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... | 1.6e75 |
[
{
"content": "Determine if the remainder is zero when the $S$-polynomial $S(f,g) = x_1^2x_2 - x_3$ is divided by the set of polynomials $\\{f = x_3 - x_1^5, g = x_2 - x_1^3\\}$ using Buchberger's algorithm with a lexicographic order where $x_1 > x_2 > x_3$. Note that $S(f,g)$ can be expressed as $-f + x_1^2g$. ... | 0 |
[
{
"content": "Let $k > 1$ be an integer. Consider the vector $e \\\\in \\mathbb{Z}^k$ with 1 in the first coordinate and 0 in every other coordinate. Determine the number of elements in $\\mathrm{SL}_k(\\mathbb{Z})$ that have $e$ as their first column.",
"role": "user"
}
] | \infty |
[
{
"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... | 153 m |
[
{
"content": "Let $\\mathbb{P}$ be the set of all prime numbers, and let $p_i$ denote the $i$th prime number, with $p_1 = 2$. Define $m = \\prod_{i=1}^n p_i$. Determine the number of solutions to the congruence $x^2 + x \\equiv 0 \\pmod{m}$. Conjecture: $2^n$. Provide the number of solutions.",
"role": "use... | 2^n |
[
{
"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... | 10.1 J |
[
{
"content": "Find the limit \\( \\lim\\limits_{t\\to\\infty} u(1,t) \\) for the solution \\( u(x,t) \\) of the heat equation\n\\[\\frac{\\partial u}{\\partial t}-\\dfrac{\\partial^{2}u}{\\partial x^{2}}=0\\]\nwith the initial condition\n\\[u(x,0)=\\frac{e^{2x}-1}{e^{2x}+1}\\]\nwhen no boundary conditions are p... | 0 |
[
{
"content": "Evaluate the limit of the improper integral \\(\\lim_{k \\to \\infty} \\int_0^\\infty e^{-kx^2} \\, dx\\) using the Dominated Convergence Theorem (DCT).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the splitting field of the polynomial \\(x^3 + x^2 + 1\\) over the real numbers \\(\\Bbb R\\).",
"role": "user"
}
] | \mathbb{C} |
[
{
"content": "Evaluate the integral \\( \\lim_{n\\rightarrow \\infty} \\int_{\\mathbb{R}^2}e^{-(x^2+y^2)^n}dxdy \\) using polar coordinates.",
"role": "user"
}
] | \pi |
[
{
"content": "Consider the arithmetic progression \\(\\{s_n = an + b : n = 1, 2, 3, \\ldots\\}\\) where \\(a\\) and \\(b\\) are positive integers. Let \\(\\alpha\\) be an irrational number, and define the sequence of fractional parts \\(r_n = \\{s_n \\alpha\\}\\) by \\(r_n = s_n \\alpha - \\lfloor s_n \\alpha \... | Yes |
[
{
"content": "Determine whether there exists a function $f(n)$ such that $f(2n) = o(f(n))$. If such a function exists, provide an example.",
"role": "user"
}
] | f(n) = 2^{-n} |
[
{
"content": "Determine the dimension of the subspace $S_n$ of $n \\times n$ matrices with real entries, where each matrix $A = (a_{ij})$ satisfies $a_{ij} = a_{kl}$ whenever $i + j = k + l$, for $n \\geq 2$. Provide your answer as a single integer.",
"role": "user"
}
] | 2n - 1 |
[
{
"content": "Consider the self-adjoint semigroup of operators $K_{t}=e^{-tK}$ for $t>0$, where $K$ is a self-adjoint operator. The semigroup extends as a $C_{0}$-semigroup with $||K_{t}||\\leq 1$. Determine if the following implication is true: If $K_{t}$ is compact for every $t$, then $K$ has only discrete sp... | Yes |
[
{
"content": "In the ring of polynomials \\( R = \\mathbb{Z}_3[x] \\), find the greatest common divisor (gcd) of the polynomials \\( p_1(x) = x^4 + 2x^2 + 1 \\) and \\( p_2(x) = x^3 + x + 2 \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to \\infty} \\sqrt{x} \\left(\\sqrt{16x^3+4x-1} - \\sqrt{16x^3+3}\\right). \\]",
"role": "user"
}
] | \dfrac{1}{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... | 7.02% |
[
{
"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... | $349,000 |
[
{
"content": "A set of identical regular pentagons has natural numbers from 1 to 5 written at each vertex. The pentagons can be rotated and flipped. They are stacked in a pile such that the sums of the numbers at each of the five vertices are equal. Determine the number of pentagons in this stack.",
