Science
Collection
5 items • Updated • 1
Question stringlengths 28 1.07k | Answer stringlengths 1 54 | Answer_type stringclasses 6
values | Picture imagewidth (px) 277 1.38k ⌀ |
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How many ways are there to divide a set of 8 elements into 5 non-empty ordered subsets? | 11760 | integer | Not supported with pagination yet |
what is the value of $\int_{-infty}^{+infty} sin(3*t)*sin(t/\pi)/t^2 dt$? | 1.0 | float | Not supported with pagination yet |
Consider the following graph, with links costs listed, and assume we are using shortest-path (or lowest-cost) routing, and that routing has equilibrated to a constant set of routing tables. The routing algorithm uses poisoned reverse, advertising an infinite weight for the poisoned paths. What distance does C advertise... | 5 | integer | |
Please solve the equation 2*x^3 + e^x = 10 using newton-raphson method. | 1.42 | float | Not supported with pagination yet |
How many ways are there to divide a set of 7 elements into 4 non-empty ordered subsets? | 4200 | integer | Not supported with pagination yet |
Let a undirected graph G with edges E = {<0,1>,<0,2>,<0,3>,<0,5>,<2,3>,<2,4>,<4,5>}, which <A,B> represent Node A is connected to Node B. What is the shortest path from node 0 to node 5? Represent the path as a list. | [0, 5] | list of integer | Not supported with pagination yet |
Let a undirected graph G with edges E = {<0,2>,<2,1>,<2,3>,<3,4>,<4,1>}, which <A,B> represent Node A is connected to Node B. What is the shortest path from node 4 to node 0? Represent the path as a list. | [4, 1, 2, 0] | list of integer | Not supported with pagination yet |
Compute $\int_{|z| = 1} z^2 sin(1/z) dz$. The answer is Ai with i denoting the imaginary unit, what is A? | -1.047 | float | Not supported with pagination yet |
A container weighs 3.22 lb force when empty. Filled with water at 60°F the mass of the container and its contents is 1.95 slugs. Find its volume in cubic feet. Assume density of water = 62.4 lb force/ft3. | 0.955 | float | Not supported with pagination yet |
Let M be the set of bounded functions (i.e. \sup_{x\in[a,b]}|f(x)|<\infty) in C[0,1]. Is the set ${F(x)=\int_0^x f(t) dt | f \in M }$ a sequentially compact set? Answer 1 for yes and 0 for no. Furthermore, it can be proved using 1. Arzelà-Ascoli theorem, 2. Riesz representation theorem, 3. Banach fixed point theorem, 4... | [1, 1] | list of integer | Not supported with pagination yet |
Find the x value of the solutions to the linear system: 7x - y = 15x, -6x + 8y = 15y. | 0 | integer | Not supported with pagination yet |
In Jules Verne's 1865 story with this title, three men went to the moon in a shell fired from a giant cannon sunk in the earth in Florida. Find the minimum muzzle speed that would allow a shell to escape from the earth completely (the escape speed). Neglect air resistance, the earth's rotation, and the gravitational pu... | 1.12 | float | Not supported with pagination yet |
Is W = {[x, y] in R^2: x >= 0 and y >= 0} a subspace of R^2? | False | bool | Not supported with pagination yet |
compute the line integral of \int_K xy dx, \int_L xy dx, where K is a straight line from (0,0) to (1,1) and L is the Parabola y=x^2 from (0,0) to (1,1). return the answer as a list | [0.333, 0.25] | list of float | Not supported with pagination yet |
True of false: one can draw a simple connected planar graph with 200 vertices and 400 faces | False | bool | Not supported with pagination yet |
Consider the basis B of R^2 consisting of vectors v_1 = [3,1] and v_2 = [-1, 3]. If x = [10, 10], find the B-coordinate vector of x | [4, 2] | list of integer | Not supported with pagination yet |
What is the number of labelled forests on 10 vertices with 5 connected components, such that vertices 1, 2, 3, 4, 5 all belong to different connected components? | 50000 | integer | Not supported with pagination yet |
