prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine the generating function for the summation: \\[ \\sum_{k=0}^m\\binom{m}{m-k}\\binom{-n-1}{m-k} \\]",
"role": "user"
}
] | (1 - x)^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... | 52.654e27 |
[
{
"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... | Fixed Cost Allocation:
Air Express: $1,320,000
Ground Service: $3,960,000
Variable Cost Allocation:
Air Express: $2,024,000
Ground Service: $1,584,000
Total Cost Allocation:
Air Express: $3,344,000
Ground Service: $5,544,000 |
[
{
"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... | 35.2 m/s |
[
{
"content": "Find the modular inverse of $x^4$ in $GF(2^5)$ modulo the polynomial $x^5 + x^2 + 1$. Provide your answer as a polynomial in $GF(2^5)$. What is the inverse?",
"role": "user"
}
] | x^3 + x + 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... | +191.9 J/K |
[
{
"content": "Determine whether the limit of the infinite product \\( (1+\\frac{1}{a_n})(1+\\frac{1}{a_{n-1}})\\cdots(1+\\frac{1}{a_1}) \\), where the sequence \\( a_n \\) is defined recursively by \\( a_n = n(1+a_{n-1}) \\) with \\( a_1 = 1 \\), is \\( \\frac{1}{2} \\).",
"role": "user"
}
] | e |
[
{
"content": "Find all functions \\( f : \\mathbb{R} \\to \\mathbb{R} \\) that satisfy the functional equation \\( f(f(x)+3y)=12x + f(f(y)-x) \\).",
"role": "user"
}
] | f(x) = 3x + 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... | {\frac{\vec{r}_1 - \vec{r}_2}{|\vec{r}_1 - \vec{r}_2|} = \frac{\vec{v}_1 - \vec{v}_2}{|\vec{v}_1 - \vec{v}_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... | 2.96e5 Pa |
[
{
"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... | 17.4 m/s |
[
{
"content": "In the figure, triangles $\\Delta ADB$, $\\Delta PCB$, and $\\Delta EFG$ are right triangles with $PB=AE$ and $AC=CB$. Given that $\\angle A = \\angle CPB$ and $EF=AC$, determine the value of $\\angle G$. \\(\\boxed{?}\\)",
"role": "user"
}
] | 45^\circ |
[
{
"content": "In \\(\\mathbb{R}^n\\), a path-connected subset \\(A\\) is also arc-connected. Given any finite subset \\(B\\) of \\(A\\), is there an arc that passes through all the points of \\(B\\)?",
"role": "user"
}
] | Yes |
[
{
"content": "Let $P$ be a torsion group where every element has an order that is a power of a prime $p$, i.e., a torsion $p$-group. Suppose $P$ acts on a finite set $X$. Is it true that every orbit of this action has a length that is a power of $p$?",
"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... | 0.27 |
[
{
"content": "Find the coefficient of \\(x^{20}\\) in the expansion of \\((x^3 + x^4 + x^5 + \\ldots)^5\\).",
"role": "user"
}
] | 126 |
[
{
"content": "Determine if there exist intervals \\((a, b)\\) such that the number of prime squares \\((p^2)\\) within the interval exceeds the number of primes \\((p)\\) within the same interval.",
"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... | $23.24 |
[
{
"content": "Evaluate the integral: $$\\int_0^{\\infty} x^{k-1} e^{-Ax^k} \\, dx$$",
"role": "user"
}
] | \dfrac{1}{A k} |
[
{
"content": "Find the maximum value of the function \\( f(x) \\) given that \\( f(x) + f\\left(\\frac{1}{x}\\right) = x \\) for all \\( x \\) in its domain.",
"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... | 1530 Hz (moving toward) or 1410 Hz (moving away) |
[
{
"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... | 181 degrees Celsius |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to \\infty}\\left[(n+1)\\int_0^1x^n\\ln(1-x)\\,dx\\right]$$",
"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... | $1.92 |
[
{
"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... | 40 hours |
[
{
"content": "Determine the number of fixed points for the function \\( f(x) = \\cos \\frac{1}{x} \\) on the interval \\((0, 1]\\).",
"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... | 2.16 |
[
{
