prompt list | ground_truth string |
|---|---|
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.50c |
[
{
"content": "Given an infinite cardinal \\( \\kappa \\le 2^{\\aleph_0} \\), consider a collection of functions \\( \\{f_i \\mid i < \\kappa\\} \\) where each function \\( f_i: i \\rightarrow \\omega \\) is defined such that the collection is triangle-free. This means there do not exist indices \\( i < j < k < ... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | E = 6.95 N/C downwards |
[
{
"content": "Determine whether the following statement is true or false: If $\\Vert I - rA \\Vert \\ge 1$ for some $r > 2 \\Vert A \\Vert^{-1}$, then $A$ must be singular.",
"role": "user"
}
] | B |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.127 m |
[
{
"content": "Find the edge-connectivity and vertex-connectivity of the Petersen graph.",
"role": "user"
}
] | 3 |
[
{
"content": "In triangle \\(ABC\\), the median \\(BK\\), the angle bisector \\(BE\\), and the altitude \\(AD\\) are given. If the lines \\(BK\\) and \\(BE\\) divide the segment \\(AD\\) into three equal parts, and \\(AB=4\\), find the length of side \\(AC\\).",
"role": "user"
}
] | \sqrt{13} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 22,242 |
[
{
"content": "The base of a right parallelepiped is a rhombus. A plane passing through one of the sides of the lower base and the opposite side of the upper base forms an angle of $45^\\circ$ with the base plane. The resulting cross-section has an area of $Q$. Determine the lateral surface area of the parallele... | 2\sqrt{2}\,Q |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.856e-16 C |
[
{
"content": "Calculate the line integral \\( \\int_C F \\cdot ds \\) for the vector field \\( F(x,y,z) = \\left(4x\\left(1+\\frac{z^2}{8}\\right),\\frac{\\pi}{3}\\cos\\left(\\frac{\\pi}{3}y\\right),\\frac{x^2z}{2}-e^{\\frac{z}{3}}\\right) \\) along the curve \\( C \\) parametrized by \\( \\gamma(t) = (e^{t(t-3... | 12 - 3e^2 |
[
{
"content": "Determine the number of different integer values of $n$ for which it is possible to find $n$ distinct lines in the plane such that each line intersects exactly 2004 other lines. Choose the correct answer from the following options:\n\\[ \\textbf{(A)}\\ 12 \\quad \\textbf{(B)}\\ 11 \\quad \\textbf{... | A |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -4.27% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.81 |
[
{
"content": "Find a polynomial \\( f(x) \\) with integer coefficients such that \\( f(\\sqrt{2} + i) = 0 \\).",
"role": "user"
}
] | x^4 - 2x^2 + 9 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 48000 V/m |
[
{
"content": "Consider the $L^1$ norm defined by \\(\\|f\\|_1=\\int_0^1 |f(y)| dy\\). Let \\(f,g :(0,1)\\to \\mathbb R\\) be functions and \\(\\{h_n :(0,1)\\to \\mathbb R\\}\\) be a sequence of functions. If \\(\\|f-h_n\\|_1\\to 0\\) as \\(n\\to\\infty\\) and \\(\\forall x\\in (0,1) ; \\lim_{n\\to\\infty}h_n(x)... | yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.1% |
[
{
"content": "Let $K$ be a field and $A$ be a division Albert algebra over $K$. Is it true that for all nonzero elements $x, y \\in A$, the equation $(xy) y^{-1} = x$ holds?",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8.76e-2 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 294.3 N |
[
{
"content": "Evaluate the limit \\( \\lim\\limits_{x\\to 0}\\frac{(1+x)^\\frac{1}{x}-e}{\\ln(1+x)} \\).",
"role": "user"
}
] | -\dfrac{e}{2} |
[
{
"content": "Given positive real numbers $P$ and $S$ such that $\\frac{S}{n} \\ge \\sqrt[n]{P}$, determine whether there exists a sequence of positive real numbers $a_1, \\dots, a_n$ such that $S = \\sum_{i=1}^n a_i$ and $P = \\prod_{i=1}^n a_i$. Answer 'yes' or 'no'.",
"role": "user"
}
] | yes |
[
{
"content": "Determine whether the following statement is true or false: If \\( \\lim_{x \\to 0} \\frac{f(x)}{x} = 1 \\), then \\( \\lim_{x \\to 0} \\frac{|f(x)|}{x} = 1 \\).",
"role": "user"
}
] | B |
[
{
