domain stringclasses 7
values | sub_source stringclasses 15
values | coding_subclass stringclasses 6
values | messages listlengths 2 24 | tools listlengths 1 94 ⌀ |
|---|---|---|---|---|
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "How many different tetrahedrons are there with whole number-long edges, and with 17 as the sum of the lengths of the edges?",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Answer: \\(\\displaystyle 7\\)**\n\n**Explanation (step‑by‑step)** \n\nLet t... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Let $\\triangle ABC$ be an acute scalene triangle with circumcircle $\\omega$. The tangents to $\\omega$ at $B$ and $C$ intersect at $T$. Let $X$ and $Y$ be the projections of $T$ onto lines $AB$ and $AC$, respectively. Suppose $BT = CT = 16$, $BC = 22$, and $TX^2 + TY^2 + XY^2... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Line $\\ell$ passes through a 2020 by 2020 grid of square cells. Let a cell be shaved if $\\ell$ cuts it into two pieces with positive areas $a$ and $b$ such that $a < \\frac{b}{2020}$. Let $S$ be the set of all cells that are shaved by $\\ell$, and let $n$ be the number of dis... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Thirty rays with a common origin are constructed on a plane. Consider all angles between any two of these rays. Let $N$ be the number of acute angles among these angles. Find the smallest value of $N$.",
"tool_calls": null
},
{
"role": "assistant",
"content": "L... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Triangle \\(ABC\\) is divided into six smaller triangles by lines drawn from the vertices through a common interior point. The areas of four of these triangles are given as 84, 35, 30, and 40. Find the area of triangle \\(ABC\\).",
"tool_calls": null
},
{
"role": "a... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Let \\(a\\) and \\(b\\) be positive coprime integers. A subset \\(S\\) of the non-negative integers is called admissible if \\(0\\) belongs to \\(S\\) and whenever \\(k\\) belongs to \\(S\\), so do \\(k + a\\) and \\(k + b\\). Find \\(f(a, b)\\), the number of admissible sets."... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "In a Secret Santa game with $n$ people, each person randomly selects another person's name from a box (excluding their own name). What is the probability that at least one two-cycle (where a person selects the same person who selects him or her) exists?",
"tool_calls": null... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Determine the best value of \\(k \\geq 0\\) such that the inequality \\((a^2+kbc)(b^2+kca)(c^2+kab) \\geq \\left(\\frac{k+1}{2}\\right)^3abc(a+b)(b+c)(c+a)\\) holds for all \\(a, b, c \\geq 0\\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Solut... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "How many natural numbers with 5 distinct digits, where the last digit is 1 and the number is divisible by 7, exist? (Example: 48321)",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Step 1 – Writing the number**\n\nA 5‑digit number whose last digit ... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "What is the length of the shortest curve that divides the area of an equilateral triangle with side length $1$ unit into $2$ nonoverlapping sections of equal area?",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let the equilateral triangle be \\(ABC\... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Edward and Alphonse each draw a circle in the Euclidean plane such that the circles do not intersect and have non-overlapping interiors. Four distinct lines, each tangent to both circles and no two parallel, divide the plane into eleven regions, three of which are bounded. One ... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "In triangle $ABC$ with sides $AB = 6\\sqrt{2}$, $BC = 8$, and $AC = 14$, a line $p$ passing through point $C$ intersects the median extension from $B$ at point $K$, the altitude extension from $B$ at point $M$, and the extension of $BA$ at point $N$. Determine the angle between... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Let ∆ABC be a triangle with integer side lengths such that angle A is 3 times angle B. Find the minimum value of its perimeter.",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let \n\n\\[\na=BC,\\qquad b=CA,\\qquad c=AB ,\n\\]\n\nso that \\(\\angle A... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Determine the maximal possible length of Harini's sequence of quadratic equations, where each equation has real roots and the coefficients for the next equation are derived from the roots of the current equation.",
"tool_calls": null
},
{
"role": "assistant",