"content": "Find the remainder when \\(2018^{2017^{16050464}}\\) is divided by 1001.",
"role": "user"
}
] | 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... | 130.6 % |
[
{
"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... | $38,112.15 |
[
{
"content": "Let $a$ be a positive real number. In the coordinate plane, denote by $S$ the area of the region bounded by the curve $y = \\sin x$ for $0 \\leq x \\leq \\pi$ and the $x$-axis. Denote by $T$ the area of the region bounded by the curves $y = \\sin x$ and $y = a \\cos x$ for $0 \\leq x \\leq \\frac{... | \dfrac{4}{3} |
[
{
"content": "Evaluate the limit: \\[ \\lim_{b \\to \\infty}\\int_{0}^{\\infty}\\frac{y}{1 + y^{2}}e^{-by}dy. \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the number of semi-direct products \\(H \\rtimes Q\\) that can be constructed for \\(H \\cong C_{42}\\) and \\(Q \\cong C_{3}\\).",
"role": "user"
}
] | 2 |
[
{
"content": "Is the direct limit of a directed set of commutative local rings a local ring? Let \\( \\{R_i\\}_{i\\in A} \\) be a directed set of commutative local rings with a directed index set \\( A \\), and let \\( R \\) be the direct limit of this set. Determine if \\( R \\) is a local ring.",
"role": ... | Yes |
[
{
"content": "Given a polynomial $P(x)$ of degree 4 with the following conditions: $P(2) = -1$, $P'(2) = 0$, $P''(2) = 2$, $P'''(2) = -12$, and $P''''(2) = 24$. Find the value of $P''(1)$.",
"role": "user"
}
] | 26 |
[
{
"content": "Calculate the residue of the function \\( f(z) = \\sin\\left(\\frac{z^2+1}{z}\\right) \\) at \\( z = 0 \\).",
"role": "user"
}
] | J_1(2) |
[
{
"content": "Given the matrices:\n$$W = \\begin{bmatrix} w_{00} & w_{01} & w_{02} \\\\ w_{10} & w_{11} & w_{12} \\\\ w_{20} & w_{21} & w_{22}\\\\ w_{30} & w_{31} & w_{32} \\end{bmatrix} \\quad \\text{and} \\quad X = \\begin{bmatrix} x_{00} & x_{01} & x_{02} & x_{03}\\\\ x_{10} & x_{11} & x_{12} & x_{13} \\\\ x... | 9 \times 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... | 23.52 m/s |
[
{
"content": "Let $H$ be a Hilbert space with an orthonormal basis $\\{e_k\\}$. Consider an operator $A: D(A) \\subset H \\to H$ that generates a strongly continuous semigroup $e^{At}$, where $A$ satisfies $Ae_k = -\\lambda_k e_k$ with eigenvalues $\\lambda_k > 0$ such that $\\inf_k \\lambda_k = \\lambda > 0$. ... | Yes |
[
{
"content": "Find the radius of convergence for the power series \\( \\sum_{n=0}^{\\infty} n^n (x-1)^n \\).",
"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... | 2Ag^+ + SO4^2- -> Ag2SO4(s) |
[
{
"content": "Calculate the limit \\( \\lim_{x\\to\\infty}\\intop_{x}^{2x}\\frac{1}{t}\\cos\\left(\\frac{1}{t^{2}}\\right)dt \\).",
"role": "user"
}
] | \ln 2 |
[
{
"content": "In \\(\\triangle ABC\\), where \\(\\angle ABC = 120^\\circ\\) and \\(AB = BC = 2\\), point \\(D\\) is located on side \\(AC\\) (excluding \\(A\\) and \\(C\\)). \\(\\triangle ABD\\) is folded along segment \\(BD\\) to form \\(\\triangle PBD\\). When the plane \\(PBD\\) is perpendicular to the plane... | 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... | -4.6667 |
[
{
"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... | 0.37 m/s^2 |
[
{
"content": "Determine whether the complex sequence \\( \\{a_n\\} \\) defined by \\( a_0=0 \\) and \\( a_n=\\frac{1}{2i+a_{n-1}} \\) for \\( n\\geq 1 \\) converges.",
"role": "user"
}
] | -i |
[
{
"content": "Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis, and a tangent line to the graph of \\( f(x) = (x + 2)^{-2} \\).",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Calculate the limit: \\( \\lim_{x \\to 0^-} (x+1)^{(x+1)^{x}} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Select numbers $a$ and $b$ between 0 and 1 independently and at random, and let $c$ be their sum. Let $A$, $B$, and $C$ be the results when $a$, $b$, and $c$, respectively, are rounded to the nearest integer. What is the probability that $A+B=C$?",