"content": "Determine the symmetry group of the following configuration: Consider six points $A_1$, $A_2$, $\\cdots$, $A_6$ on a circle $(O_A)$ and a point $B_1$ on another circle $(O_B)$. Let the circle $(A_iA_{i+1}B_i)$ meet $(O_B)$ again at $B_{i+1}$ for $i=1,\\cdots, 5$. Then the four points $A_6$, $A_1$,... | D_6 |
[
{
"content": "Each face of a cube is assigned a different integer. Then each vertex is assigned the sum of the integer values on the faces that meet at the vertex. Finally, the vertex numbers are added. What is the largest number that must divide the final sum for every possible numbering of the faces?",
"r... | 4 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 11.1 J |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 360 lb-in |
[
{
"content": "Given a set of linearly independent $d \\times d$ complex unitary matrices $\\{U_i\\}_{i=1}^n \\subseteq M_d$ with $n \\geq d$, determine if there exists a vector $v \\in \\mathbb{C}^d$ such that the span of $\\{U_1v, U_2v, \\ldots , U_nv\\}$ is $\\mathbb{C}^d$. Answer with 'yes' or 'no'.",
"r... | yes |
[
{
"content": "Evaluate the 2-form \\( dxdy + 3dxdz \\) on the oriented triangle with vertices \\((0,0,0)\\), \\((1,2,3)\\), and \\((1,4,0)\\) in that order.",
"role": "user"
}
] | -\dfrac{7}{2} |
[
{
"content": "Given non-negative real numbers $a, b, c$ such that $ab + bc + ca = 1$, determine the maximum value of \\[ P = \\frac{\\sqrt{a+bc} + \\sqrt{b+ca} + \\sqrt{c+ab}}{\\sqrt{3a+3b+3c+10}}. \\]",
"role": "user"
}
] | \dfrac{3}{4} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 82.92 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Island area |
[
{
"content": "Calculate the work done (in joules) during the isothermal compression of an ideal gas in a cylinder. The gas is initially at atmospheric pressure (103.3 kPa). The piston compresses the gas by moving inside the cylinder by 0.2 meters. The cylinder has a radius of 0.1 meters and an initial height of... | 900 |
[
{
"content": "Calculate \\(\\lim\\limits_{(x,y) \\to (0,0)} \\frac{\\sin(2x)}{x(y^{2} - 1)} \\).",
"role": "user"
}
] | -2 |
[
{
"content": "Given two prime numbers \\( p \\) and \\( q \\) such that \\( 3 \\) does not divide \\( p-1 \\) nor \\( q-1 \\), and let \\( n = pq \\). Determine the number of elements in the multiplicative group \\( \\mathbb{Z}_n^{*} \\) that can be expressed as \\( b^3 \\) for some integer \\( b \\).",
"ro... | (p-1)(q-1) |
[
{
"content": "Evaluate the double integral \\( \\int _{ 0 }^{ \\frac { \\pi }{ 2 } } \\int _{ 0 }^{ x }{ e^{ \\sin(y) } \\sin(x)\\,dydx } \\).",
"role": "user"
}
] | e - 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.2 |
[
{
"content": "$k$ stones are distributed into $2012$ boxes such that each box contains at most $20$ stones. Determine the minimum value of $k$ such that it is always possible to choose some boxes and remove some stones from them so that the remaining stones in the chosen boxes are equal and their total is at le... | D |
[
{
"content": "Calculate the area under the curve of the integral \\( \\int_{0}^{3} x f(x^2) \\, dx \\), where \\( f(x) = \\sqrt{-x^2 + 4x} \\).",
"role": "user"
}
] | \pi |
[
{
"content": "Given the function \\( g(x) = \\sum_{i=2}^{n} a_i(ix^{i-1}-1) \\), where \\( g(1) = g(-1) = 0 \\), determine if \\( g(x) \\) must have at least two distinct real roots.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.10 |
[
{
"content": "If \\( p \\) is a prime number and \\( k \\) is an even integer, what is the probability that \\( p + k \\) is also a prime number?",
"role": "user"
}
] | 0 |
[
{
"content": "A hotel has 300 rooms and follows an overbooking policy to maximize room usage. Each reservation holder has a 20% chance of canceling or not showing up. Determine the largest number of reservations the hotel can accept while ensuring at least a 95% probability that all guests who arrive will have ... | 360 |
[
{
"content": "Find the coefficient of \\(x^{21}\\) in the expansion of \\((1 + x + x^2 + x^3 + x^4 + x^5 + x^6)^6\\).",
"role": "user"
}
] | 7872 |
