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... | 6.6% |
[
{
"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... | ACEGH |
[
{
"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... | 401.26 J/g |
[
{
"content": "Determine the number of lines that are both normal and tangent to the curve \\(y^2 = x^3\\), intersecting the curve at two distinct points.",
"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... | 19.06 |
[
{
"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... | 10,000 for material and 10,050 for conversion |
[
{
"content": "Find the largest natural number \\( n \\) such that \\( n^{6033} < 2011^{2011} \\).",
"role": "user"
}
] | 12 |
[
{
"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... | 2.15 s |
[
{
"content": "The graph of $y=ax^2 + bx + c$ is a parabola with vertical axis of symmetry. The vertex of this parabola is $(2,3)$ and the parabola contains the point $(4,4)$. Find the value of $y$ when $x=6$.",
"role": "user"
}
] | 7 |
[
{
"content": "Find the order of the entire function \\( f_k(z) = \\prod\\limits_{n=1}^{\\infty} \\left(1-\\frac{z}{n^k}\\right) \\). The order \\( \\lambda \\) is defined as: \\[ \\lambda = \\limsup_{r\\to \\infty} \\frac{\\log \\log M(r)}{\\log r}, \\] where \\( M(r) = \\max \\{|f_k(z)|:|z| = r\\} \\).",
"... | \dfrac{1}{k} |
[
{
"content": "Determine the degree of the splitting field of the polynomial $x^3 - \\pi$ over the field $\\mathbb{R}(\\pi)$. Provide your answer as a single integer.",
"role": "user"
}
] | 6 |
[
{
"content": "Determine whether \\(-2\\) is a quadratic residue modulo 307.",
"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... | 4.5165 x 10^23 |
[
{
"content": "Given a linear modulo function of the form \\( y = ax + b \\pmod{n} \\), where \\( n \\) is a known integer and \\( \\gcd(a, n) = 1 \\), determine how many integer points \\((x, y)\\) are needed to uniquely determine the integers \\( a \\) and \\( b \\). Assume \\( x \\) and \\( y \\) are integers... | 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... | 800 m |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0}\\frac{\\sin^2x - x\\tan x}{x^4}$$",
"role": "user"
}
] | -\dfrac{2}{3} |
[
{
"content": "The table shows some of the results of a survey by radio station KAMC. What percentage of the males surveyed listen to the station? [asy]\nsize(3inch, 1.5inch);\ndraw((0,0)--(7,0)--(7,2.5)--(0,2.5)--cycle);\n\nlabel(scale(.75)*\"Listen\", (2.5, 2), N);\nlabel(scale(.75)*\"Don't Listen\", (4.5, 2),... | 75\% |
[
{
"content": "Consider a 10x10 symmetric matrix \\(A\\) where all diagonal entries are \\(a+1\\) and all off-diagonal entries are 1. The sum of the largest and smallest eigenvalues of \\(A\\) is 24. Find the value of \\(a\\).",
"role": "user"
}
] | 7 |
[
{
"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... | 3.96 km/h |
[
{
"content": "Determine the number of functions \\( \\phi : \\mathbb{N} \\cup \\{0\\} \\to \\mathbb{N} \\cup \\{0\\} \\) such that \\( \\phi(ab) = \\phi(a) + \\phi(b) \\) for all \\( a, b \\in \\mathbb{N} \\cup \\{0\\} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Let $A$ be a square matrix of dimension $n$ and let $\\lambda \\in \\mathbb{C}$ be an element of the spectrum of $A$. $X_\\lambda$ denotes the eigenspace of $A$ associated with $\\lambda$. Under what condition do we have $AX_\\lambda = \\{0\\}$?",
"role": "user"
}
] | \lambda = 0 |
[
{
"content": "Find all even perfect numbers that can be expressed as the sum of two cubes of positive integers.",
"role": "user"
}
] | 28 |
[
{
"content": "Given the series \\( y = \\frac{2}{5} + \\frac{1 \\cdot 3}{2!} \\left(\\frac{2}{5}\\right)^2 + \\frac{1 \\cdot 3 \\cdot 5}{3!} \\left(\\frac{2}{5}\\right)^3 + \\ldots \\), find the value of \\( y^2 + 2y \\).",