"c... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Kelvin and Quinn are collecting trading cards; there are 6 distinct cards that could appear in a pack. Each pack contains exactly one card, and each card is equally likely. Kelvin buys packs until he has at least one copy of every card, then he stops buying packs. If Quinn is m... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Determine the minimum number of lottery tickets needed to ensure a win, where each ticket has a 6x6 grid and the player marks 6 cells. The player wins if none of the marked cells are among the 6 \"black\" cells revealed after the draw.",
"tool_calls": null
},
{
"rol... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "On a $5 \\times 5$ board, there is a squadron of two ships - a \"battleship\" (4-cell ship) and a \"cruiser\" (3-cell ship). How many squares must be hit in order to hit at least one of the ships of the squadron?",
"tool_calls": null
},
{
"role": "assistant",
"c... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Consider a string of length 6 composed of the characters \\(a\\), \\(b\\), and \\(c\\). If two \\(a\\)'s are next to each other, replace \\(aa\\) by \\(b\\). If two \\(b\\)'s are next to each other, replace \\(bb\\) by \\(a\\). If \\(a\\) and \\(b\\) are next to each other, or ... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "How many sequences of 0s and 1s of length \\( n \\) contain the substring \"010\"?",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Step 1 – Complementary counting** \nLet \n\n\\[\nA_n=\\#\\{\\text{binary strings of length }n\\text{ that avoid the... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Let \\( d \\) be the tangent to the circle \\( (O, R) \\) at a fixed point \\( T \\). As \\( M \\) moves on \\( (O, R) \\), the line \\( MM \\) intersects \\( d \\) at \\( P \\). A circle \\( (C) \\) with center \\( I \\) passes through \\( M \\) and is tangent to \\( d \\) at ... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "A total of $731$ objects are put into $n$ nonempty bags where $n$ is a positive integer. These bags can be distributed into $17$ red boxes and also into $43$ blue boxes so that each red and each blue box contain $43$ and $17$ objects, respectively. Find the minimum value of $n$... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Eight identical dice are arranged in a 2x2x2 cube. Two touching dice are said to \"match\" if the side they share has the same number on both dice. If these 8 dice are put together randomly, what is the probability that all 12 pairs of touching dice will match?",
"tool_call... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Find the number of distinguishable repeating parts of the sequence generated by $k,j$ in terms of $j$ using the function $D_{k,j}$ defined as follows:\n- $D_{k,j}(0) = k$\n- For $n \\geq 1$,\n \\[\n D_{k,j}(n) = \\begin{cases} \n \\varsigma(D_{k,j}(n-1)) \\pmod{10^j} & \\tex... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "For each arrangement of the ten numbers $1, 4, 7, 10, 13, 16, 19, 22, 25, 28$ around a circle, let $N$ denote the largest of the ten sums obtained by adding each number to the sum of its neighbors. What is the smallest value of $N$ that can be obtained?",
"tool_calls": null... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "A large white cube is painted red, then cut into 27 identical smaller cubes. These smaller cubes are shuffled randomly and reassembled into a large cube by a blind man. What is the probability that the outside of the large cube is completely red?",
"tool_calls": null
},
... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Martina Combinova receives ten different tennis rackets in a fixed order. She signs and returns the most recently arrived racket each time she decides to sign. Given that she has signed the 9th racket that arrived during lunch, how many possible post-lunch racket signing sequen... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Vines must prepare envelopes containing a positive integer amount of memes such that he can distribute exactly \\( p \\) memes to Bruh and exactly \\( q \\) memes to Really N, where \\( p \\) and \\( q \\) are positive integers with \\( p + q \\leq 2016 \\). What is the minimum... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Given that $a > 1$ and $\\gcd(a, 6) = 1$, find the greatest value of $n$ in terms of $a$ such that the equation $a^2x + 6ay + 36z = n$ does not have natural roots $(x,y,z)$.",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Step 1 – rewrite the equat... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Let \\( S = \\{1, 2, 3, \\ldots, n\\} \\). A subset of \\( S \\) is called \"permitable\" if it does not contain three elements \\( a, b, c \\) such that \\( a \\mid b \\) and \\( b \\mid c \\). What is the maximum number of elements that a permitable subset can have?",