Let g(x) be the inverse of f(x) = x + cos(x). What is g'(1)? | 1 | integer | Not supported with pagination yet |
Let V be the space of all infinite sequences of real numbers. Consider the transformation T(x_0, x_1, x_2, ...) = (x_1, x_2, x_3, ...) from V to V. Is the sequence (1,2,3,...) in the image of T? | True | bool | Not supported with pagination yet |
Let W(t) be the standard Brownian motion. Define X(t) = exp{W(t)}, for all t \in [0, \infty). Let 0 < s < t. Find Cov(X(s=1/2), X(t=1)). | 1.3733 | float | Not supported with pagination yet |
Consider a random walk on a connected graph with 4 edges. What is the highest possible entropy rate? Use base 2 logarithm and return the entropy rate in bits. | 1.094 | float | Not supported with pagination yet |
If u is the real part of a function, and v is the imaginary part, then the Cauchy-Riemann equations for u and v take the following form in polar coordinates: r\frac{\partial u}{\partial r} = \frac{\partial v}{\partial \theta} and r\frac{\partial v}{\partial r} = -\frac{\partial u}{\partial \theta}. Is this argument Tru... | True | bool | Not supported with pagination yet |
The shock absorbers in an old car with mass 1000 kg are completely worn out. When a 980-N person climbs slowly into the car at its center of gravity, the car sinks 2.8 cm. The car (with the person aboard) hits a bump, and the car starts oscillating up and down in SHM. Model the car and person as a single body on a sing... | 0.9 | float | Not supported with pagination yet |
Find the smallest positive integer that leaves a remainder of 1 when divided by 2, a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, a remainder of 4 when divided by 5, and a remainder of 5 when divided by 6. | 59 | integer | Not supported with pagination yet |
the matrix in ./mingyin/mc.png represents a markov chain. What is the period of state 0? What is the period of state 1? Return the two answers as a list. | [2, 2] | list of integer | |
$\lim_{x \to c}((x^2 - 5x - 6) / (x - c))$ exists. What is the value of c? | [-1, 6] | list of integer | Not supported with pagination yet |
Aisha graduates college and starts a job. She saves $1000 each quarter, depositing it into a retirement savings account. Suppose that Aisha saves for 30 years and then retires. At retirement she wants to withdraw money as an annuity that pays a constant amount every month for 25 years. During the savings phase, the ret... | 1898.27 | float | Not supported with pagination yet |
Let $g_\theta(x_1,x_2)=f_\theta(x_1)f_\theta(x_2)$. Let $J_f(\theta)$ be the Fisher information of $f_\theta$. What is the relationship between $J_f(\theta)$ and $J_g(\theta)$? (a) $J_g(\theta) = 0.5J_f(\theta)$. (b) $J_g(\theta) = J_f(\theta)$. (c) $J_g(\theta) = 2J_f(\theta)$. (d) $J_g(\theta) = 4J_f(\theta)$. Which... | (c) | option | Not supported with pagination yet |
An auto magazine reports that a certain sports car has 53% of its weight on the front wheels and 47% on its rear wheels. (That is, the total normal forces on the front and rear wheels are 0.53w and 0.47w, respectively, where w is the car’s weight.) The distance between the axles is 2.46 m. How far in front of the rear ... | 1.3 | float | Not supported with pagination yet |
A parachutist with mass m=80 kg is undergoing free fall. The drag force applied on him is $F_D = kv^2$, where v is the velocity measured relative to the air. The constant k=0.27 [Ns^2/m^2] is given. Find the distance traveled h in meters, until v=0.95$v_t$ is achieved, where $v_t$ is the terminal velocity. Return the n... | 345.0 | float | Not supported with pagination yet |
ABCD is a parallelogram. E is the midpoint, F is also a midpoint. Area of AFG = 10, Area of EGH = 3. What is Area CDH? | 7 | integer | |
