prompt list | ground_truth string |
|---|---|
[
{
"content": "Evaluate the double integral \\(\\iint_R(y-2x^2)\\,dx\\,dy\\) where \\(R\\) is the region inside the square defined by \\(|x|+|y|=1\\).",
"role": "user"
}
] | -\dfrac{2}{3} |
[
{
"content": "Determine if there exists a constant $c$ such that for sufficiently large $n$, the inequality \\( \\binom{2n}{n+10} \\geq c\\cdot\\frac{2^{2n}}{\\sqrt{\\pi n}} \\) holds true.",
"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... | Current liabilities:
Accounts payable $204,100
Notes payable (due May 1 2018) 26,000
Unearned rent revenue 312,000
FICA taxes payable 10,140
Interest payable 52,000
Income taxes payable 4,550
Sales taxes payable 2,210
Total current liabilities $611,000
Non-current liabilities:
Bonds payable (due 2021) 1,170,000
Less: 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... | 117,500 shares |
[
{
"content": "Evaluate the complex integral \\(\\int_{|z|=2}\\frac{e^{3z}}{z^3}dz\\) using the limit formula for higher order derivatives.",
"role": "user"
}
] | 9\pi i |
[
{
"content": "In the expansion of \\((1+2x)^{100}\\), let \\(a_k\\) be the coefficient of \\(x^k\\). Determine how many integers \\(r\\) satisfy \\(0 \\leq r \\leq 99\\) such that \\(a_r < a_{r+1}\\).",
"role": "user"
}
] | 67 |
[
{
"content": "If a sequence of random variables \\(\\{X_n\\}\\) converges almost surely to a constant \\(c\\), does the sequence \\(\\{X_n^3\\}\\) converge almost surely to \\(c^3\\)? Answer \"Yes\" or \"No\" and justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to a} \\left(\\frac{\\sin(x)}{\\sin(a)}\\right)^{\\frac{1}{x-a}}$$ where $a$ is any real number.",
"role": "user"
}
] | e^{\cot(a)} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.96 V |
[
{
"content": "A regular $2008$-gon is positioned in the Cartesian plane such that $(x_1,y_1)=(p,0)$ and $(x_{1005},y_{1005})=(p+2,0)$, where $p$ is a prime number. The vertices are arranged in counterclockwise order as \\((x_1,y_1),(x_2,y_2),(x_3,y_3),\\ldots,(x_{2008},y_{2008})\\). Define \\(S=(x_1+y_1i)(x_3+y... | 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... | 382.8 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... | 10235 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... | 461 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... | $3,244.64 |
[
{
"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... | 1.6e3 kg/m^3 |
[
{
"content": "Determine whether $10^{8}!$ is greater than $10^{10^9}$. Answer with 'yes' or 'no'.",
"role": "user"
}
] | no |
[
{
"content": "Let $G$ be a group of order $pq$, where $p$ and $q$ are distinct prime numbers. Determine the order of the center $Z(G)$. Choose the correct option: (i) 1 or $p$, (ii) 1 or $q$, (iii) 1 or $pq$, (iv) None of these.",
"role": "user"
}
] | iii |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\rightarrow \\infty}n^2\\left[\\left(1+\\frac{1}{1+n}\\right)^{n+1}-\\left(1+\\frac{1}{n}\\right)^{n}\\right].$$",
"role": "user"
}
] | \dfrac{e}{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... | 1.58e-8 ohm m |
[
{
"content": "It takes Michael 0.30 hours to walk to school. How many seconds does it take him to walk to school?",
"role": "user"
}
] | 1080 |
[
{
"content": "An insurance policy covers two employees of a company, reimbursing no more than one loss per employee per year, up to a company-wide maximum of $8000. The probability of an employee incurring a loss is $40\\%$, with losses uniformly distributed between $(1000, 5000)$, independent of other employee... | \dfrac{2}{51} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 99.7% |
[
{
"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... | 133 rev |
[
{
"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... | $4,860 |
[
{
"content": "Find the value of \\( \\frac{\\partial w}{\\partial x} \\) at the point \\((x=0,y=0)\\) for the function \\( w = \\ln\\left(e^{(x^2+y)^2} + e^{(y^2+x)^2}\\right) \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Let $a$, $b$, and $c$ be positive real numbers such that \\[ \\frac{a^3+2a}{a^2+1} + \\frac{b^3+2b}{b^2+1} + \\frac{c^3+2c}{c^2+1} = \\frac{9}{2}. \\] Determine whether the inequality \\[ \\frac{1}{a} + \\frac{1}{b} + \\frac{1}{c} \\ge 3 \\] holds true.",