[
{
"content": "The $24^\\text{th}$ day of a particular month is a Saturday. On what day of the week was the first day of that month?",
"role": "user"
}
] | \text{Thursday} |
[
{
"content": "Is the decomposition of a finite group $G$ into a direct product of indecomposable groups $G = \\prod_i G_i$ unique up to permutation and isomorphism?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine if $x = 2$ is the only real solution to the equation $a^x + b^x = c^x$ when $(a, b, c)$ is a Pythagorean triplet.",
"role": "user"
}
] | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.218 mm |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0}\\frac {1}{x}\\int_x^{2x}e^{-t^2}dt$$",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 10.016 m |
[
{
"content": "Determine all real numbers \\(k\\) such that the inequality \\[ a^{3} + b^{3} + c^{3} + d^{3} + 1 \\geq k(a + b + c + d) \\] holds for any \\(a, b, c, d \\in [-1, +\\infty)\\).",
"role": "user"
}
] | \dfrac{3}{4} |
[
{
"content": "Given the joint probability density function for continuous random variables $X$ and $Y$ as $f(x) = \\frac{3}{2}x$ for $0 < x < 2$, $0 < y < 1$, and $x < 2y$, calculate the probability $\\Pr(x < 1.5 \\mid y > 0.5)$. Provide your answer as a single probability value.",
"role": "user"
}
] | \dfrac{23}{28} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Glucose + 4 ADP + 4 Pi + 10 NAD+ + 2 FAD -> 6 CO2 + 4 ATP + 10 NADH + 2 FADH2 + 4H+ + 2 CoA |
[
{
"content": "Find the shortest distance from the point \\((5,5)\\) to the curve defined by the equation \\(xy = 4\\).",
"role": "user"
}
] | \sqrt{17} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.52 |
[
{
"content": "Determine the values of the positive real number \\( b \\) for which the series \\( \\sum_{k=1}^\\infty \\frac{b^{k^{2}}}{k!} \\) is convergent.",
"role": "user"
}
] | (0, 1] |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 0^+} \\left(\\ln\\left(\\cot(x)\\right)\\right)^{\\tan(x)}$$",
"role": "user"
}
] | 1 |
[
{
"content": "Let $v_1, \\dots, v_n \\in \\mathbb{R}^n$ be vectors that form a basis. Consider the kernel of the matrix formed by these vectors as follows:\n\\[ \\mathrm{Ker}\\begin{pmatrix}v_1-v_n\\\\\\vdots \\\\ v_{n-1}-v_n\\end{pmatrix}. \\]\nDoes there exist a non-zero vector $N$ in this kernel such that th... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 11.89 |
[
{
"content": "Consider the polynomial \\( p(x) = x^{2021} - x + 1 \\). Calculate the sum \\( r_1^{2021} + r_2^{2021} + \\ldots + r_{2021}^{2021} \\), where \\( r_i \\) are the roots of \\( p(x) \\).",
"role": "user"
}
] | -2021 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 17.00 |
[
{
"content": "Determine the range of \\(a\\) such that the equation \\(e^{|\\sin x|} + e^{- |\\sin x|} + 4a = 0\\) has exactly four different solutions in the interval \\([0, 2\\pi]\\). Choose the correct option:\n\n(A) \\(a \\in \\left[\\frac{-e}{4}, \\frac{-1}{4}\\right]\\)\n(B) \\(a \\in \\left[\\frac{-1-e^2... | D |
[
{
"content": "Let $X, Y$ be locally convex spaces over $\\mathbb{R}$ and $f: X \\to Y$. Suppose $f$ is Fréchet differentiable at a point $x_{0} \\in X$. Given an interval $0 \\in I \\subset \\mathbb{R}$, we call a smooth curve $\\gamma: I \\to X$ an integral curve for $x_{0}$ if $\\gamma(0) = x_{0}$. Determine ... | True |
[
{
"content": "Calculate the area of the spherical triangle defined by the points \\((0, 0, 1)\\), \\((0, 1, 0)\\), and \\(\\left(\\frac{1}{\\sqrt{2}}, 0, \\frac{1}{\\sqrt{2}}\\right)\\) on the unit sphere.",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Compute the limit: \\[ \\lim_{z \\to 0} \\left(\\dfrac{1}{z^2} - \\dfrac{1}{\\sin^2 z}\\right) \\]",
"role": "user"
}
] | -\dfrac{1}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $40.57 |
[
{
"content": "Evaluate the limit \\( \\lim\\limits_{x\\to0}\\frac{e^{-1/x^2}}{x} \\) without using l'Hopital's rule.",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.48E12 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.69 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $\sqrt {13}$ |