In how many ways can a set of 6 distinct letters be partitioned into 3 non-empty groups if each group must contain at least 2 letters? | 15 | integer | Not supported with pagination yet |
Consider $x(t)$ to be given as, $$ x(t)=\cos (1000 \pi t) $$ . Let the sampling frequency be $700 \mathrm{~Hz}$. Does aliasing occur? | True | bool | Not supported with pagination yet |
For a\geq 0, we define $S_a={x | dist(x, S) \leq a}$, where $dist(x,S)=inf_{y\in S}||x-y||$. Suppose S is convex. Is S_a convex? Return 1 for yes and 0 for no. | 1.0 | float | Not supported with pagination yet |
suppose the 10-by-10 matrix A has the form: if i \neq j, A_{i,j}=a_i*b_j; if i=j, A_{i,j}=1+a_i*b_j for all 1<=i,j<=10. Here a_i = 1/i, b_i=1/(i+1). Find the determinant of A. return the numeric. | 1.9 | float | Not supported with pagination yet |
Find the area of the region between the graphs of the functions f(x) = x^2 - 4x + 10, g(x) = 4x - x^2, 1 <= x <= 3. | 5.333 | float | Not supported with pagination yet |
Does the following transformation have an eigenvector: Counterclockwise rotation through an angle of 45 degrees followed by a scaling by 2 in R^2. | False | bool | Not supported with pagination yet |
How many ways are there to arrange 6 pairs of parentheses such that they are balanced? | 132 | integer | Not supported with pagination yet |
Find the fraction of 7.7-MeV alpha particles that is deflected at an angle of 90° or more from a gold foil of 10^-6 m thickness. | 4e-05 | float | Not supported with pagination yet |
In how many ways can a group of 9 people be divided into 3 non-empty subsets? | 3025 | integer | Not supported with pagination yet |
Suppose there is a 50-50 chance that an individual with logarithmic utility from wealth and with a current wealth of $20,000 will suffer a loss of $10,000 from a car accident. Insurance is competitively provided at actuarially fair rates. Compute the utility if the individual buys full insurance. | 9.616 | float | Not supported with pagination yet |
The returns on a stock are 2.45% at 2018, 5.42% at 2019, -13.83% at 2020. What is the compound annual rate (between -1 and 1) of return over the three years. | -0.023669 | float | Not supported with pagination yet |
Does $p(x) = x^5 + x − 1$ have any real roots? | True | bool | Not supported with pagination yet |
Find integer $n \ge 1$, such that $n \cdot 2^{n+1}+1$ is a perfect square. | 3 | integer | Not supported with pagination yet |
Does cos(x) = x^k have a solution for k = 2023? | True | bool | Not supported with pagination yet |
Find $\int_{0}^{\sqrt{3}} \frac{dx}{1+x^2}$. | 1.0472 | float | Not supported with pagination yet |
A box contains 4 red, 3 green, and 2 blue balls. Balls are distinct even with the same color. In how many ways can we choose 4 balls, if at least 2 are red? | 81 | integer | Not supported with pagination yet |
Let X_1, X_2,... be independent variables each taking values +1 or -1 with probabilities 1/2 and 1/2. It is know that $\sqrt{3/n^3}*\sum_{k=1}^n k*X_k$ converges in distribution normal distribution N(a,b) as n goes to infinity. Here a is the expectation and b is the variance. What are the values of a and b? Return the ... | [0, 1] | list of integer | Not supported with pagination yet |
Sum the series $\sum_{m=1}^{\infty} \sum_{n=1}^{\infty}\frac{m^2 n}{3^m(n3^m+m3^n)}$ | 0.28125 | float | Not supported with pagination yet |
You want to move a 500-N crate across a level floor. To start thecrate moving, you have to pull with a 230-N horizontal force.Once the crate breaks loose and starts to move, you can keep itmoving at constant velocity with only 200 N. What are the coefficients of static and kinetic friction? | 0.4 | float | Not supported with pagination yet |
Let’s assume that the 10-year annual return for the S&P 500 (market portfolio) is 10%, while the average annual return on Treasury bills (a good proxy for the risk-free rate) is 5%. The standard deviation is 15% over a 10-year period. Whats the market Sharpe Ratio? | 0.33 | float | Not supported with pagination yet |
