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... | 1.25 |
[
{
"content": "In triangle $ABC$, the medians from vertices $A$ and $B$ are perpendicular. Given that $BC = 36$ and $AC = 48$, find the area of the square with side $AB$. Express your answer in square units.",
"role": "user"
}
] | 720 |
[
{
"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... | 4.04e-3 % |
[
{
"content": "Evaluate the integral \\( I(z) = \\int_0^{2\\pi} \\frac{e^{-it} \\, dt}{e^{it} - z} \\) for \\( |z| < 1 \\). Determine if \\( I(z) = 0 \\) for these values of \\( z \\).",
"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... | 355.26 |
[
{
"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... | 0.263 M |
[
{
"content": "Evaluate the line integral \\( \\int_{\\vert x \\vert + \\vert y \\vert = 5 } -\\frac{y}{x^2 + y^2} \\, dx + \\frac{x}{x^2 + y^2} \\, dy \\) for the vector field \\( F(x,y)=\\left(-\\frac{y}{x^2 + y^2} , \\frac{x}{x^2+y^2}\\right) \\) in \\( \\mathbb{R}^2 \\).",
"role": "user"
}
] | 2\pi |
[
{
"content": "Evaluate the limit \\( \\lim_{x\\to+\\infty} x \\cdot e^{-ax^2} \\) for \\( a > 0 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to \\infty}{\\frac{\\int_{x^2}^{3x^2}{t\\cdot \\sin{\\frac{2}{t}}dt}}{x^2}}$$",
"role": "user"
}
] | 4 |
[
{
"content": "Determine the minimum number of points that must be marked inside a convex $n$-gon so that every triangle formed by the vertices of the $n$-gon contains at least one marked point inside.",
"role": "user"
}
] | n - 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... | 1.09e5 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... | 81 degrees |
[
{
"content": "Consider a random 2D walk starting at the origin. Take \\( n \\) independent steps of length 1, where each step is in the direction of \\( \\theta_i \\), uniformly distributed on \\([0, 2\\pi]\\). Let \\( X, Y \\) be the position after \\( n \\) steps, and define \\( D = X^2 + Y^2 \\). What is the... | 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 million |
[
{
"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... | 8.316 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... | 2444.1 kW |
[
{
"content": "Egor encoded a number using a letter puzzle, where different letters correspond to different digits and the same letters to the same digits. The encoded result was the word \"ГВАТЕМАЛА\". How many different numbers could Egor have originally written if the number was divisible by 30?",
"role":... | 21600 |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{\\infty} \\left(\\frac{\\sin x}{x}\\right)^2\\,dx \\) using the residue theorem, considering the presence of a pole of the second order on the real axis.",
"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... | $82,885.37 |
[
{
"content": "Find the volume of the set \\(S_n(a) = \\{(x_1, \\ldots, x_n) \\in \\mathbb{R}^n : x_1 + \\cdots + x_n < a, \\text{ and } x_i > 0\\}\\).",
"role": "user"
}
] | \dfrac{a^n}{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... | 0.33 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... | 8.51% |
[
{
"content": "Determine whether the matrix $X^TX$ can have zero eigenvalues when $X$ is a real $n \\times p$ matrix with $p > n$. Provide a derivation to support your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Solve the equation \\( \\frac{72_8!}{18_2!} = 4^x \\), where \\( n_a! \\) is defined as \\( n_a!:=n(n-a)(n-2a)\\ldots(n-ka) \\) for \\( n>ka \\). Find the value of \\( x \\).",
"role": "user"
}
] | 9 |
[
{
"content": "Calculate the value of the expression \\(\\sqrt{86+41 \\sqrt{86+41 \\sqrt{86+\\ldots}}}\\) rounded to one decimal place.",
"role": "user"
}
] | 43.0 |
[
{
"content": "Let \\( U \\) be the unit circle. Define \\( V \\) as the set of all points on the unit circle that have a rational angle from the positive X-axis. Let \\( H \\) be the boundary of the convex hull of \\( V \\). Determine if \\( H \\) is equal to either \\( U \\) or \\( V \\).",
"role": "user"
... | U |
[
{
"content": "How many positive integer values of $x$ are solutions to the inequality $10 < -x + 13$?",
"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... | Factors such as a fall in consumer income, a fall in the prices of substitute goods, availability of new alternatives, and change in the taste and preference of the consumers may decrease the demand. |
[
{
"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... | 0.45 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... | 4.30e9 rev/day |
[
{
"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... | 10.07 V |
[
{
"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... | 1907.54 |
[
{
"content": "Can a metric be defined on a set $Y$, which contains more than one element, such that every continuous mapping $f: \\mathbb{R} \\rightarrow Y$ is constant? 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... | v_a = -7.5 m/s, v_b = 2.5 m/s |