"role": "user"
}
] | 4 |
[
{
"content": "Determine whether there exists a random variable $X$ such that:\n\n1. $X \\geq 0$ almost surely,\n2. $E[X] \\leq \\epsilon$ for some $\\epsilon > 0$,\n3. $E[X^2] \\geq 1$,\n4. $E[X^3] \\leq 10^{100}$. \n\nProvide a justification for 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... | {eq}\vec{a}=(-4.4\;\times 10^{11}\;\hat{i}-15.8\times 10^{11}\;\hat{j})\;m/s^{2}{/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... | 2437.78946 m |
[
{
"content": "Determine the asymptotic behavior of the expression \\( \\prod_{i=1}^{k}\\left(1+\\frac{2i}{3^k}\\right) \\) as \\( k \\to \\infty \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Determine the dimension of the quotient space $V/W$ over $\\mathbb{R}$, where $V = \\mathbb{R}[x]$ is the vector space of all polynomials over $\\mathbb{R}$ in the indeterminate $x$, $S = \\{x^n - x^{n+3} : n\\in \\mathbb{N}\\cup\\{0\\}\\}$, and $W = \\langle S\\rangle$. Provide your answer as a s... | 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... | 1.6020 |
[
{
"content": "Determine whether the sequence of functions \\( f_n(x) = x + x^n(1 - x)^n \\) converges uniformly to \\( x \\) on the interval \\([0,1]\\).",
"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... | 7,165.16 |
[
{
"content": "Compute\n\\[\\frac{\\lfloor \\sqrt[4]{1} \\rfloor \\cdot \\lfloor \\sqrt[4]{3} \\rfloor \\cdot \\lfloor \\sqrt[4]{5} \\rfloor \\dotsm \\lfloor \\sqrt[4]{2015} \\rfloor}{\\lfloor \\sqrt[4]{2} \\rfloor \\cdot \\lfloor \\sqrt[4]{4} \\rfloor \\cdot \\lfloor \\sqrt[4]{6} \\rfloor \\dotsm \\lfloor \\sqr... | \frac{5}{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... | 134.94 Newton |
[
{
"content": "Determine the Euler characteristic of the surface \\( M=\\left\\{(x,y,z); \\sqrt{x^2+y^2}=1+z^{2n}, 0< z< 1\\right\\} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Let $a, b, c \\in \\mathbb{R}$ satisfy the following equations:\n\\[ a^2 + b^2 + c^2 = 2018 \\]\n\\[ 2a + 2b - c = 15 \\]\n\\[ 2b + 2c - a = 36 \\]\nDetermine the maximum value of the expression $2c + 2a - b$. Provide your answer as a single number.",
"role": "user"
}
] | 129 |
[
{
"content": "Determine whether there exists an integer \\( x \\) such that \\( x^2 + 1 \\) is divisible by a prime number \\( p \\) of the form \\( 4k + 1 \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Find the measure \\( \\lambda_3(A) \\) of the set \\( A = \\{ (x,y,z) \\in \\mathbb{R}^3 \\mid z^2 < \\frac{x^2}{4} + \\frac{y^2}{9} < 2z \\} \\).",
"role": "user"
}
] | 8\pi |
[
{
"content": "Evaluate the integral \\( \\int_{|z|=1} \\frac{(1-\\cos z)}{(e^z-1)\\sin z} \\, dz \\) using Cauchy's residue theorem.",
"role": "user"
}
] | 0 |
[
{
"content": "Let $k$ be an arbitrary field, and let $\\varphi:A\\to B$ be a morphism of abelian varieties over $k$. Determine whether $\\varphi(A)$ has the structure of an abelian subvariety of $B$ which is defined over $k$.",
"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... | $3,988 |
[
{
"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... | 1.255e-8 M |
[
{
"content": "Determine whether the function spaces $C^0[a,b]$ and $C^0[0,1]$, both equipped with the $L^1$-Norm, are isometrically isomorphic.",
"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... | 0.251 L |
[
{
"content": "Find the maximum value of the function $f(x,y,z)=xy^2z$ subject to the constraint $x+y+z=4$ in the first octant ($x>0, y>0, z>0$).",
"role": "user"
}
] | 4 |
[
{