"role": "user"
}
] | \frac{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... | $477,586.92 |
[
{
"content": "Given a circle \\( \\circ O \\) centered at point \\( O \\) with a point \\( A \\) on it, inscribe a square \\( \\square ABCD \\) within the circle using exactly seven compass-and-straightedge steps. The first two steps should use the compass, the third step should use the straightedge, and the la... | ABCD |
[
{
"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... | Regulatory price method |
[
{
"content": "Find the minimum value of the function \\( \\fermi(k) = \\int_{0}^{1} |x^{2} - k^{2}| \\, dx \\) for \\( k \\in [-1, 1] \\).",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Given \\(x=\\frac{2z^2}{1+z^2}, y=\\frac{2x^2}{1+x^2}, z=\\frac{2y^2}{1+y^2}\\), find the value of \\(\\left[\\frac{1}{x}+\\frac{1}{y}+\\frac{1}{z}\\right]\\).",
"role": "user"
}
] | 3 |
[
{
"content": "Given a linear operator $Q: V \\rightarrow V$ that is a projection, meaning $Q \\circ Q = Q$, find a basis $E = \\{e_1, \\ldots, e_n\\}$ and an integer $k \\in \\{1, \\ldots, n\\}$ such that $Q$ can be represented by a block diagonal matrix with an $I_k$ identity matrix of size $k \\times k$, and ... | k = \dim(\operatorname{Im}(Q)) |
[
{
"content": "In a triangle, if the segments of the medians that lie inside the incircle are of equal length, does it necessarily mean that the triangle is equilateral? Answer 'yes' or 'no' and justify your answer.",
"role": "user"
}
] | yes |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 0} \\frac{1}{x^3}\\int_{0}^{x} \\sin^{2}(3t)\\,dt \\]",
"role": "user"
}
] | 3 |
[
{
"content": "Is there an operator $T: X \\rightarrow Y$ that factors through a Banach space $Z$ containing no complemented copy of $l_1$, but does not factor through any Banach space $W$ containing no copy of $l_1$?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the angle between an antisymmetric matrix $A$ and a symmetric matrix $S$ in $M_n(\\mathbb{R})$ using the inner product defined as $(A,B)=\\text{tr}(AB^T)$. Express your answer in terms of the matrices' properties.",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "Consider the region in the first quadrant bounded by the curves \\( y = x^2 \\) and \\( y = 9 \\). This region is rotated around the vertical line \\( x = 3 \\) to form a solid. Determine the height \\( m \\) of the horizontal line that divides the volume of this solid into two equal parts.",
... | 5.18 |
[
{
"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... | 0.26 meter |
[
{
"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... | $10,627 |
[
{
"content": "Find the extreme values of the function \\(f(x,y,z)=x^2+y^2+z^2\\) subject to the constraint \\(z=xy+2\\).",
"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... | 6437.46 |
[
{
"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... | 1068.74 |
[
{
"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... | 15.905 |
[
{
"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... | 738 mL |
[
{
"content": "Determine whether the following statement is true or false: A sequence $(x_n)$ converges if every subsequence of $(x_n)$ has a further subsequence that converges, without assuming that all convergent subsequences have the same limit.",
"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... | 50 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... | 0.0096 kg |
[
{
"content": "Determine whether the following statement is true or false:\n\nLet \\( f:\\mathbb{R}\\to\\mathbb{R} \\) be a continuous function. For every non-negative sequence of real numbers \\( x_n \\) such that \\( \\lim_{n\\to\\infty}x_n=\\infty \\), the sequence \\( f(x_n) \\) has a convergent subsequence ... | 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... | 0.00161 mol |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty}\\frac{[x]+[2^2x]+\\dots +[n^2x]}{n^3} \\] where \\([.]\\) denotes the floor function.",