What is the value of the integral $\int_2^4 \frac{\sqrt{log(9-x)}}{\sqrt{log(9-x)}+\sqrt{log(x+3)}} dx$? | 1.0 | float | Not supported with pagination yet |
Suppose there are 100 identical firms in a perfectly competitive industry. Each firm has a short-run total cost function of the form C(q) = rac{1}{300}q^3 + 0.2q^2 + 4q + 10. Suppose market demand is given by Q = -200P + 8,000. What will be the short-run equilibrium price? | 25 | integer | Not supported with pagination yet |
A state issues a 15 year $1000 bond that pays $25 every six months. If the current market interest rate is 4%, what is the fair market value of the bond? | 1111.97 | float | Not supported with pagination yet |
In how many ways can we color a loop of 5 vertices with 3 colors such that no two adjacent vertices have the same color? | 30 | integer | Not supported with pagination yet |
The dependence between adjacent n-blocks of a stationary process grows linearly with n. True or False? | False | bool | Not supported with pagination yet |
Let $C$ be a variable length code that satisfies the Kraft inequality with equality but does not satisfy the prefix condition. Then $C$ has finite decoding delay. True or False? | False | bool | Not supported with pagination yet |
What is the order of group Z_{18}? | 18 | integer | Not supported with pagination yet |
Is 80 dB twice as loud as 40 dB? | False | bool | Not supported with pagination yet |
Is x-1 a factor of 2*x^4+3*x^2-5x+7? | False | bool | Not supported with pagination yet |
A load dissipates 1.5kW of power in an ac series RC circuit. Given that the power factor is 0.75, what is its reactive power $(P_r)$? What is its apparent power $(P_a)$? Represent the answer in a list [$P_r, P_a$] with unit kVA and kVAR respectively. | [2.0, 1.32] | list of float | Not supported with pagination yet |
dy/dt = \sqrt{t}, y(1) = 1. What is y(4)? | 5.667 | float | Not supported with pagination yet |
For the two linear equations $2 * x + 3 * y = 10$ and $4 * x + 4 * y = 12$ iwth variables x and y. Use cramer's rule to solve these two variables. | [-1, 4] | list of integer | Not supported with pagination yet |
In how many ways can 10 distinct balls be placed into 4 identical boxes if each box must have at least 1 balls? | 26335 | integer | Not supported with pagination yet |
If x(n) and X(k) are an N-point DFT pair, then x(n+N)=x(n). Is it true? | True | bool | Not supported with pagination yet |
what is the limit of $2/\sqrt{\pi}*\sqrt{n}\int_0^1(1-x^2)^n dx$ as n goes to infinity? | 1.0 | float | Not supported with pagination yet |
Assuming we are underground, and the only thing we can observe is whether a person brings an umbrella or not. The weather could be either rainy or sunny. Assuming the P(rain)=0.6 and P(sunny)=0.4. Assuming the weather on day $k$ is dependent on the weather on day $k-1$. We can write the transition probability as P(sunn... | [1, 0, 1] | list of integer | Not supported with pagination yet |
If there exists an ordered numbering of the nodes such that for each node there are no links going to a lower-numbered node, then there are no directed cycles in a directed graph. True or false? | True | bool | Not supported with pagination yet |
Coloring the edges of a complete graph with n vertices in 2 colors (red and blue), what is the smallest n that guarantees there is either a 4-clique in red or a 5-clique in blue? | 25 | integer | Not supported with pagination yet |
Assume the Black-Scholes framework. For $t \ge 0$, let $S(t)$ be the time-$t$ price of a nondividend-paying stock. You are given:
(i) $S(0)=0.5
(ii) The stock price process is $\frac{dS(t)}{S(t)} = 0.05dt+0.2dZ(t)$ where $Z(t)$ is a standart Brownian motion.