[
{
"content": "Evaluate the infinite series: \\[ \\sum_{n=0}^{\\infty} \\frac{16n^2 + 20n + 7}{(4n+2)!} \\]",
"role": "user"
}
] | e + \sin 1 |
[
{
"content": "Given the continuous function $f(x)$ that satisfies the differential equation $$f(x) = (1+x^2)\\left(1+\\int_0^x \\frac{f^2(t)dt}{1+t^2}\\right),$$ find the value of $f(1)$. \\(f(0) = 1\\).",
"role": "user"
}
] | -6 |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{1} (\\log(x))^2 x^{3/2} \\, dx \\) using the function \\( f(x,t) = x^t \\) and the theorem of switching differentiation and integration.",
"role": "user"
}
] | \dfrac{16}{125} |
[
{
"content": "Determine the maximum value of the integral \\( \\int_{0}^{y}\\sqrt{x^4 + (y - y^2)^2}\\,dx \\) for \\( y \\in [0, 1] \\).",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 75.37 mT |
[
{
"content": "Determine which of the following functions is differentiably redundant of order 6: (a) $e^{-x} + e^{-x/2} \\cos\\left(\\frac{\\sqrt{3x}}{2}\\right)$, (b) $e^{-x} + \\cos(x)$, or (c) $e^{\\frac{x}{2}}\\sin\\left(\\frac{\\sqrt{3x}}{2}\\right)$. Consider the significance of the complex numbers $1/2 \... | C |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.0248 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.9 |
[
{
"content": "Evaluate the limit: $$ \\lim_{n \\to \\infty} \\frac{1}{n}\\sum_{k=1}^{n} \\cos\\left(\\sin\\left(\\frac{1}{k}\\right)\\right) $$",
"role": "user"
}
] | 1 |
[
{
"content": "Determine if there exists a positive integer other than 34 such that each of the numbers, the number minus one, and the number plus one, is the product of two distinct prime numbers.",
"role": "user"
}
] | 86 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 22.76 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.321*mol*L^-1 |
[
{
"content": "A line segment has one endpoint at $(6,8)$ and midpoint at $(1,1)$. What is the sum of the coordinates of the other endpoint?",
"role": "user"
}
] | -10 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | a, b, c |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.035 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^\\infty x^3 e^{-x^2} \\, dx \\) using the properties of Gaussian random variables and probability density functions.",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $48,400 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 34000 |
[
{
"content": "In a plane, 20 points are chosen such that no three points lie on the same line. Determine if there exists a triangle with vertices at these points that has at least one angle smaller than $10^{\\circ}$. Answer 'Yes' or 'No'.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | {eq}\frac{\lambda n_g}{n_w}{/eq} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $484,146.51 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | t_{1/2} = \frac{\ln 2}{\lambda} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.82e-8 cm |
[
{
"content": "Given a Hilbert space $V$ and a linear map $T: V \\rightarrow V$, if there exists a constant $C$ such that the inequality $|\\langle T(v), w \\rangle| \\leq C\\|v\\| \\|w\\|$ holds for all $v, w \\in V$, must $T$ be a bounded operator? Answer with 'Yes' or 'No' and justify your answer.",
"role... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.300 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.417 m/sec |
[
{
"content": "Compute the line integral of the vector field $\\textbf{F}(x,y)=(x+y,x^2)$ along the path $y=x^2$ from $(0,0)$ to $(2,4)$. Provide your answer as a single numerical value.",
"role": "user"
}
] | \dfrac{38}{3} |
[
{
"content": "Let $\\{W_t\\}_{t\\ge 0}$ be a standard 2D Brownian motion starting at $(1,1)$ in $\\mathbb{R}^2$. Determine the probability that $W_t$ hits the positive x-axis before it hits the negative x-axis.",
"role": "user"
}
] | \dfrac{3}{4} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 49 m |
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