how the diffusion coefficient of an ideal gas changes when the temperature and pressure are adjusted. Let me start by recalling what the diffusion coefficient depends on. The problem says it's proportional to the mean free path and the mean speed. Hmm, right, the diffusion coefficient D is... | 4 | 33 | {
"question_source": "daman1209arora/jeebench"
} | LGAI-EXAONE/EXAONE-Deep-32B | 1 |
In neutral or faintly alkaline solution, 8 moles of permanganate anion quantitatively oxidize thiosulphate anions to produce $\mathbf{X}$ moles of a sulphur containing product. What is the magnitude of $\mathbf{X}$?
Please reason step by step, and put your final answer within \boxed{}. | Okay, so I need to figure out how many moles of a sulfur-containing product are formed when 8 moles of permanganate anion oxidize thiosulfate anions in a neutral or faintly alkaline solution. Hmm, redox reactions can be a bit tricky, but let me start by recalling the basics.
First, I remember that permanganate (MnO4^-... | 6 | 34 | {
"question_source": "daman1209arora/jeebench"
} | LGAI-EXAONE/EXAONE-Deep-32B | 1 |
"What is the total number of distinct $x \\in \\mathbb{R}$ for which $\\left|\\begin{array}{ccc}x & (...TRUNCATED) | "Okay, so I need to find the number of distinct real numbers x such that the determinant of this 3x3(...TRUNCATED) | 2 | 50 | {
"question_source": "daman1209arora/jeebench"
} | LGAI-EXAONE/EXAONE-Deep-32B | 1 |
"Let $m$ be the smallest positive integer such that the coefficient of $x^{2}$ in the expansion of $(...TRUNCATED) | "Okay, so I need to find the smallest positive integer m such that the coefficient of x2 in the expa(...TRUNCATED) | 5 | 51 | {
"question_source": "daman1209arora/jeebench"
} | LGAI-EXAONE/EXAONE-Deep-32B | 1 |
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