"to... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "How many integers $1 < k \\le 2015$ satisfy $2015^{2015} \\equiv 1 \\pmod{k}$?",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Solution Overview**\n\nWe have \n\n\\[\na=2015=5\\cdot13\\cdot31 ,\\qquad n=2015 .\n\\]\n\nThe condition \n\n\\[\n2015^{... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Let \\( x, y, z \\) be positive real numbers such that \\( x + y + z = 3 \\) and \\( k > 0 \\). If\n\\[ \\sum_{\\text{cyc}} \\frac{1}{x^n + \\frac{k}{y^n}} \\ge \\frac{3}{1 + k} \\]\nfor all \\( x, y, z, k > 0 \\), determine the minimum value of \\( n \\).",
"tool_calls": n... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Determine the largest natural number $ N $ such that every $ 5\\times 5 $ array consisting of pairwise distinct natural numbers from $ 1 $ to $ 25 $ contains a $ 2\\times 2 $ subarray of numbers whose sum is at least $ N. $",
"tool_calls": null
},
{
"role": "assista... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Let $n$ be a natural number. Find the least natural number $k$ for which there exist $k$ sequences of $0$ and $1$ of length $2n+2$ such that any sequence of $0$ and $1$ of length $2n+2$ coincides with at least one of these $k$ sequences in at least $n+2$ positions.",
"tool_... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Tom colours 2006 vertices on a circle using 17 colours. Marry connects pairs of vertices with bowstrings such that the vertices are of the same colour and the bowstrings do not intersect except at the vertices. Determine the greatest number of bowstrings Marry can draw.",
"... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Determine the minimum value of $k \\in \\mathbb{N}^*$ such that for any subset $S$ of the set $\\{1,2,3,\\ldots,15\\}$ with $|S| \\ge k$, there exist $a, b, c \\in S$ such that $abc$ is a perfect square.",
"tool_calls": null
},
{
"role": "assistant",
"content": ... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "On an 8x8 board, a ship in the form of a 2x2 square occupies 4 cells. A player makes shots by naming any cell on the board and is informed whether the shot hits the ship or not. What is the minimum number of shots required to determine the exact location of the ship with certai... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "$239$ wise men stand in a circle near an opaque baobab. The king places a hat of one of $16$ colors on each wise man's head. Each wise man can only see the hats of the two nearest wise men on each side. Without communicating, each wise man must guess the color of their own hat.... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "There are $k$ heaps of stones, with a total of $n^2$ stones ($k, n \\in \\mathbb{N}$). It is known that no matter how one divides any heap into two smaller non-empty heaps, there will always be two heaps with the same number of stones among the $(k+1)$ heaps obtained. Find the ... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "What is the smallest number of copies of the same scalene triangle needed to form a square?",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let \n\n* the square be \\(S\\) (side length \\(L\\)), \n* the given triangle be \\(\\triangle\\) with angles... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "How many non-bijective functions \\( f \\) exist such that \\( f(f(f(x))) = f(f(x)) \\) for all real \\( x \\), where the domain of \\( f \\) is the set \\(\\{1,2,3,5,6,7,9\\}\\) and the range is the set \\(\\{1,2,4,6,7,8,9\\}\\)? Constants must be ignored to avoid an infinite ... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "In a regular quadrangular pyramid $SABCD$ with all edges equal to $b$, a plane $\\beta$ is drawn through points $B$ and $D_1$. Find the smallest possible area of the polygon formed at the intersection of the plane $\\beta$ and the pyramid $SABCD$.",
"tool_calls": null
},
... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Let \\(\\{a_n\\}\\) be a sequence of integers where \\(a_1\\) is odd, and for any positive integer \\(n\\), we have \\(n(a_{n+1} - a_n + 3) = a_{n+1} + a_n + 3\\). Additionally, \\(2010\\) divides \\(a_{2009}\\). Find the smallest \\(n \\geq 2\\) such that \\(2010\\) divides \\... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Let \\(a_1, a_2, \\dots, a_n\\) be positive real numbers. Find the smallest constant \\(c\\) such that \n\\[\n\\sum_{k=1}^n \\frac{k}{\\sum_{j=1}^k \\frac{1}{a_j}} \\leq c \\sum_{k=1}^n a_k.\n\\]",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let \n... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "There are \\( k \\) people standing in a circle. Starting with the first person labeled 0, every \\( n \\)-th person is eliminated from the circle, and the counting restarts. Determine the last person left standing. Provide a closed-form solution if available.\n\nExample: For \... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "How many solutions in distinct positive integers are there to the equation $x_1 + x_2 + \\cdots + x_k = n$?",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Step 1 – a necessary condition**\n\nIf the \\(k\\) numbers are distinct and positive, the sm... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Call a sequence of rolls $a_1, a_2, ..., a_n$ generated from a standard fair 6-sided die fluctuating if the $n-1$ sets of two consecutive rolls, placed in order, alternately fluctuate between having a sum greater than or equal to 7 and having a sum less than or equal to 7. The ... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Given non-negative real numbers \\(x, y, z\\), find the value of \\(\\frac{1}{9}(x+y+z)(x^3+y^3+z^3)(x^2y^2+y^2z^2+z^2x^2)\\).",
"tool_calls": null
},
{
"role": "assistant",
"content": "**Solution**\n\nLet \n\n\\[\nS=x+y+z,\\qquad \nA=x^3+y^3+z^3,\\qquad \nB=x^... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Define a swap as the exchange of two positions in a permutation of the integers $1, 2, 3, 4, 5, 6, 7, 8$. Let $F(x)$ be the number of integers that remain in their original positions after $x$ swaps. Let $P_i(x)$ be the probability that $F(x) = i$ after $x$ swaps. Determine whi... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Let \\( n \\geq 2 \\) be a positive integer. Find the maximum number of segments with lengths greater than 1, determined by \\( n \\) points which lie on a closed disc with radius 1.",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let \n\n\\[\nP=\\{p... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Given $n^2$ points in the plane, where no three points are collinear and $n \\ge 4$ is a positive integer of the form $3k+1$, what is the minimal number of connecting segments among the points such that for each $n$-tuple of points, there exists a subset of four points that are... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "There are several counters of various colours and sizes, with no two counters having the same colour and size simultaneously. On each counter $F$, two numbers are written: one is the number of counters that have the same colour as $F$ but a different size, and the other is the ... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Let \\( A \\) be a \\( 3 \\times 9 \\) matrix with all elements being positive integers. An \\( m \\times n \\) submatrix of \\( A \\) is called \"ox\" if the sum of its elements is divisible by 10. An element of \\( A \\) is called \"carboxylic\" if it is not part of any \"ox\... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Solve the recurrence relation $a_n(a_{n+1}-a_n)=n(a_{n+1}-a_n)^2+1$.",
"tool_calls": null
},
{
"role": "assistant",
"content": "\\[\na_n\\bigl(a_{n+1}-a_n\\bigr)=n\\bigl(a_{n+1}-a_n\\bigr)^2+1,\n\\qquad n=0,1,2,\\dots \n\\]\n\n-----------------------------------... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "With how many zeros can the decimal writing of $1^n + 2^n + 3^n + 4^n$ end, where $n$ is a positive integer?",
"tool_calls": null
},
{
"role": "assistant",
"content": "Let \n\n\\[\nS(n)=1^{n}+2^{n}+3^{n}+4^{n}\\qquad (n\\in \\mathbb Z_{>0}).\n\\]\n\nThe number ... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Find the number of mappings \\( F: \\{(1, \\ldots, n)\\} \\times \\{(1, \\ldots, n)\\} \\to \\{0, \\ldots, n\\} \\) that satisfy the following conditions:\na) \\( F(i, n) = F(n, i) = i \\) for all \\( i \\).\nb) \\( F(i, j) \\leq F(i, j+1) \\) and \\( F(i+1, j) \\leq F(i, j) + ... | null |
Math | nemotron-math-v2-high-aime-style | null | [
{
"role": "user",
"content": "Given that cars arrive as a Poisson process with rate $\\nu$ and parking times are exponentially distributed with mean $\\mu$, determine the fraction of time that the parking space labelled $i$ is occupied.",
"tool_calls": null
},
{
"role": "assistant",