[
{
"content": "Evaluate the limit: $$\\lim \\limits_{x \\rightarrow 0}\\left(\\frac{1}{x^2}-\\frac{1}{\\sin^2(x)}\\right)$$",
"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... | 0.389 J/g.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... | 91000 |
[
{
"content": "Determine the largest positive integer \\( n \\) such that there exists a set of \\( n \\) distinct positive integers, each at most 2002, with the property that for any integers \\( a \\) and \\( b \\) in the set, neither \\( a^2 \\) nor \\( ab \\) is in the set.",
"role": "user"
}
] | 1958 |
[
{
"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... | 1.60A |
[
{
"content": "Use Green's theorem to evaluate the line integral \\( \\int_{L} (x+2xy)dy + y^{2}dx \\) where \\( L \\) is the circle defined by \\( x^2 + y^2 = y \\).",
"role": "user"
}
] | \dfrac{\pi}{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... | 13.82 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... | $7,680,000 |
[
{
"content": "Find the limit of the sum \\( \\frac{1}{n} \\sum_{k=1}^n n^{1/k} \\) as \\( n \\) approaches infinity.",
"role": "user"
}
] | 2 |
[
{
"content": "What is the best known bound on the index of an abelian subgroup in a discrete subgroup of the Euclidean isometry group \\( \\isom(\\mathbb{R}^n) \\)?",
"role": "user"
}
] | 2^n 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... | 10.59% |
[
{
"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... | F=m(1-(v^2)/(c^2))^(-3/2)(dv)/(dt) |
[
{
"content": "Find the value of $w(0,\\pi)$ for the function $w(x,t)$ that satisfies the partial differential equation \\( w_{xx} - w_{tt} = 0 \\), where \\( x \\in \\mathbb{R} \\) and \\( t > 0 \\), with the initial conditions \\( w(x,0) = \\cos(x) + x^2 \\) and \\( w_{t}(x,0) = 0 \\) for every \\( x \\in \\ma... | \pi^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... | 0.0544 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... | 0.023 kg-m^2 |
[
{
"content": "Can a one-to-one correspondence be established between the interval $[0,1]$ and the natural numbers by mapping the decimal representation of a real number to a natural number formed by concatenating its digits?",
"role": "user"
}
] | No |
[
{
"content": "Compute the limit: \\[ \\lim_{n\\to\\infty}\\int_{0}^{\\infty}\\frac{dx}{x^{n}+1}. \\]",
"role": "user"
}
] | 1 |
[
{
"content": "Determine the complexity of an algorithm that tests whether a given polynomial is a square in a finite field with small characteristic.",
"role": "user"
}
] | O(n^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... | 3.51 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... | $146.5 |
[
{
"content": "Determine the value of $q$ for which the integral \\( \\int^{1}_{0}\\frac{1}{(\\tan (x))^{q}}dx \\) converges.",
"role": "user"
}
] | q < 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... | 16.58 |
[
{
"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... | 30319.4N |
[
{
"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... | 56422.85271 years |
[
{
"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... | 1.72e19 electrons |
[
{
"content": "In a right triangle $ABC$ with hypotenuse $\\overline{AC}$ and circumcenter $O$, point $E$ is on $\\overline{AB}$ such that $AE = 9$ and $EB = 3$. Point $F$ is on $\\overline{BC}$ such that $BF = 6$ and $FC = 2$. Let $W, X, Y$, and $Z$ be the midpoints of $\\overline{EB}$, $\\overline{BF}$, $\\ove... | 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... | -22.4 cm |
[
{
"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... | 46.35 m/s, 62.76 degrees west of north |
[
{
"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... | 8.89 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... | R1 = 3.408 ohms and R2 = 26.591 ohms |
[
{
"content": "Consider the set \\( A = \\{1, 2, 3, 4, \\cdots, 2^n\\} \\), where \\( n \\geq 2 \\). If the sum of two elements in set \\( A \\) is a power of 2, then exactly one of them belongs to subset \\( B \\). Determine the number of such subsets \\( B \\) in set \\( A \\).",
"role": "user"
}
] | 2^{n+1} |
[
{
"content": "In a metric space $X$, if $E$ is an open subset, is the set of all limit points of $E$, denoted as $E'$, a subset of $E$? Answer with 'Yes' or 'No'.",
"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... | 7.94% |
[
{
"content": "Evaluate the triple integral \\( \\int \\int \\int z(x^2+y^2+z^2)^{-\\frac{3}{2}} \\, dx \\, dy \\, dz \\) over the region defined by \\( x^2+y^2+z^2 \\leq 36 \\) and \\( z \\geq 3 \\).",
"role": "user"
}
] | \dfrac{3\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... | $8,587 |
[
{
"content": "Determine whether there exists a continuous function \\( f: \\mathbb{R} \\setminus \\mathbb{Q} \\rightarrow \\mathbb{R} \\setminus \\mathbb{Q} \\) such that \\( f \\) does not have a fixed point.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether there exists a continuous function \\( f: \\Bbb R \\to \\Bbb R \\) such that \\( f(\\Bbb Q) \\subseteq \\Bbb R \\setminus \\Bbb Q \\) and \\( f(\\Bbb R \\setminus \\Bbb Q) \\subseteq \\Bbb Q \\). Answer 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... | 0.61 |