(iii) $E[S(1)^\alpha]=1.4$, where $\alpha$ is a negative cons... | 1.372 | float | Not supported with pagination yet |
Determine the multiplicity of the root ξ = 1, of the polynomial P(x) = x^5 - 2x^4 + 4x^3 - x^2 - 7x + 5 = 0 using synthetic division. What is P'(2) + P''(2)? Please return the decimal number. | 163 | integer | Not supported with pagination yet |
For the function $f(x,y)$ defined by $f(x,y)=1$ if $x=y$, $f(x,y)=0$ otherwise. Can we measure its integraion over the rectangle $[0,1]\times[0,1]$ using the Tonelli's Theorem? Answer true or false. | False | bool | Not supported with pagination yet |
The cross section for neutrons of energy 10 eV being captured by silver is 17 barns. What is the probability of a neutron being captured as it passes through a layer of silver 2 mm thick? | 0.2 | float | Not supported with pagination yet |
What is the determinant of matrix [[0, 1, 2], [7, 8, 3], [6, 5, 4]]? | -36 | integer | Not supported with pagination yet |
Let a undirected graph G with edges E = {<0,1>,<4,1>,<2,0>,<2,1>,<2,3>,<1,3>}, which <A,B> represent Node A is connected to Node B. What is the minimum vertex cover of G? Represent the vertex cover in a list of ascending order. | [1, 2] | list of integer | Not supported with pagination yet |
The two-digit integers from 19 to 92 are written consecutively to form the large integer N = 192021 · · · 909192. Suppose that 3^k is the highest power of 3 that is a factor of N. What is k? | 1 | integer | Not supported with pagination yet |
Apply the Graeffe's root squaring method to find the roots of the following equation x^3 - 2x + 2 = 0 correct to two decimals. What's the sum of these roots? | 1 | integer | Not supported with pagination yet |
A glider with mass m = 0.200 kg sits on a frictionless horizontalair track, connected to a spring with force constant k = 5.00 N/m.You pull on the glider, stretching the spring 0.100 m, and release itfrom rest. The glider moves back toward its equilibrium position (x = 0).What is its x-velocity when x = 0.080 m? (Unit... | -0.3 | float | Not supported with pagination yet |
Toss a coin repeatedly until two consecutive heads appear. Assume that the probability of the coin landing on heads is 3/7. Calculate the average number of times the coin needs to be tossed before the experiment can end. | 7.77778 | float | Not supported with pagination yet |
Julian is jogging around a circular track of radius 50 m. In a coordinate system with its origin at the center of the track, Julian's x-coordinate is changing at a rate of -1.25 m/s when his coordinates are (40, 30). Find dy/dt at this moment. | 1.667 | float | Not supported with pagination yet |
Calculate the momentum uncertainty of a tennis ball constrained to be in a fence enclosure of length 35 m surrounding the court in kg m/s. | 3e-36 | float | Not supported with pagination yet |
Let {X_n: n \geq 1} be independent, identically distributed random variables taking integer values {1,-1}. Let S_0=0, S_n=\sum_{i=1}^n X_i. Let P(X_i=1)=0.8 and P(X_i=-1)=0.2. The range R_n of S_0,S_1,...,S_n is the number of distinct values taken by the sequence. Then what is the limit of n^{-1}E[R_n] as n goes to inf... | 0.6 | float | Not supported with pagination yet |
Find the arc length of y = x^{-1} over the interval [1,2] using the Simpson's Rule S_8. | 1.132 | float | Not supported with pagination yet |
Is the Fourier transform of the signal x(t)=(1-e^{-|t|})[u(t+1)-u(t-1)] real? | True | bool | Not supported with pagination yet |
compute the integral $\iint_V \frac{d x d y d z}{(1+x+y+z)^3}$, where V={(x, y, z): x, y, z \geq 0, x+y+z\leq 1}. | 0.034 | float | Not supported with pagination yet |
For matrix A = [[5, 4], [1, 2]], what are its eigen values? | [1, 6] | list of integer | Not supported with pagination yet |
What is the minimum number of people needed in a room to guarantee that there are 4 mutual friends or 4 mutual strangers? | 18 | integer | Not supported with pagination yet |