"content... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Consider the Penrose diagram of a charged black hole (Reissner-Nordström black hole). Which of the following statements accurately describes the global structure of this spacetime?\n\nA) The Penrose diagram consists of a single diamond-shaped region representing the entire spac... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "A clock is placed at the surface of a planet with a mass \\( M \\) and radius \\( R \\). The gravitational time dilation factor \\( \\gamma \\) at the surface of the planet is given by:\n\n\\[\n\\gamma = \\sqrt{1 - \\frac{2GM}{c^2 R}}\n\\]\n\nwhere \\( G \\) is the gravitationa... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Consider a system of three entangled qubits in the state \\( \\frac{1}{\\sqrt{2}}(|000\\rangle + |111\\rangle) \\). If the first qubit is measured and found to be in the state \\( |0\\rangle \\), what is the state of the remaining two qubits?\n\nA) \\( |00\\rangle \\)\nB) \\( |... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "In the context of the kinetic theory of gases, consider a sealed container with an ideal gas at temperature \\( T \\) and pressure \\( P \\). The average kinetic energy of the gas molecules is given by \\( \\frac{3}{2} k_B T \\), where \\( k_B \\) is the Boltzmann constant. If ... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "In a medium with a refractive index \\( n \\), a charged particle moves with a velocity \\( v \\) greater than the phase velocity of light in that medium. Which of the following statements correctly describes the conditions under which Cherenkov radiation is emitted?\n\nA) Cher... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "A block of mass \\( m \\) is placed on a frictionless inclined plane making an angle \\( \\theta \\) with the horizontal. The block is connected to a massless spring with spring constant \\( k \\) that is fixed at the top of the incline. When the block is displaced a small dist... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Which of the following transition metal catalysts is most suitable for a Suzuki-Miyaura cross-coupling reaction between an aryl bromide and an aryl boronic acid under mild conditions?\n\nA) Palladium(II) acetate (Pd(OAc)₂)\nB) Nickel(0) bis(cycloocta-1,5-diene) (Ni(0)(cod)₂)\nC... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "In colloid and interface science, which of the following statements accurately describes the behavior of a system involving a highly charged colloid in an electrolyte solution under the influence of an external electric field?\n\nA) The colloid particles will aggregate due to i... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "A source emits sound waves at a frequency \\( f_0 \\) and moves at a speed \\( v_s \\) towards a stationary observer. The speed of sound in the medium is \\( v \\). Now, consider a scenario where the source is moving in a circular path of radius \\( R \\) with a constant speed ... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Which of the following statements is true regarding the alkaline earth metals (Group 2 elements) in their reactions with water?\n\nA) All alkaline earth metals react vigorously with cold water to form their respective hydroxides and hydrogen gas.\nB) Only beryllium does not rea... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Consider a thermodynamic system in equilibrium described by the Helmholtz free energy \\( F(T, V, N) \\). Suppose the system undergoes a reversible process at constant temperature \\( T \\) and number of particles \\( N \\). During this process, the volume \\( V \\) changes fro... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Which of the following principles is not part of the 12 Principles of Green Chemistry?\n\nA) Prevention\nB) Atom Economy\nC) Less Hazardous Chemical Syntheses\nD) Use of Renewable Feedstocks\nE) Use of Auxiliary Substances\nF) Design for Energy Efficiency\nG) Use of Catalysis\n... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Consider the operators \\(\\hat{A}\\) and \\(\\hat{B}\\) in quantum mechanics, where \\([\\hat{A}, \\hat{B}] = \\hat{A} \\hat{B} - \\hat{B} \\hat{A}\\) is their commutator. Suppose \\([\\hat{A}, \\hat{B}] = i\\hbar \\hat{C}\\), where \\(\\hat{C}\\) is another operator. Which of... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "A dipole antenna is oriented along the z-axis and radiates electromagnetic waves. Which of the following statements correctly describes the electric field distribution in the far-field region of the antenna?\n\nA) The electric field is strongest along the z-axis and zero in the... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Which of the following best describes the phenomenon of coevolution in the context of host-parasite interactions?\n\nA) Hosts evolve resistance to parasites, and parasites evolve countermeasures to overcome this resistance.\nB) Hosts and parasites evolve independently without i... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "During the process of translation, which of the following correctly describes the role of ribosomal RNA (rRNA)?\n\nA) rRNA serves as the template for protein synthesis.\nB) rRNA carries the genetic code from DNA to the ribosome.