"role":... | 5 |
[
{
"content": "Calculate the Lebesgue integral \\( \\int_{[0,\\pi]} \\sin x \\: \\epsilon[\\mathbb{R}\\setminus\\mathbb{Q}] \\, d\\mu,\\) where \\(\\epsilon\\) is the characteristic function of the irrationals. Provide your answer as a single number.",
"role": "user"
}
] | 2 |
[
{
"content": "In a tetrahedron \\( S-ABC \\), let \\( A_1 \\) be the centroid of \\( \\triangle SBC \\). A point \\( G \\) is located on segment \\( AA_1 \\) such that \\( \\frac{|AG|}{|GA_1|} = 3 \\). The line \\( SG \\) intersects the plane of \\( \\triangle ABC \\) at point \\( M \\). Find the value of \\( \... | \dfrac{1}{3} |
[
{
"content": "Determine whether the elements $sr$ and $s^2r$ can generate the dihedral group $D_n$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Let $W$ be a vector space with a linear action of a group $G$. If $W$ is a simple $G$-module of dimension greater than 1, determine the value of the sum $\\sum_{g\\in G} g(w)$ for any $w\\in W$.",
"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... | 2.29e7 Hz |
[
{
"content": "For a positive integer $n$, an $n \\times n$ grid is filled with the numbers $1, 2, \\ldots, n^2$. The partial range of a row or column is defined as the difference between the largest and smallest numbers in that row or column, excluding any empty cells. Determine the minimum possible sum of the ... | n(n^2 - 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... | 62.5e6 J |
[
{
"content": "Given the functions \\( f(t) = \\left( \\int_0^{\\sqrt{t}} e^{-x^2} \\, dx \\right)^2 \\) and \\( g(t) = \\int_0^1 \\frac{e^{-t(1+x^2)}}{1+x^2} \\, dx \\) for \\( t > 0 \\), find the value of \\( f'(t) + g'(t) \\).",
"role": "user"
}
] | 0 |
[
{
"content": "In triangle ABC, where AB = 84, BC = 112, and AC = 98, angle B is bisected by line segment BE, with point E on AC. Angles ABE and CBE are further bisected by line segments BD and BF, respectively. Determine the length of segment FC.",
"role": "user"
}
] | 32 |
[
{
"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... | first-in, first-out method |
[
{
"content": "Does there exist a closed set $E$ that is a subset of $[a,b]$, with $E \\neq [a,b]$, such that the measure of $E$ is $b-a$?",
"role": "user"
}
] | No |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to \\infty} \\frac{i}{n}\\left(\\frac{1+i}{\\sqrt{2}}\\right)^n \\] where \\(i=\\sqrt{-1}\\).",
"role": "user"
}
] | 0 |
[
{
"content": "One of the asymptotes of a hyperbola has equation $y=3x.$ The foci of the hyperbola have the same $x-$coordinate, which is $5.$ Find the equation of the other asymptote of the hyperbola, giving your answer in the form \"$y = mx + b$\".",
"role": "user"
}
] | y = -3x + 30 |
[
{
"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... | 0.88 atm |
[
{
"content": "Let $M_n(\\mathbb{R})$ be the space of $n\\times n$ matrices. Let $P$ be a non-zero matrix in $M_n(\\mathbb{R})$. Define $L$ as the set of matrices $X$ in $M_n(\\mathbb{R})$ such that $\\operatorname{Tr}(PX)=0$. Determine the dimension of the set $L$.",
"role": "user"
}
] | n^2 - 1 |
[
{
"content": "Let \\( f(x) \\) be a function mapping real numbers to real numbers. Given that \\( f(f(x)) = \\frac{1}{3x} \\) and \\( f(2) = \\frac{1}{9} \\), find \\( f\\left(\\frac{1}{6}\\right) \\).",
"role": "user"
}
] | 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... | 21000 N/m |
[
{
"content": "Determine whether the following statement is true: A map $f: X \\rightarrow Y$ is continuous if and only if for each subset $A$ of $X$, the image of the interior of $A$ is contained in the interior of the image of $A$. Provide a justification for your answer.",
"role": "user"
}
] | False |
[
{
"content": "Is it possible for $\\sup \\{\\langle p,x \\rangle, x \\in S_+\\} = 1$ under the same conditions as in the original question?",