[
{
"content": "Determine which of the following graphs cannot have its edges partitioned into triangles:\n\n(a) K7\n(b) K12\n(c) K3,3,3\n(d) K5,5,5\n\nSelect the correct option.",
"role": "user"
}
] | B |
[
{
"content": "In the given geometric figure, calculate the ratio \\( \\frac{\\text{area}(\\triangle CDF)}{\\text{area}(\\triangle CEF)} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the convergence rate of the Newton iteration for the polynomial \\( f(x) = 8x^4 - 12x^3 + 6x^2 - x \\) when started close to the root \\( r = 0 \\).",
"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... | 138 N |
[
{
"content": "In a Hilbert space $X$, let $C \\in L(X, \\mathbb{C})$, $B \\in L(\\mathbb{C}, X)$, and $(sI-A)^{-1} \\in L(X)$, where $A$ generates a holomorphic semigroup. Determine the rank of the operator $C(sI-A)^{-1}B$. Provide a justification for your answer.",
"role": "user"
}
] | 1 |
[
{
"content": "If $|z_1 - z_2| = |z_1 + z_2|$, prove that $\\arg(z_1) - \\arg(z_2) = \\frac{\\pi}{4}$. ",
"role": "user"
}
] | \frac{\pi}{2} |
[
{
"content": "Determine whether there exists a function $f$ such that at a point $c$, the second derivative $f''(c) = 1$, the first derivative $f'(c) = 0$, and the second derivative $f''$ is not continuous on any open interval containing $c$. Provide 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... | 9.09% |
[
{
"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... | 0.25 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... | 123300 |
[
{
"content": "Given the equation \\(x^5 - 2x^4 + 3 = 0\\) with roots \\(\\alpha, \\beta, \\gamma, \\delta, \\epsilon\\), use the substitution \\(y = x^4\\) to find the value of \\(\\alpha^8 + \\beta^8 + \\gamma^8 + \\delta^8 + \\epsilon^8\\).",
"role": "user"
}
] | 64 |
[
{
"content": "Find a function \\( f(m, n) \\) that satisfies the following conditions for every pair of non-negative integers \\( m, n \\):\n1. \\( 2f(m, n) = 2 + f(m+1, n-1) + f(m-1, n+1) \\) for \\( m \\geq 1 \\) and \\( n \\geq 1 \\);\n2. \\( f(m, 0) = f(0, n) = 0 \\).",
"role": "user"
}
] | f(m, n) = mn |
[
{
"content": "Let $f$ be a continuous function on the interval $[0, \\pi]$. If \\( \\int_{0}^{\\pi} f(x) \\sin(nx)\\,dx = 0 \\) for all integers \\( n \\geq 1 \\), is $f$ necessarily the zero function on $[0, \\pi]$?",
"role": "user"
}
] | Yes |
[
{
"content": "Find \\( \\lim_{x \\to \\infty}\\int_0^x{e^{-x^2+t^2}}\\,dt \\).",
"role": "user"
}
] | 0 |
[
{
"content": "In a right triangle, the height dropped onto the hypotenuse is $h$. Determine the minimum length of the median that bisects the longer leg of the triangle.",
"role": "user"
}
] | \dfrac{3h}{2} |
[
{
"content": "If $f, g: \\mathbb{R} \\rightarrow \\mathbb{R}$ are differentiable functions and $h: \\mathbb{R} \\rightarrow \\mathbb{R}$ is such that $f = g \\circ h$, must $h$ also be differentiable? Answer 'yes' or 'no' and justify your answer.",
"role": "user"
}
] | no |
[
{
"content": "Compute \\(12^{45} \\mod 47\\) using an efficient method other than repeated squaring.",
"role": "user"
}
] | 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... | 1828.9 N |
[
{
"content": "Given a symmetric positive semi-definite matrix $A = \\{a_{ij}\\}$, where $0 < a_{ij} < 1$, determine if the matrix $B = \\{\\frac{1}{1 - a_{ij}}\\}$ is also a symmetric positive semi-definite matrix.",
"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... | 35.7 m |
[
{
"content": "Does there exist a sequence of functions \\(\\{g_n\\}\\) defined on \\([0, 1]\\) such that each \\(g_n\\) is discontinuous at a dense subset of \\([0, 1]\\), yet the sequence converges uniformly to a function that is continuous on \\([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... | 2.085e-21 kg |
[
{
"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... | 1.9e3 degrees Celsius |
[
{
"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... | 10.95% |
[
{
"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... | C=A/(epsilon*l) |
[
{
"content": "Solve the Cauchy problem for the partial differential equation $u_x + (x+y) u_y = 1$ with the initial condition $u(x, -x) = 0$ using the method of characteristics.",
"role": "user"
}
] | \ln(x + y + 1) |
[
{
"content": "In a Boolean algebra \\( A = (A, \\vee, \\wedge) \\), which of the following conditions is sufficient to ensure that \\( \\overline{x} = y \\) for all \\( x, y \\in A \\)?\n\n1. \\( x + y = 1_A \\).\n2. \\( x \\cdot y = 0_A \\; \\wedge \\; x \\neq 0_A \\).\n3. \\( x \\cdot (x + y) = \\overline{y} ... | D |
[
{
"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... | $9,233.51 |
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