"role": "user"
}
] | 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... | 0.147 |
[
{
"content": "Determine the number of complex numbers \\( z \\) such that \\( z^{60} = -1 \\) and \\( z^k \\neq -1 \\) for all integers \\( k \\) where \\( 0 < k < 60 \\).",
"role": "user"
}
] | 32 |
[
{
"content": "Evaluate the integral: \\[ \\int_0^{\\ln 2}\\left(\\frac{1}{e^x-1} - \\left\\lfloor\\frac{1}{e^x-1}\\right\\rfloor\\right)dx \\]",
"role": "user"
}
] | 1 - \ln 2 |
[
{
"content": "Determine the number of subgroups of the group \\( \\Bbb Z_{10} \\oplus \\Bbb Z_{15} \\) using Goursat's Theorem.",
"role": "user"
}
] | 32 |
[
{
"content": "Evaluate the limit \\( \\lim_{y \\to 0}\\frac{1}{\\ln(y)}\\int_{y}^1\\frac{1-\\cos(x)}{x^3}dx \\). Justify the steps used in your calculation.",
"role": "user"
}
] | -\dfrac{1}{2} |
[
{
"content": "Determine the set of statistical cluster points of sub-sequences of the sequence \\( \\frac{n}{e}-\\left[\\frac{n}{e}\\right] \\).",
"role": "user"
}
] | [0,1] |
[
{
"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... | 0.095 M HCl |
[
{
"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... | 85.99 m |
[
{
"content": "Calculate the Laplacian of the function \\( \\frac{1}{r^2} \\), where \\( r = |x| = \\sqrt{x_1^2 + x_2^2 + x_3^2} \\).",
"role": "user"
}
] | \dfrac{2}{r^4} |
[
{
"content": "Given a function \\(f:(a,b)\\to\\mathbb{R}\\) with \\(f'\\) continuous, satisfying \\(f'(x)+(f(x))^2+1\\geq 0\\) for all \\(x\\in(a,b)\\), and the limits \\(\\lim_{x\\to a}f(x)=\\infty\\) and \\(\\lim_{x\\to b}f(x)=-\\infty\\), find the value of \\(b-a\\).",
"role": "user"
}
] | \pi |
[
{
"content": "Let $\\mathbf{u}$ and $\\mathbf{v}$ be unit vectors, and let $\\mathbf{w}$ be a vector such that\n\\[\\mathbf{w} + \\mathbf{w} \\times \\mathbf{u} = \\mathbf{v}.\\]Find the largest possible value of $(\\mathbf{u} \\times \\mathbf{v}) \\cdot \\mathbf{w}.$",
"role": "user"
}
] | \frac{1}{2} |
[
{
"content": "Find all entire functions \\( f(z) \\) such that \\( f(2z) = f(z)^2 \\) and \\( f(0) \\neq 0 \\).",
"role": "user"
}
] | e^{cz} |
[
{
"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... | $229,800 |
[
{
"content": "Evaluate the double integral \\( \\iint\\limits_H \\exp(-(x+y)^2) \\, dx \\, dy \\), where \\( H \\) is the region in the first quadrant of the Cartesian plane, i.e., \\( x, y \\geq 0 \\).",
"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... | $507,136.00 |
[
{
"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... | 25.6 |
[
{
"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... | 9.87 m/s^2 |
[
{
"content": "Determine the optimal step size \\(\\nabla t\\) for the Forward-Backward splitting algorithm, which is used to minimize the sum of two convex functions \\(f(x)\\) and \\(g(x)\\). The iteration is given by:\n\n$$x_{t+1} = \\arg\\min_u \\left\\{ \\frac{1}{2} \\| u - (w_t - \\nabla t \\partial f(w_t)... | \frac{1}{L} |
[
{
"content": "In a game involving two players, A and B, two standard six-sided dice are rolled repeatedly. Player A wins if a total of 2 is rolled first, while player B wins if two consecutive totals of 7 are rolled first. What is the probability that player A wins the game?",
"role": "user"
}
] | \dfrac{7}{13} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.44 mm |
[
{
"content": "Many states use a sequence of three letters followed by a sequence of three digits as their standard license-plate pattern. Given that each three-letter three-digit arrangement is equally likely, the probability that such a license plate will contain at least one palindrome (a three-letter arrange... | 59 |
[
{
"content": "Given two independent exponential random variables $X_1$ and $X_2$ with mean 1, find the probability that the larger of the two, $X_{(2)}$, is greater than three times the smaller, $X_{(1)}$. That is, calculate $P(X_{(2)} > 3X_{(1)})$. Assume $X_1$ and $X_2$ are identically distributed with rate p... | \dfrac{1}{2} |
[
{
"content": "Determine whether a group of order 48 must have a normal subgroup of order 8 or 16.",