"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... | $\frac{\sum_{i=1}^{16}\frac i2\cdot\frac{100}{1.03^{i+1}}+\frac{16}2\cdot\frac{5000}{1.03^{17}}}{\sum_{i=1}^{16}\frac{100}{1.03^{i}}+\frac{5000}{1.03^{16}}}$ |
[
{
"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 L |
[
{
"content": "Given three linearly independent vectors $u, v, w$ in $\\mathbb{R}^7$, determine the value of $k$ such that the set $S = \\{u - 5v, v - 3w, w - ku\\}$ is linearly dependent.",
"role": "user"
}
] | \dfrac{1}{15} |
[
{
"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... | 30 Hz |
[
{
"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... | Goldman Inc.\nStockholders' Equity Section\nAs of December 31, 2014\n\n ParticularsAmount ($)Calculation\n Stockholders' Equity: \n Preferred stock300,00012,000 * $25\nAdd: Common stock836,00076,000 * $11\nAdd: Paid-in capital in excess of stated value-Preferred stock24,00012,000 * $2\nAdd: Paid-in capital in excess of par-Common stock540,000(17,000 * $4) + (59,000 * $8)\nAdd: Retained earnings0\n Total stockholder's equity1,700,000 |
[
{
"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... | 81.4% |
[
{
"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... | 1969500 |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\rightarrow \\infty }\\sum_{k=n}^{5n}\\binom{k-1}{n-1}\\left( \\frac{1}{5} \\right )^n\\left( \\frac{4}{5} \\right )^{k-n}$$",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Find the minimum value of \\(\\sin \\alpha + 2 \\cos \\beta\\) given that \\(\\alpha, \\beta \\geq 0\\) and \\(\\alpha + \\beta \\leq 2\\pi\\).",
"role": "user"
}
] | -\sqrt{5} |
[
{
"content": "Evaluate the sum of the series: \\[ \\sum_{k=0}^\\infty \\frac{(-1)^{k+1}}{2k+1} \\]",
"role": "user"
}
] | -\dfrac{\pi}{4} |
[
{
"content": "Find a function $f$ such that $f \\notin L^{p}(\\mathbb{R})$ for all $p > 0$, but there exists a constant $c > 0$ such that for all $t > 0$, the measure of the set $\\{x \\in \\mathbb{R} : |f(x)| > t\\}$ is bounded by $\\frac{c}{t}$. Provide an example of such a function.",
"role": "user"
}
... | f(x) = \dfrac{1}{|x|} |
[
{
"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... | $65,950 |
[
{
"content": "Let $a$, $b$, $c$, and $d$ be real numbers with $|a-b|=2$, $|b-c|=3$, and $|c-d|=4$. What is the sum of all possible values of $|a-d|$?",
"role": "user"
}
] | 18 |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{\\infty}\\frac{dv}{v\\cosh v} \\).",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "Given two local martingales $M_1$ and $M_2$, each defined by stochastic integrals with respect to independent Brownian motions, find the covariation $[M]$ of the local martingale $M = M_1 + M_2$ in terms of $[M_1]$ and $[M_2]$. Provide the specific formula for $[M]$.",
"role": "user"
}
] | [M] = [M_1] + [M_2] |
[
{
"content": "An infinite geometric series has common ratio $\\frac{-1}{3}$ and sum $25.$ What is the second term of the sequence?",
"role": "user"
}
] | \frac{-100}{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... | 5652.06 |
[
{
"content": "Suppose we have two independent real random variables $X$ and $Y$, and $X+Y$ has the same distribution as $X$. Does this imply that the distribution of $Y$ is degenerate at 0?",
"role": "user"
}
] | Yes |
[
{
"content": "Given an equilateral triangle $\\Delta ABC$ and a point $P$ outside the triangle but inside $\\angle ABC$, the distances from $P$ to the sides $BC$, $CA$, and $AB$ are $h_1$, $h_2$, and $h_3$ respectively. If $h_1 - h_2 + h_3 = 6$, find the area of $\\Delta ABC$. \\(\\Delta ABC\\).",
"role": "... | 12\sqrt{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... | 6C^(III) -> 6C^(IV) + 6e^(-) |
[
{
