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've got this problem here about a metal being heated in a furnace, and there's a sensor above it measuring the power radiated, P. The sensor displays the logarithm base 2 of P over P0, where P0 is a constant. When the metal is at 487°C, the sensor shows a value of 1. Now, they want to know what the sensor dis... | 9 | 14 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-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 undergoes beta decay to an excited state of Carbon-12. Hmm, let me think about this step by step.
First, I remember that in beta decay, a neutron in the nucleus converts into a proton, emitting a beta particle (electron) and an antin... | 9 | 15 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-32B | 0 |
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 are present when a hydrogen atom in its ground state is irradiated by light with a wavelength of 970 Angstroms. Hmm, let's break this down step by step.
First, I remember that when atoms absorb energy, they can get excited to higher energy levels, and when they dr... | 6 | 16 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-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 two spheres, P and Q. Both spheres have the same density, 8 gm/cm³, but different diameters. Sphere P has a diameter of 1 cm, and Sphere Q has a diameter of 0.5 cm. They are dropped into different liquids with different densities and viscosities. Sphere P ... | 3 | 17 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-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've got this problem here with two inductors and a resistor all connected in parallel across a 5V battery. The question is asking for the ratio of the maximum to the minimum current drawn from the battery, which is I_max over I_min. Hmm, alright, let me try to figure this out step by step.
First, I remember ... | 8 | 18 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-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've got this problem here about mole fractions, molarity, molality, and density. Hmm, I need to find the ratio of the molecular weights of the solute and solvent. Let me try to break this down step by step.
First, let me recall what mole fraction is. The mole fraction of a solute is the number of moles of th... | 9 | 32 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-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 both its absolute temperature and pressure are altered. The problem states that the temperature is increased four times and the pressure is doubled. I remember that the diffusion coefficient depends on the mean free path and the me... | 4 | 33 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-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've got this chemistry problem here, and I need to figure out how many moles of a sulfur-containing product are produced when permanganate anions oxidize thiosulfate anions in a neutral or faintly alkaline solution. The problem states that 8 moles of permanganate anion are used, and they quantitatively oxidiz... | 6 | 34 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-32B | 0 |
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 number of distinct real solutions x for which the determinant of this 3x3 matrix is equal to 10. Let me write down the matrix first to get a clear picture.
The matrix is:
| x x² 1 + x³ |
| 2x 4x² 1 + 8x³ |
| 3x 9x² 1 + 27x³ |
So, determinant equals 10. Hmm, determina... | 2 | 50 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-32B | 1 |
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 \( (1+x)^2 + (1+x)^3 + \cdots + (1+x)^{49} + (1+mx)^{50} \) is equal to \( (3n + 1) \binom{51}{3} \) for some positive integer \( n \). Then, I need to determine the value of \( n \).
First, let me ... | 5 | 51 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-32B | 1 |
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 number of distinct solutions \( x \) in the interval \([0,1]\) that satisfy the equation:
\[
\int_{0}^{x} \frac{t^{2}}{1+t^{4}} dt = 2x - 1
\]
Hmm, let's break this down step by step. First, I know that the integral on the left is a function of \( x \), so let me denote that as \( F(x) \).... | 1 | 52 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-32B | 1 |
Let $\alpha, \beta \in \mathbb{R}$ be such that $\lim _{x \rightarrow 0} \frac{x^{2} \sin (\beta x)}{\alpha x-\sin x}=1$.Then what is the value of $6(\alpha+\beta)$?
Please reason step by step, and put your final answer within \boxed{}. | Okay, so I need to find the value of \(6(\alpha + \beta)\) given that the limit as \(x\) approaches 0 of \(\frac{x^{2} \sin (\beta x)}{\alpha x - \sin x}\) is equal to 1. Hmm, let me break this down step by step.
First, I remember that when dealing with limits involving trigonometric functions like sine, it's often us... | 7 | 53 | {
"question_source": "daman1209arora/jeebench"
} | deepseek-ai/DeepSeek-R1-Distill-Qwen-32B | 1 |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 9