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bool 2
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bool 2
classes | gptoss_high_correct
bool 2
classes |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. The volume of a certain liquid varies with temperature as
$$
V=V^{\prime}\left\{0.75+3.9 \times 10^{-4}(T / \mathrm{K})+1.48 \times 10^{-6}(T / \mathrm{K})^2\right\}
$$
where $V^{\prime}$ is its volume at $300 \mathrm{~K}$. Calculate its expansion coefficient, $\alpha$, at $320 \mathrm{~K}$.
(A) $1.33 \times 10^{-3}\mathrm{~K}^{-1}$
(B) $1.19 \times 10^{-3}$$\mathrm{~K}^{-1}$
(C) $1.22 \times 10^{-3}$$\mathrm{~K}^{-1}$
(D) $1.31 \times 10^{-3}$$\mathrm{~K}^{-1}$
(E) $1.38 \times 10^{-3}\mathrm{~K}^{-1}$
(F) $1.15 \times 10^{-3}\mathrm{~K}^{-1}$
(G) $1.27 \times 10^{-3}\mathrm{~K}^{-1}$
(H) $1.45 \times 10^{-3}$$\mathrm{~K}^{-1}$
(I) $1.50 \times 10^{-3}\mathrm{~K}^{-1}$
(J) $1.05 \times 10^{-3}\mathrm{~K}^{-1}$
|
D
|
supergpqa_Science:cot
|
1418
|
149678f3ccf94a9391a65e36952ea147
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: We now define an algorithm: The definition of a(n) is the number of ways to write n as the sum of two squares, allowing permutations of the squares. Given the input x_list (a series of values): [98, 99, 100, 101, 102, 103, 104, 105, 106, 107], determine the corresponding output sequence y_list.
(A) [1, 1, 0, 0, 0, 1, 0, 1, 0, 2]
(B) [1, 0, 1, 2, 0, 0, 0, 1, 1, 0]
(C) [0, 0, 1, 0, 2, 1, 0, 1, 0, 1]
(D) [1, 0, 0, 1, 1, 0, 2, 0, 0, 1]
(E) [0, 1, 1, 0, 1, 0, 0, 1, 0, 1]
(F) [0, 1, 0, 1, 0, 1, 2, 0, 1, 0]
(G) [1, 1, 0, 0, 1, 2, 0, 0, 1, 0]
(H) [0, 0, 1, 1, 0, 0, 1, 1, 0, 2]
(I) [0, 0, 1, 0, 0, 1, 1, 0, 2, 0]
(J) [1, 0, 2, 1, 0, 0, 1, 0, 1, 0]
|
J
|
supergpqa_Science:cot
|
2370
|
a7453f72a8e24a19b46011a867524b58
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Let \(A\) be an \(m \times n\) matrix, \(B\) be an \(n \times m\) matrix, and satisfy \(AB = E\), then ( ).
(A) the row vector set of \(A\) is linearly independent, the column vector set of \(B\) is linearly independent
(B) the row vector set of \(A\) is linearly dependent, the column vector set of \(B\) is linearly independent
(C) the column vector set of \(A\) is linearly independent, the row vector set of \(B\) is linearly independent
(D) the row vector set of \(A\) is linearly independent, the column vector set of \(B\) is linearly dependent
(E) the column vector set of \(A\) is linearly independent, the column vector set of \(B\) is linearly independent
(F) the column vector set of \(A\) is linearly dependent, the row vector set of \(B\) is linearly independent
(G) the row vector set of \(A\) is linearly dependent, the row vector set of \(B\) is linearly dependent
(H) the row vector set of \(A\) is linearly independent, the row vector set of \(B\) is linearly independent
(I) the column vector set of \(A\) is linearly dependent, the row vector set of \(B\) is linearly dependent
(J) the row vector set of \(A\) is linearly independent, the row vector set of \(B\) is linearly dependent
|
A
|
supergpqa_Science:cot
|
3018
|
6755fe0ce12f4f37be4977b083989657
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: $P$ and $Q$ are two points on the axis and the perpendicular bisector respectively of an electric dipole. Both the points are far away from the dipole and at equal distances from it. If $\overrightarrow{E_P} = \overrightarrow{E_Q}$ are fields at $P$ and $Q$, then
(A) $$\overrightarrow{E_P} = \overrightarrow{E_Q}$$
(B) $$\overrightarrow{E_P} = \dfrac{3}{2}\overrightarrow{E_Q}$$
(C) $$\overrightarrow{E_P} = \dfrac{1}{3}\overrightarrow{E_Q}$$
(D) $$\overrightarrow{E_P} = 3\overrightarrow{E_Q}$$
(E) $$\overrightarrow{E_P} = \dfrac{1}{2}\overrightarrow{E_Q}$$
(F) $|E_Q| = \dfrac{1}{2} |E_P|$, and $\overrightarrow{E_Q}$ is perpendicular to $\overrightarrow{E_P}$.