"content": "Calculate the limit: $$\\lim_{x\\to1}{\\sqrt{\\frac{\\pi}{2}-\\arctan\\left(\\frac{1}{(x-1)^2}\\right)}}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the fractal dimension of a structure formed by repeatedly dividing a $2r \\times 2r \\times 2r$ cube into smaller cubes, removing the cubes along the axes, and continuing this process for every odd number raised to the power of three.",
"role": "user"
}
] | \dfrac{\log 20}{\log 3} |
[
{
"content": "Let $\\lfloor x \\rfloor$ denote the greatest integer less than or equal to $x$. How many real numbers $x$ satisfy the equation $x^2 + 10000\\lfloor x \\rfloor = 10000x$?",
"role": "user"
}
] | 199 |
[
{
"content": "Let \\( \\{X(t); t \\geq 0\\} \\) be a Poisson process with parameter \\( \\lambda = 2 \\). Find \\( E[X(s) | X(t) = n] \\), where \\( 0 < s < t \\).",
"role": "user"
}
] | \dfrac{n s}{t} |
[
{
"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... | 66.5 Hz |
[
{
"content": "Find the Zariski closure of the set \\( A = \\{ (a^2 + 1, a^3 + a) \\mid a \\in \\mathbb{R} \\} \\) in \\( \\mathbb{R}^2 \\).",
"role": "user"
}
] | y^2 = x^3 - x^2 |
[
{
"content": "Determine the degree of the differential equation \\( \\left(\\frac{d^2y}{dx^2}\\right)^{\\frac{3}{2}} + \\left(\\frac{dy}{dx}\\right)^{\\frac{2}{3}} + y^2 = 0 \\) after eliminating the radicals.",
"role": "user"
}
] | 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... | 0.01926 m |
[
{
"content": "Determine the smallest number of points in n-dimensional space \\(\\mathbb{R}^n\\) such that every point in \\(\\mathbb{R}^n\\) is an irrational distance from at least one of these points.",
"role": "user"
}
] | n + 1 |
[
{
"content": "Find \\( g'(2) \\) for the function \\( g(x) = \\int_0^{x^2} y \\tan(\\pi y) \\, dy \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Consider a probability space $(\\Omega, \\mathcal{F}, \\mu)$. Define the essential supremum of a function $f : \\Omega \\to \\mathbb{R}$ as\n\\[ \\esssup f = \\inf_{A : \\mu(A) = 0} \\sup_{x \\notin A} f(x). \\]\nIs the set of equivalence classes of almost everywhere equal, bounded $\\mathbb{R}$-v... | Yes |
[
{
"content": "Let $G$ be a finite group such that for any two non-identity elements $a,b$ in $G$, there exists an automorphism of $G$ sending $a$ to $b$. Determine whether $G$ must be abelian.",
"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... | 8.47% |
[
{
"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... | 1.72 mol |
[
{
"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... | 3.7e-6 N/C |
[
{
"content": "Determine the range of values for the parameter \\(\\lambda\\) such that the transformation \\(T\\) defined by \\((Tf)(x) = x + \\lambda \\int_0^x (x-t)f(t)dt\\) is a contraction mapping with respect to the supremum norm on the space of continuous functions \\(C([0,1])\\).",
"role": "user"
}... | (-2, 2) |
[
{
"content": "Find the volume of the solid $S$ described by the inequalities $\\frac{x+y}{2} < z < \\sqrt{x+y}$ in the first quadrant of the $(x, y)$-plane.",
"role": "user"
}
] | \dfrac{32}{15} |
[
{
"content": "Consider the direct sum of left $R$-modules $A \\oplus B$. Is it possible to have a non-zero submodule $X$ of $A \\oplus B$ such that $X \\cap A = 0$ and $X \\cap B = 0$? Justify your answer.",
"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... | 5.94e7 s |
[
{
"content": "Determine the values of $x$ for which the series \\( \\sum_{n=1}^\\infty x^n \\sin(xn) \\) converges.",
"role": "user"
}
] | (-1, 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... | Cook Company
Flexible Budget Report for October
Actual Flexible Budget Spending Variance Static Budget Volume Variance
Direct labor hours 27,000 27,000 0 25,000 5,000 F
Budgeted variable manufacturing overhead:
Indirect labor (Budget = $126,000 / 300,000 = $0.42 per unit) $12,432 $11,340 $1,092 U $10,500 $840 U
Indirect materials 7,680 8,100 420 F 7,500 600 U
Repairs 4,800 4,860 60 F 4,500 360 U
Utilities 6,840 6,480 360 U 6,000 480 U
