question stringlengths 111 1.39k | answer_content stringlengths 2.03k 141k | reference_answer stringlengths 1 17 | id stringlengths 1 29 | metadata dict | model_name stringclasses 1
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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 need to figure out the value displayed by the sensor when the temperature of the metal surface is raised from 487°C to 2767°C. The sensor shows log base 2 of (P/P0), where P0 is a constant. When the temperature is 487°C, the sensor reads 1. I remember that the power radiated by a surface is related to its te... | 9 | 14 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-14B |
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 a beta-particle when the isotope _{5}^{12}B decays into _{6}^{12}C^*, which is an excited state. Hmm, beta decay... Right, in beta decay, a neutron turns into a proton, emitting an electron (beta particle) and an antineutrino. The mass of the parent and daughter nuc... | 9 | 15 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-14B |
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 lines are present in the emission spectrum of a hydrogen atom when it's irradiated by light with a wavelength of 970 A. Hmm, I remember that hydrogen's emission spectrum relates to electron transitions between energy levels. Let me try to recall the steps involved.
First, the ene... | 6 | 16 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-14B |
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 two spheres, P and Q. Both spheres have a density of 8 g/cm³. Sphere P has a diameter of 1 cm, and Sphere Q has a diameter of 0.5 cm. They are dropped into different liquids. Sphere P is in a liquid with density 0.8 g/cm³ and viscosity 3 poiseuilles, while... | 3 | 17 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-14B |
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 with two inductors and a resistor all connected in parallel across a 5V battery. The goal is to find the ratio of the maximum to the minimum current drawn from the battery, which is I_max over I_min. Hmm, let's see.
First, I remember that when inductors are connected in parallel, their cu... | 8 | 18 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-14B |
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. Hmm, let's see. The problem gives me the mole fraction of the solute, which is 0.1. The temperature is 298 K, and it's mentioned that the molarity of the solution is the same as its molality. Also, the density of the solution is 2.0 g... | 9 | 32 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-14B |
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 both the absolute temperature is quadrupled and the pressure is doubled. Hmm, let me recall what I know about diffusion coefficients and the factors that influence them.
First, I remember that the diffusion coefficient, D, for an ... | 4 | 33 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-14B |
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 anions oxidize thiosulphate anions in a neutral or faintly alkaline solution. Hmm, this sounds like a redox reaction problem. I remember that redox reactions involve the transfer of electrons, so I should... | 6 | 34 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-14B |
What is the total number of distinct $x \in \mathbb{R}$ for which $\left|\begin{array}{ccc}x & x^{2} & 1+x^{3} \\ 2 x & 4 x^{2} & 1+8 x^{3} \\ 3 x & 9 x^{2} & 1+27 x^{3}\end{array}\right|=10$?
Please reason step by step, and put your final answer within \boxed{}. | Okay, so I need to find the total number of distinct real numbers \( x \) that satisfy the determinant equation:
\[
\left|\begin{array}{ccc}
x & x^{2} & 1 + x^{3} \\
2x & 4x^{2} & 1 + 8x^{3} \\
3x & 9x^{2} & 1 + 27x^{3}
\end{array}\right| = 10
\]
Hmm, determinants can sometimes be tricky, but let me recall how to com... | 2 | 50 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-14B |
Let $m$ be the smallest positive integer such that the coefficient of $x^{2}$ in the expansion of $(1+x)^{2}+(1+x)^{3}+\cdots+(1+x)^{49}+(1+m x)^{50}$ is $(3 n+1){ }^{51} C_{3}$ for some positive integer $n$. Then what is the value of $n$?
Please reason step by step, and put your final answer within \boxed{}. | Okay, so I need to find the smallest positive integer \( m \) such that the coefficient of \( x^2 \) in the expansion of the given expression is equal to \( (3n + 1) \times \dbinom{51}{3} \) for some positive integer \( n \). Then, I have to find the value of \( n \).
First, let me understand the problem step by step.... | 5 | 51 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-14B |
What is the total number of distinct $x \in[0,1]$ for which $\int_{0}^{x} \frac{t^{2}}{1+t^{4}} d t=2 x-1$?
Please reason step by step, and put your final answer within \boxed{}. | Okay, so I need to find the total number of distinct x in the interval [0,1] that satisfy the equation:
∫₀ˣ (t²)/(1 + t⁴) dt = 2x - 1
Hmm, this looks like an integral equation. I remember that sometimes when an integral equals an expression involving the variable of integration, taking derivatives can be helpful. May... | 1 | 52 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-14B |
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