"content": "Given the symmetric matrix \\( A = \\begin{bmatrix} 2 & 0 & 0 \\\\ 0 & 7 & -1 \\\\ 0 & -1 & 7 \\end{bmatrix} \\), use the Min-Max Principle to determine the second smallest eigenvalue \\( \\lambda_2 \\). Consider 2-dimensional subspaces of \\( \\mathbb{R}^3 \\) and evaluate the Rayleigh quotient \... | 6 |
[
{
"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... | If the Fed buys $200 worth 1 million bonds, with a reserve requirement ratio of 10%, the change in money supply will be $200 * 10 = $2,000 |
[
{
"content": "Let $S$ be a flat, geodesically convex submanifold of $\\mathbb{R}^n$. Determine whether there exists an isometric slice chart for $S$ in $\\mathbb{R}^n$ around a point $p \\in S$. Specifically, is there a diffeomorphism $\\phi: U \\to V$ such that $U$ is an open neighborhood of $p$ in $\\mathbb{R... | Yes |
[
{
"content": "Evaluate the integral: \\[ \\int_0^{ + \\infty } \\frac{x \\ln x}{(x^2 + 1)^2} \\, \\mathrm{d}x \\]",
"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... | x ray > green light > yellow light > infrared wave > FM radio wave > AM radio wave |
[
{
"content": "In an acute triangle \\(ABC\\), the altitudes \\(AD\\) and \\(BE\\) intersect at point \\(H\\). The circumcircle of triangle \\(ABH\\) intersects sides \\(AC\\) and \\(BC\\) at points \\(F\\) and \\(G\\) respectively. If \\(DE = 5\\) cm, find the length of \\(FG\\).",
"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... | CONARD CORPORATION
Condensed Income Statements
For the Years Ended December 31
2014 2013
Amount Percent Amount Percent
Net sales$752,210100%$601,150100%
Cost of goods sold470,41062.5%404,16067.2%
Gross Profit281,80037.5%196,99032.8%
Selling expenses 104,32013.9%82,48013.7%
Administrative expenses 74,6409.9%57,090... |
[
{
"content": "Find the sum of the infinite series: \\[ \\frac{4}{1!} + \\frac{8}{2!} + \\frac{14}{3!} + \\frac{22}{4!} + \\cdots \\]",
"role": "user"
}
] | 5e - 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... | $8,485.82 |
[
{
"content": "Given that $\\sum_{k=1}^{35}\\sin 5k=\\tan \\frac mn,$ where angles are measured in degrees, and $m$ and $n$ are relatively prime positive integers that satisfy $\\frac mn<90,$ find $m+n.$",
"role": "user"
}
] | 177 |
[
{
"content": "Determine whether the differential equation \\( \\sin(t)y' + y\\cos(t) = (\\sin(t))^2 \\) has a singular point at \\( t = 0 \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the integral \\( \\int_C \\frac {3z^5 - 10z^3} {z^6-5z^4+10}\\ dz \\) where \\( C = \\{z \\in \\Bbb C : |z| < 2 \\} \\).",
"role": "user"
}
] | 4\pi i |
[
{
"content": "If \\( \\lim_{x\\to 0}\\frac{1}{x^3}\\left(\\frac{1}{\\sqrt{1+x}}-\\frac{1+ax}{1+bx}\\right)=l \\), find the value of \\( \\frac{1}{a}-\\frac{2}{l}+\\frac{3}{b} \\).",
"role": "user"
}
] | 72 |
[
{
"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... | 1.876 |
[
{
"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 |
[
{
"content": "In \\(\\mathbb{R}^3\\), a sphere has a diameter \\(d\\). What is the most probable length of random secants (including tangents, where the length is 0) drawn through the sphere?",
"role": "user"
}
] | d |
[
{
"content": "Calculate the flow of the vector field \\( F(x,y,z) = (xz, yz, -z^2) \\) out of the surface \\( S = \\{(x,y,z) \\in \\mathbb{R}^3 : z^2 = 1 + x^2 + y^2, 2 \\leq z \\leq 3\\} \\). Use the definition of surface integrals to find the result.",
"role": "user"
}
] | 60\pi |
[
{
"content": "Find the coefficient of \\(x^{18}\\) in the expansion of \\((x^2+x^3+x^4)^3(1-x^5)^{-3}\\) using generating functions.",
"role": "user"
}
] | 36 |
[
{
"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. O5 stars have short lifespans (a few million years), which is insufficient for life to develop.