Lubricants 1,920 1,620 300 U 1,500 120 U
Total variable manufacturing costs $33,672 $32,400 $1,272 U $30,000 $2,400 U
Budgeted fixed manufacturing overhead
Supervision 8,000 8,000 0 8,000
Depreciation 6,000 6,000 0 6,000
Insurance 2,460 2,500 40 F 2,500
Rent 2,000 2,000 0 2,000
Property taxes 1,500 1,500 0 1,500
Total fixed cost $19,960 $20,000 $40F $20,000 0 |
[
{
"content": "Is every open set in \\(\\mathbb{R}\\) expressible as a countable union of disjoint open intervals in the standard topology?",
"role": "user"
}
] | Yes |
[
{
"content": "Let $(S_n)_{n\\ge0}$ be a symmetric, simple random walk. Evaluate the limit: $$\\lim_{n\\to \\infty}\\mathbb{P}\\left(n^{-1}\\sum_{i=1}^n |S_i|>a\\right)$$",
"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... | 9.09% |
[
{
"content": "A $2018 \\times 2018$ square is divided into rectangles with integer side lengths. Some of these rectangles are used to form a $2000 \\times 2000$ square. The remaining rectangles are used to form another rectangle whose length differs from its width by less than 40. What is the perimeter of this ... | 1078 |
[
{
"content": "Let $(X,\\mathcal{A},\\mu)$ be a measurable space and $\\{u_n\\}_{n=1}^\\infty$ be a sequence in $\\mathcal{L}^1(\\mu)$ that converges pointwise to $u \\in \\mathcal{L}^1(\\mu)$. If $\\int u_n \\, d\\mu \\to 0$, prove that $\\int u \\, d\\mu = 0$. Provide a justification for your answer.",
"ro... | 0 |
[
{
"content": "Evaluate the definite integral: $$\\int_0^1 x\\sqrt{1-x^2}\\arcsin x \\, dx$$",
"role": "user"
}
] | \dfrac{2}{9} |
[
{
"content": "The second and fifth terms of an arithmetic sequence are 17 and 19, respectively. What is the eighth term?",
"role": "user"
}
] | 21 |
[
{
"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... | -0.96 m/s^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... | 12.00 |
[
{
"content": "Evaluate the limit \\( \\lim _ {x\\rightarrow + \\infty } \\int _ { 3 } ^ { 4 } \\frac { \\cos ( x + y ) } { \\cos \\left(x^{2}+y^{2} \\right) } d y\\) using the dominated convergence theorem.",
"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... | 4670.07 L |
[
{
"content": "A frog starts at point \\( P \\) on the ground, which is 0.27 meters away from point \\( C \\). The frog makes a series of symmetric jumps: the first jump is symmetric with respect to point \\( A \\), the second with respect to point \\( B \\), the third with respect to point \\( C \\), and the fo... | 54 |
[
{
"content": "Evaluate the integral \\( \\int _0^\\infty\\frac{x \\sin x}{1+x^2}dx \\) using the residue theorem.",
"role": "user"
}
] | \dfrac{\pi}{2e} |
[
{
"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... | -150.59 atm |
[
{
"content": "Does there exist a sequence of smooth functions $(f_n) \\subset C^\\infty([0,1])$ such that $\\|f_n\\|_{L^2} = 1$ for all $n$, but $\\|f'_n\\|_{L^2} \\to \\infty$?",
"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... | 56.0692852714 MeV |
[
{
"content": "Evaluate the series: \\( \\sum_{k=0}^{\\infty} (-1)^k \\dfrac{\\pi^{2k}}{(2k)!} \\)",
"role": "user"
}
] | -1 |
[
{
"content": "Calculate $\\sqrt{75x} \\cdot \\sqrt{2x} \\cdot \\sqrt{14x}$ . Express your answer in simplest radical form in terms of $x$.",
"role": "user"
}
] | 10x \sqrt{21x} |
[
{
"content": "Find a set of natural numbers \\((a, b, c, d)\\) such that the number formed by concatenating them, denoted as \\(\\overline{abcd}\\), equals the product of their powers, \\(a^b \\times c^d\\).",
"role": "user"
}
] | (2, 5, 9, 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... | 1.67e26 mol |
[
{
"content": "Determine the number of ways to distribute $7m$ indistinguishable items into $m$ distinguishable groups such that each group can receive at most $7$ items, and not all items need to be distributed.",
"role": "user"
}
] | 8^m |
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