If polygon ABCDE ~ polygon PQRST, AB = BC = 8, AE = CD = 4, ED = 6, QR = QP, and RS = PT = 3, find the perimeter of polygon PQRST. | 22.5 | float | Not supported with pagination yet |
What is the effective rates (between 0 and 1) for 18% compounded quarterly? Return the numeric value. | 0.1925 | float | Not supported with pagination yet |
What is the effective rates for 3% compounded monthly? | 0.0304 | float | Not supported with pagination yet |
Let f be a real function on [0,1]. If the bounded variation of f on [0,1] equals f(1)-f(0), then: (a) f is increasing on [0,1]; (b) f is decreasing on [0,1]; (c) None of the above. Which one is correct? | (a) | option | Not supported with pagination yet |
If a stock pays a $5 dividend this year, and the dividend has been growing 6% annually, what will be the stock’s intrinsic value, assuming a required rate of return of 12%? | 88.33 | float | Not supported with pagination yet |
Malus' law: $I=I_0*cos^2($\theta$)$. Where I is the intensity of polarized light that has passed through the polarizer, I_0 is the intensity of polarized light before the polarizer, and $\theta$ is the angle between the polarized light and the polarizer. Unpolarized light passes through a polarizer. It then passes thro... | 54.8 | float | Not supported with pagination yet |
In Image processing, opening is a process in which first dilation operation is performed and then erosion operation is performed. Is it true? | False | bool | Not supported with pagination yet |
Determine the number of positive real zero of the given function: $f(x)=x^5+4*x^4-3x^2+x-6$. | [3, 1] | list of integer | Not supported with pagination yet |
Consider a source X with a distortion measure $d(x, \hat{x})$ that satisfies the following property: all columns of the distortion matrix are permutations of the set $\{d_1, d_2, \ldots, d_m\}$. The function $\phi(D) = \max_{b:\sum_{i=1}^m p_i d_i \leq D} H(p)$ is concave. True or False? | True | bool | Not supported with pagination yet |
Consider a file with a size of 350 Kbytes storing in a web server. Client A sends a request to the server to retrieve the file from a remote location. It is known that the link capacity between client A and the server is 10 Mbps and the round trip time (RTT) between the server and client is fixed at 20ms. Assume that t... | 344 | integer | Not supported with pagination yet |
Fig. Q4 shows the contour of an object. Represent it with an 8-directional chain code. The resultant chain code should be normalized with respect to the starting point of the chain code. Represent the answer as a list with each digit as a element. | [0, 2, 0, 2, 1, 7, 1, 2, 0, 3, 0, 6] | list of integer | |
What is the Cramer-Rao lower bound on $E_\theta(\hat{\theta}(X)-\theta)^2$, where $\hat{\theta}(X)$ is an unbaised estimator of $\theta$ for the Gaussian distribution family $f_\theta(x)=N(0,\theta)$? (a) $2\theta$. (b) $2\theta^2$. (c) $0.5\theta^{-1}$. (d) $0.5\theta^{-2}$. Which option is correct? | (b) | option | Not supported with pagination yet |
Square ABCD. Rectangle AEFG. The degree of ∠AFG=20. Please find ∠AEB in terms of degree. Return the numeric value. | 25.0 | float |
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Dataset Card for "TheoremQA"
Introduction
We propose the first question-answering dataset driven by STEM theorems. We annotated 800 QA pairs covering 350+ theorems spanning across Math, EE&CS, Physics and Finance. The dataset is collected by human experts with very high quality. We provide the dataset as a new benchmark to test the limit of large language models to apply theorems to solve challenging university-level questions. We provide a pipeline in the following to prompt LLMs and evaluate their outputs with WolframAlpha.
How to use TheoremQA
from datasets import load_dataset
dataset = load_dataset("TIGER-Lab/TheoremQA")
for d in dataset['test']:
print(d)
Arxiv Paper:
https://arxiv.org/abs/2305.12524
Code
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