"role": "user"
}
] | Yes |
[
{
"content": "Let \\( \\{v_n\\} \\) be a sequence defined by \\( v_0 = b \\in [1,3) \\) and \\( v_n = \\frac{v_{n-1}^3 - 1}{n^2} \\) for all \\( n \\in \\mathbb{N}^* \\). Find \\( \\lim_{n \\to +\\infty} (v_n \\sqrt[3]{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... | 12.35% |
[
{
"content": "Suppose $E$ is an extension field of $\\mathbb{Z}_5$ and $E$ has exactly $78125$ elements. Determine the degree $\\deg(a/\\mathbb{Z}_5)$ for every $a \\in E - \\mathbb{Z}_5$. Provide your answer as a single integer.",
"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... | $87,933.40 |
[
{
"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... | 523,554 |
[
{
"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... | 8.4 x 10-2 M |
[
{
"content": "In a finite group $G$, can there exist a subset $S$ that is closed under multiplication but does not include the inverse of every element in $S$? Answer 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... | $12,797.13 |
[
{
"content": "Find the mass of the solid $E$ enclosed by the planes $z = 0$, $z = x + y + 5$, and the cylinders $x^2 + y^2 = 4$, $x^2 + y^2 = 9$. The density at any point is equal to its distance from the $yz$-plane.",
"role": "user"
}
] | \dfrac{380}{3} |
[
{
"content": "Solve the system of equations for $y$:\n\n$$(4x)^{\\ln 4}=(9y)^{\\ln 9}$$\n$$9^{\\ln x}=4^{\\ln y}$$",
"role": "user"
}
] | \dfrac{1}{9} |
[
{
"content": "Find the value of the product \\( \\sin 1^\\circ \\sin 3^\\circ \\sin 5^\\circ \\cdots \\sin 179^\\circ \\).",
"role": "user"
}
] | \dfrac{1}{2^{89}} |
[
{
"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... | -3.58 ft/sec |
[
{
"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... | 170.0 kJ/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... | 4.75 |
[
{
"content": "If the projections of a space curve \\( \\gamma:[0,1] \\to \\mathbb{R}^3 \\) onto the planes perpendicular to the coordinate axes are rectifiable, does it imply that the space curve \\( \\gamma \\) itself is rectifiable?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the conditional expectation \\( \\mathbb{E}(Y \\mid X) \\) for a random vector \\((X, Y)\\) that is uniformly distributed over the triangle with vertices \\((0,0), (1,0)\\), and \\((1,1)\\).",
"role": "user"
}
] | \dfrac{X}{2} |
[
{
"content": "Find the constant \\( c \\) such that \\( \\sum_{k=1}^{\\infty}\\frac{c \\sin (x+k\\pi)}{2^k} = c\\sin 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... | {"speed": "v_U = \frac{ m_\alpha}{m_U} \sqrt{2K_\alpha}", "direction": "opposite to the motion of alpha particle"} |
[
{
"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... | 20.09 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... | Gaining generativity and integrity |
[
{
"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... | 11.561 |
[
{
"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... | 1330g |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0^+} \\left(\\frac{x}{\\sin x}\\right)^2 \\left(\\frac{\\cos x-1}{x^2}+\\frac{x-\\sin x}{x^3}\\right) \\left(\\cos x+\\frac{\\sin x}{x}\\right)$$",
"role": "user"
}
] | -\dfrac{2}{3} |
[
{
"content": "Let $\\mathbb{C}$ be the field of complex numbers and $\\mathbb{Q}$ the field of rational numbers. Let $G$ be an additive subgroup of $\\mathbb{Q}$. Consider a commutative algebra $R$ over $\\mathbb{C}$ that is a domain and $G$-graded, with each $G$-graded space being 1-dimensional. Is it true tha... | \mathbb{C}[G] |
[
{
"content": "Find the equation of the locus of the centroid of triangle PQR, where the family of lines \\(bx-2y+5=0\\) (with \\(b\\) as a variable) intersect the lines \\(2x+y-4=0\\) and \\(x+2y-5=0\\) at points R and S, respectively.",
"role": "user"
}
] | 4x + 2y = 7 |
[
{
"content": "Determine whether the statement $|S_{n}| = O( \\frac{1}{\\sqrt n} )$ is true, where $|S_{n}|$ represents the surface area of the n-dimensional sphere.",
"role": "user"
}
] | True |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 908.50 |
[
{