\nC) rRNA forms part of the ribosome and catalyzes... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "In Fourier optics, which of the following statements is true regarding the Fourier transform of a complex amplitude function \\( U(x, y) \\) representing an optical field at the input plane of a lens?\n\nA) The Fourier transform of \\( U(x, y) \\) provides the spatial frequency... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "According to Hubble's Law, the recessional velocity \\( v \\) of a galaxy is directly proportional to its distance \\( d \\) from us, expressed as \\( v = H_0 d \\), where \\( H_0 \\) is the Hubble constant. If the Hubble constant is approximately \\( 70 \\, \\text{km/s/Mpc} \\... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "A particle moves in a plane under the influence of a force that depends on its position and velocity. The position of the particle at time \\( t \\) is given by \\( \\mathbf{r}(t) = (x(t), y(t)) \\), and its velocity is \\( \\mathbf{v}(t) = (v_x(t), v_y(t)) \\). The force actin... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "In nonlinear acoustics, consider a medium where the wave equation is given by\n\\[ \\frac{\\partial^2 p}{\\partial t^2} - c^2 \\nabla^2 p - \\beta \\left( \\frac{\\partial p}{\\partial t} \\right)^2 = 0, \\]\nwhere \\( p \\) is the acoustic pressure, \\( c \\) is the speed of s... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "In Minkowski space, consider a four-vector \\( A^\\mu = (A^0, A^1, A^2, A^3) \\) where \\( A^0 = 5 \\), \\( A^1 = 3 \\), \\( A^2 = 4 \\), and \\( A^3 = 0 \\). What is the magnitude (norm) of the four-vector \\( A^\\mu \\)?\n\nA) \\( 0 \\)\nB) \\( 5 \\)\nC) \\( 4 \\)\nD) \\( 3 \... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "In a strongly correlated electron system, a polaron forms when an electron interacts with the lattice, creating a local distortion. Consider a situation where an electron in a crystal lattice creates a polaron with an effective mass \\( m^* \\). Which of the following statement... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "In the context of the quantum harmonic oscillator, what is the energy difference between the first excited state and the ground state?\n\nA) \\( \\hbar \\omega \\)\nB) \\( 2 \\hbar \\omega \\)\nC) \\( \\frac{\\hbar \\omega}{2} \\)\nD) \\( \\frac{\\hbar \\omega}{4} \\)\nE) \\( \... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Which of the following molecules is least likely to be found in the dense interstellar medium (ISM) due to its low abundance and high reactivity?\n\nA) H2 (molecular hydrogen)\nB) CO (carbon monoxide)\nC) CH4 (methane)\nD) H2O (water)\nE) NH3 (ammonia)\nF) HCN (hydrogen cyanide... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "In a population genetics study, a population has undergone significant admixture events with multiple source populations over several generations. The source populations have distinct allele frequencies, and the admixture proportions vary over time. Given the complex history of... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Consider a cavity quantum electrodynamics (QED) system with a single atom coupled to a single mode of the electromagnetic field in a cavity. The atom has two energy levels, and the cavity mode is driven by an external coherent field. Which of the following statements is true re... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Consider a parallel-plate capacitor with plate area \\( A \\) and separation \\( d \\), initially filled with a dielectric material of permittivity \\( \\epsilon_1 \\). The capacitor is then disconnected from the voltage source, and a second dielectric material of permittivity ... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "In a strongly coupled system of fermions, such as those found in high-temperature superconductors, which of the following phenomena is most likely to be observed due to strong electron-electron interactions?\n\nA) Fermi liquid behavior with a well-defined quasiparticle peak\nB)... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Consider a plane electromagnetic wave traveling in vacuum with electric field \\( \\mathbf{E} \\) and magnetic field \\( \\mathbf{B} \\). The energy density \\( u \\) and momentum density \\( \\mathbf{g} \\) of the electromagnetic field are given by \\( u = \\frac{1}{2} \\epsil... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Which of the following petrochemicals is primarily used as a feedstock for the production of synthetic rubber?\n\nA) Ethylene\nB) Propylene\nC) Butadiene\nD) Benzene\nE) Toluene\nF) Xylene\nG) Styrene\nH) Isoprene\nI) Methane\nJ) Propane",
"tool_calls": null
},
{