"role": "user"
}
] | \dfrac{x}{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... | 8,000 units |
[
{
"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... | 0.313 g |
[
{
"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... | Sn + H2O + e- -> HSnO2- + H+ |
[
{
"content": "Is the set \\( \\{(x,y,z) \\in \\mathbb{R}^3 : x^2 - y^2z^2 = 0\\} \\) Zariski closed?",
"role": "user"
}
] | Yes |
[
{
"content": "Given that \\(0 < \\alpha \\leqslant \\beta \\leqslant \\gamma\\) and \\(\\alpha + \\beta + \\gamma = \\pi\\), find the range of possible values for \\(\\min \\left\\{\\frac{\\sin \\beta}{\\sin \\alpha}, \\frac{\\sin \\gamma}{\\sin \\beta}\\right\\}\\).",
"role": "user"
}
] | \left[1, \frac{1 + \sqrt{5}}{2}\right] |
[
{
"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... | 14.0175 feet per second |
[
{
"content": "Given the system of equations:\n\\[\\frac{2x+3y}{a-2b} = \\frac{4y+7z}{3b-c} = \\frac{6z+5x}{2c-3a}\\]\nDetermine the value of \\(11x+17y+20z\\) using a clever approach, without employing matrices or determinants.",
"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... | 190 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... | 6.74 J |
[
{
"content": "Let $A$ be a finitely generated $k$-algebra, where $k$ is an algebraically closed field, and $A$ is of dimension one and integrally closed in its quotient field $K$. Let $R \\subseteq K$ be a valuation ring. Is it true that $A \\subseteq R$?",
"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... | 541Hz |
[
{
"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... | $7,299.82 |
[
{
"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... | 50424 |
[
{
"content": "Determine if there exists a differentiable function \\( f(x, y) \\) for vectors \\( x \\) and \\( y \\), such that \\( f(x, y) = -f(y, x) \\), where the output of \\( f \\) is a single real number.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the remainder when \\(15! \\times 10!\\) is divided by 2023, where 2023 is a prime number.",
"role": "user"
}
] | 609 |
[
{
"content": "Evaluate the limit of the complex function as \\( z \\to 0 \\): \\[ \\lim_{z \\to 0} z \\log(\\sin \\pi z) \\] where \\( z \\in \\mathbb{C} \\).",
"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... | 520 nm |
[
{
"content": "Let $1 < k < d$ be integers. Suppose $A \\in \\text{End}(\\bigwedge^k \\mathbb{R}^d)$ and $A = \\bigwedge^k B$ for some complex matrix $B \\in \\text{End}(\\mathbb{C}^d)$. Does there exist a real matrix $M \\in \\text{End}(\\mathbb{R}^d)$ such that $A = \\bigwedge^k M$?",
"role": "user"
}
] | No |
[
{
"content": "Let \\( V \\) be an open connected subset of \\( \\mathbb{R}^2 \\). Determine whether it is true that for every compact set \\( K \\subseteq V \\), there exist a compact set \\( A \\) and an open connected set \\( B \\subseteq \\mathbb{R}^2 \\) such that \\( K \\subseteq B \\subseteq A \\subseteq ... | True |
[
{
"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... | 432 |
[
{
"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... | 1.04e-2 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... | 40 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... | 5.75e-4 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... | 6.42 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... | 2.49e11 kg m^2/s |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to1}\\frac{e^{(x^x-1)}-x^x}{(x^x-1)^2(x^{x}+1)^2}$$",
"role": "user"
}
] | \dfrac{1}{8} |
[
{
"content": "A square $ABCD$ has an area of $4 \\sqrt{3}$. Its vertices lie on a circle $\\Gamma$. The circle $\\Gamma$ is tangent to the sides $[MN]$, $[NP]$, and $[PM]$ of an equilateral triangle $MNP$. Find the area of triangle $MNP$.",
"role": "user"
}
] | 18 |
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