2. O5 stars become red giants or supernovae, destroying nearby planets. |
[
{
"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... | 76 degrees |
[
{
"content": "Determine if the limit can be moved inside the natural logarithm function for the expression \\( \\lim_{z\\to0}\\ln\\left\\lvert\\frac{iz-1}{iz+1}\\right\\rvert \\). If so, verify whether the simplification to \\( \\ln 1 = 0 \\) is correct.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit analytically without using L'Hôpital's rule: \\[ \\lim_{x \\rightarrow 0^+}(e^{\\frac{1}{x}}x^2) \\]",
"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... | 163 degrees C |
[
{
"content": "Find the residue and the Laurent series expansion of the function \\( w = \\sin(z) \\cdot \\sin\\left(\\frac{1}{z}\\right) \\) at the point \\( z_0 = 0 \\). Determine the coefficient of the \\( z^{-1} \\) term in the expansion, which represents the residue at this point.",
"role": "user"
}
] | 0 |
[
{
"content": "Find the limiting value of the function \\( f(x) = \\sum\\limits_{n=1}^\\infty \\frac{x}{x^2+n^2} \\) as \\( x \\) approaches infinity.",
"role": "user"
}
] | \dfrac{\pi}{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... | 9.59% |
[
{
"content": "Determine the number of solutions for the equation \\(x^3 - x \\sin(x) = 2 + \\cos(x)\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Given a non-zero sequence \\(r_n\\) such that \\(\\lim_{n \\to \\infty}{r_{2n}} = \\frac{1}{2008}\\) and \\(\\lim_{n \\to \\infty}{r_{2n + 1}} = \\frac{1}{2009}\\), and a sequence \\(a_n\\) defined by \\(a_1 = x\\) and \\(a_{n+1} = a_n \\cdot r_n\\) where \\(x \\in \\mathbb{R}\\), find \\(\\lim_{n... | 0 |
[
{
"content": "Find the extreme values of the function \\( f(x,y,z) = x^2 + y^2 + z^2 \\) subject to the constraint \\( xy + yz + zx = 3a^2 \\).",
"role": "user"
}
] | 3a^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... | 0.9082 kgm/s |
[
{
"content": "Calculate the maximum value of the surface integral of the curl of the vector field \\( F = (xy^2, 3z-xy^2, 4y-x^2y) \\) over a simply closed surface \\( S \\) in the plane \\( x+y+z=1 \\). What is the surface that maximizes this integral?",
"role": "user"
}
] | \dfrac{\pi}{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... | M^(-3/2) min^-1 |
[
{
"content": "Calculate the expected number of rolls of a fair six-sided die until the sum of the outcomes is a multiple of 3.",
"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... | 106e12 grams |
[
{
"content": "Find the limit of \\( S_n \\) as \\( n \\to \\infty \\), where \\( S_n = \\int_{0}^{1} \\frac{n x^{n-1}}{1+x} \\, dx \\) for \\( n \\ge 1 \\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Find all non-zero polynomials \\( P(x) \\) such that \\( P\\left(x^{2}-2 x\\right) \\equiv [P(x-2)]^{2} \\) for all \\( x \\in \\mathbf{R} \\).",
"role": "user"
}
] | (x + 1)^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... | 2.91e5 J |
[
{