"r... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "During DNA replication, which enzyme is responsible for adding nucleotides to the growing DNA strand and ensures the continuity of the lagging strand by removing RNA primers and replacing them with DNA?\n\nA) DNA ligase\nB) DNA polymerase I\nC) DNA polymerase II\nD) DNA polymer... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Select the best answer A, B, C or other.\n\nIn the context of relativistic beaming, consider a source moving at a speed \\( v \\) towards an observer at an angle \\( \\theta \\) relative to the line of sight. The observed flux is given by the beaming factor \\( F(\\theta) \\). ... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Think step by step and select the correct letter option and put it in \\boxed{<letter>}.\n\nIn a closed system, the total charge is conserved. If a system initially has a net charge of +5 C and during a process, 3 C of charge is added to the system, what is the net charge of th... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Consider a Schwarzschild black hole with a mass \\( M \\). An observer far from the black hole measures the time it takes for an infalling object to reach the event horizon. Which of the following statements correctly describes the observed behavior of the infalling object as i... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Which of the following epigenetic modifications can lead to gene silencing and is influenced by environmental factors such as diet and stress?\n\nA) DNA methylation\nB) Histone acetylation\nC) Histone methylation\nD) Non-coding RNA interference\nE) Chromatin remodeling\nF) DNA ... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Consider the strong interaction described by Quantum Chromodynamics (QCD) in the limit of large number of colors \\( N_c \\). Which of the following statements about the behavior of mesons and baryons in this limit is true?\n\nA) Mesons become massless, while baryons become inf... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Consider the synthesis of a cyclic ester (lactone) from a linear compound with the general structure \\( \\text{R-CH}_2-\\text{CH(OH)-COOH} \\). Which of the following conditions is essential for the formation of a five-membered lactone ring from this compound?\n\nA) Acidic con... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "In a complex synthesis involving a molecule with multiple functional groups, including an alcohol, an amine, and a carboxylic acid, which combination of protecting groups would be appropriate to selectively protect these functional groups in the presence of each other?\n\nA) Ac... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Which of the following inherited diseases is caused by a mutation in the CFTR gene?\n\nA) Sickle cell anemia\nB) Cystic fibrosis\nC) Hemophilia\nD) Huntington's disease\nE) Tay-Sachs disease\nF) Phenylketonuria (PKU)\nG) Duchenne muscular dystrophy\nH) Marfan syndrome\nI) Turne... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "A particle of mass \\( m \\) moves along a curve in a plane under the influence of a conservative force field given by the potential \\( V(x, y) = k(x^2 + y^2)^2 \\), where \\( k \\) is a positive constant. The particle starts from rest at the point \\( (1, 0) \\) and moves to ... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Which of the following transcription factors is known to regulate gene expression by binding to the promoter region and enhancing the binding of RNA polymerase to DNA?\n\nA) p53\nB) NF-κB\nC) TATA-binding protein (TBP)\nD) c-Myc\nE) STAT3\nF) HIF-1α\nG) Oct-4\nH) Sox2\nI) β-cat... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Select the best answer A, B, C or other.\n\nIn observational astronomy, which instrument or technique is best suited for detecting exoplanets through the transit method?\n\nA) Spectroscopy\nB) Adaptive optics\nC) Radio interferometry\nD) Transit photometry\nE) Gravitational len... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Consider a Carnot engine operating between two temperatures, \\( T_H \\) and \\( T_L \\), where \\( T_H = 400 \\, \\text{K} \\) and \\( T_L = 300 \\, \\text{K} \\). Suppose this engine is used to power a reversible refrigerator that operates between two other temperatures, \\( ... | null |
Science (STEM) | Nemotron-Science-V1-MCQ | null | [
{
"role": "user",
"content": "Think step by step and select the correct letter option and put it in \\boxed{<letter>}.\n\nConsider a jet engine producing noise due to turbulence. Which of the following factors primarily contributes to the noise generation in the jet engine exhaust?\n\nA) Viscous boundary la... | null |
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