"content": "Calculate the determinant of the following matrix, where $a, b, c, d$ are distinct variables:\n\n$$\\begin{vmatrix}\n1 & -(a+b) & ab & 0 \\\\\n0 & 1 & -(c+d) & cd \\\\\n0 & a+b-(c+d) & cd-ab & 0 \\\\\n0 & 1 & -(c+d) & cd\n\\end{vmatrix}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Compute the expected value \\( E[X_{n+1} | X_0, \\dots, X_n] \\) given that \\( X_n = X_0 e^{\\mu S_n} \\), where \\( X_0 > 0 \\), \\( S_n \\) is a symmetric random walk, and \\( \\mu > 0 \\).",
"role": "user"
}
] | X_n \cosh(\mu) |
[
{
"content": "What is the area, in square units, of the interior region formed by the lines $y = 4x - 6, y = -2x +12$ and the $y$-axis?",
"role": "user"
}
] | 27 |
[
{
"content": "Find the value of $x$ such that $2^{33} \\equiv x \\pmod{4725}$ using the Chinese Remainder Theorem and the prime factorization $4725 = 3^3 \\times 5^2 \\times 7$. Calculate $2^{33} \\pmod{3^3}$, $2^{33} \\pmod{5^2}$, and $2^{33} \\pmod{7}$ to determine $x$. Provide a simplified approach for these... | 2717 |
[
{
"content": "Is it true that for every dense subset $S$ of $\\mathbb{R}^3$ and every convex polyhedron $P$, there exists a combinatorially equivalent polyhedron whose vertices all belong to $S$?",
"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... | 8.94% |
[
{
"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... | -284.59 J/mol-K |
[
{
"content": "Find the limit of the sequence \\(x_{n}=\\frac{1}{n+2^{0}}+\\frac{1}{n+2^{1}}+\\ldots+\\frac{1}{n+2^{n}}\\) as \\(n\\) approaches infinity.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the infinite series: \\[ \\sum_{n=1}^{\\infty} \\frac{2^{\\langle n\\rangle}+2^{-\\langle n\\rangle}}{2^n}, \\] where \\( \\langle n \\rangle \\) denotes the integer nearest to \\( \\sqrt{n} \\).",
"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... | 44% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 48.5 KW |
[
{
"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... | 486 |
[
{
"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... | 22.9 g |
[
{
"content": "In quadrilateral \\(ABCD\\), the area is 45. Diagonals \\(AC\\) and \\(BD\\) intersect at point \\(P\\). Points \\(M\\) and \\(N\\) are on sides \\(AB\\) and \\(CD\\) respectively, with \\(MB = \\frac{1}{3} AB\\), \\(BP = \\frac{3}{5} BD\\), \\(NC = \\frac{2}{3} DC\\), and \\(PC = \\frac{2}{3} AC\... | \dfrac{79}{3} |
[
{
"content": "Let $A \\in M_{n}(\\mathbb{C})$. Prove or disprove: If $-2 \\in \\sigma(A^2 + 2A)$, then $-4 \\in \\sigma(A^4)$. Here, $\\sigma$ denotes the spectrum of the matrix.",
"role": "user"
}
] | -4 \in \sigma(A^4) |
[
{
"content": "Let \\( F_{p^n} \\) be a finite field and consider a subfield of order \\( p^d \\) where \\( d \\mid n \\). Suppose we have an irreducible polynomial of degree \\( k \\) over this subfield such that \\( n = dk \\). Is this polynomial a factor of \\( X^q - X \\) where \\( q = p^n \\)?",
"role":... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | {K_{{
m{sp}}}} = \left[ {{
m{S}}{{
m{r}}^{2 + }}} \right]\left[ {{
m{SO}}_4^{2 - }} \right] |
[
{
"content": "Evaluate the limit of the expression as \\( M \\to \\infty \\):\n\\[\n\\lim_{M \\rightarrow \\infty} \\frac{1}{\\sum_{i=0}^{\\infty} \\frac{M!}{(M+i)!} x^i}\n\\]\nwhere \\( x \\) is a positive real constant \\( (x > 0) \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the expected value of the area of triangle $OAB$ in the plane, where point $A$ is at $(1, 0)$ and point $B$ is randomly chosen on the unit circle centered at the origin.",
"role": "user"
}
] | \dfrac{1}{\pi} |
[
{
"content": "Find the product of the divisors of $50$.",
"role": "user"
}
] | 125,\!000 |
[
{
"content": "Is the orthogonal projection of a lattice $L$ in $\\mathbb{R}^n$ onto a vector subspace $E$ of $\\mathbb{R}^n$ always a lattice?",
"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... | 0.13 |
[
{
"content": "Find the maximum possible length of the smallest side of a triangle with vertices in or on the unit cube. What is this length?",
"role": "user"
}
] | \sqrt{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... | 4NH_3 + 5O_2 -> 4NO + 6H_2O |
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