"content": "Evaluate the limit: $$ \\lim_{x \\to 0} \\left[1 + x\\sin(\\pi - x) \\right]^{1/x}. $$",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether there exists a commutative integral domain $R$ such that every nonzero prime ideal $Q$ is maximal, and there are maximal ideals $Q$ with residue fields of sizes $3$, $11$, and $27$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit as an integral: $$\\lim_{n \\rightarrow \\infty} \\frac{1}{n} \\left[\\left(\\frac{1}{n}\\right)^2 + \\left(\\frac{2}{n}\\right)^2 + \\cdots + \\left(\\frac{3n}{n}\\right)^2\\right].$$ Express the sum as an integral given that \\(\\Delta x = \\frac{1}{n}\\) and \\(f(x) = x^2\\).... | 9 |
[
{
"content": "A player pays $\\$5$ to play a game. A six-sided die is rolled. If the number on the die is odd, the game is lost. If the number on the die is even, the die is rolled again. In this case the player wins some amount of money if the second number matches the first and loses otherwise. How much money... | 60 |
[
{
"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... | 0.885 mm |
[
{
"content": "Everyone in a class of 35 students takes math and history. 8 students received an A in history, 15 received an A in math and 3 received an A in both courses. How many students did not receive an A in either course?",
"role": "user"
}
] | 15 |
[
{
"content": "Given a group $G$ and two subgroups $H$ and $K$ such that $H, K \\subseteq G$, if for a fixed element $k \\in K$, the conjugate $kHk^{-1}$ is a subset of $H$, does it necessarily follow that $kHk^{-1} = H$? Answer \"yes\" or \"no.\"",
"role": "user"
}
] | no |
[
{
"content": "Determine whether the statement \"All Eulerian graphs are also Hamiltonian\" is true or false.",
"role": "user"
}
] | False |
[
{
"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... | 0.38 |
[
{
"content": "A merchant bought a quantity of cotton and exchanged it for oil, which he then sold. The number of kilograms of cotton, the number of liters of oil obtained per kilogram, and the number of rupees for which he sold the oil form a decreasing geometric progression. If he had obtained 1 kilogram more ... | 64000 |
[
{
"content": "Find the last three digits of \\(19^{100}\\).",
"role": "user"
}
] | 001 |
[
{
"content": "Evaluate the limit using L'Hopital's Rule, considering the fifth derivative of the numerator and denominator: $$\\lim_{x\\to 0}\\frac{x^4 - \\sin x^2}{x^6 + \\cos x}$$",
"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... | $28,420 |
[
{
"content": "Let \\( x_n = 2^{2^n} + 1 \\) and let \\( m \\) be the least common multiple of \\( x_2, x_3, \\ldots, x_{1971} \\). Find the last digit of \\( m \\).",
"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... | 0.57 m |
[
{
"content": "Does a convergent and bounded sequence of positive semidefinite matrices always converge to a positive semidefinite matrix?",
"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... | 11.00% |
[
{
"content": "Evaluate the limit: \\( \\lim_{n \\to \\infty} n^2 C_n \\), where \\( C_n = \\int^{1/n}_{1/(n+1)} \\frac{\\tan^{-1}(nx)}{\\sin^{-1}(nx)} \\, dx \\). Choose the correct answer from the following options: (a) 1, (b) 0, (c) -1, (d) \\( \\frac{1}{2} \\).",
"role": "user"
}
] | D |
[
{
"content": "Compute the triple integral \\( I = \\int_{-1}^{1} \\int_{x^{2}}^{1} \\int_{0}^{z} (4+z) \\, dz \\, dy \\, dx \\) and describe its region of integration.",
"role": "user"
}
] | \dfrac{122}{35} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.