(G) $$\overrightarrow{E_P} = -2\overrightarrow{E}_P$$
(H) $$\overrightarrow{E_P} = \dfrac{4}{3}\overrightarrow{E_Q}$$
(I) $$\overrightarrow{E_P} = 2\overrightarrow{E_Q}$$
|
A
|
supergpqa_Science:cot
|
1973
|
c1fbf8afc191453ebac1b47926651280
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| false
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Suppose that you can measure independent variables z and $y$ and that you have a dependent variable $f ( x, y )$ . The average values are $\bar{x}$, $\bar{y}$ and $\bar{f}$ . We define the error in $x$ as the deviations $\varepsilon_{x}=x-\bar{x},$ in $y$ as $\varepsilon_{y}=y-\bar{y},$ and in $f \mathrm{~ a s ~} \varepsilon_{f}=f-\bar{f}.$ Use a Taylor series expansion to express the error, $\varepsilon_{f}$ in $f,$ as a function of the errors $\varepsilon_{x}$ and $\varepsilon_{y}$ in $x$ and $y$ ,$\varepsilon_{f}$ is ().
(A) $$
\varepsilon_{f} \approx\left. \frac{\partial^2 f} {\partial x \partial y} \right|_{\bar{x}, \bar{y}} \varepsilon_{x} \varepsilon_{y}
$$
(B) $$
\varepsilon_{f} \approx\left. \frac{\partial^2 f} {\partial y^2} \right|_{\bar{y}} \varepsilon_{y}^2
$$
(C) $$
\varepsilon_{f} \approx\left. \frac{\partial f} {\partial z} \right|_{\bar{z}} \varepsilon_{y}
$$
(D) $$
\varepsilon_{f} \approx\left. \frac{\partial f} {\partial x} \right|_{\bar{y}} \varepsilon_{y}
$$
(E) $$
\varepsilon_{f} \approx\left. \frac{d f} {d x} \right|_{\bar{x}} \varepsilon_{x}
$$
(F) $$
\varepsilon_{f} \approx\left. \frac{\partial f} {\partial z} \right|_{\bar{z}} \varepsilon_{z}
$$
(G) $$
\varepsilon_{f} \approx\left. \frac{\partial^2 f} {\partial x^2} \right|_{\bar{x}} \varepsilon_{x}^2
$$
(H) $$
\varepsilon_{f} \approx\left. \frac{\partial f} {\partial y} \right|_{\bar{y}} \varepsilon_{x}
$$
(I) $$
\varepsilon_{f} \approx\left. \frac{\partial f} {\partial y} \right|_{\bar{x}} \varepsilon_{x}
$$
(J) $$
\varepsilon_{f} \approx\left. \frac{\partial f} {\partial x} \right|_{\bar{x}} \varepsilon_{y}
$$
|
E
|
supergpqa_Science:cot
|
3380
|
d30f33eea5634540bca96743cf47475c
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Potassium having atomic mass $=39.1$ u contains 93.10 atom % $_{}^{39}\textrm{K}$, having atomic mass 38.96371 u; 0.0118 atom % $_{}^{40}\textrm{K}$, which has mass of 40.0 u and is radioactive with $t_{1/2}=1.3\times10^9y,$ and 6.88 atom % $_{}^{41}\textrm{K}$ having a mass of 40.96184 u. Calculate the specific activity of naturally occurring potassium.
(A) None of these
(B) Specific activity $=14.06\:dis.\:g^{-1}S^{-1}$
(C) Specific activity $=60.06\:dis.\:g^{-1}S^{-1}$
(D) Specific activity $=45.09\:dis.\:g^{-1}S^{-1}$
(E) Specific activity $=16.03\:dis.\:g^{-1}S^{-1}$
(F) Specific activity $=15.09\:dis.\:g^{-1}S^{-1}$
(G) Specific activity $=30.69\:dis.\:g^{-1}S^{-1}$
(H) Specific activity $=15.06\:dis.\:g^{-1}S^{-1}$
(I) Specific activity $=30.03\:dis.\:g^{-1}S^{-1}$
(J) Specific activity $=14.03\:dis.\:g^{-1}S^{-1}$
|
G
|
supergpqa_Science:cot
|
3921
|
be6c01a2b9aa4ec8a63f57b45c4b3161
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Mix 75 cm³ of 0.20 mol·dm⁻³ NaOH solution with 25 cm³ of 0.40 mol·dm⁻³ H₂C₂O₄ solution. What is the concentration of $c(\mathrm{H}^{+})$ in this solution?
(A) $$
6. 7 \times1 0^{-7} \mathrm{~ m o l ~ \cdot~ d m}^{-3}
$$
(B) $$
4. 5 \times1 0^{-6} \mathrm{~ m o l ~ \cdot~ d m}^{-3}
$$
(C) $$
4. 0 \times1 0^{-4} \mathrm{~ m o l ~ \cdot~ d m}^{-3}
$$
(D) $$
9. 0 \times1 0^{-3} \mathrm{~ m o l ~ \cdot~ d m}^{-3}
$$
(E) $$
3. 2 \times1 0^{-3} \mathrm{~ m o l ~ \cdot~ d m}^{-3}
$$
(F) $$
7. 1 \times1 0^{-8} \mathrm{~ m o l ~ \cdot~ d m}^{-3}
$$
(G) $$
1. 8 \times1 0^{-4} \mathrm{~ m o l ~ \cdot~ d m}^{-3}
$$
(H) $$
5. 4 \times1 0^{-5} \mathrm{~ m o l ~ \cdot~ d m}^{-3}
$$
(I) $$
8. 6 \times1 0^{-9} \mathrm{~ m o l ~ \cdot~ d m}^{-3}
$$
(J) $$
2. 3 \times1 0^{-5} \mathrm{~ m o l ~ \cdot~ d m}^{-3}
$$
|
H
|
supergpqa_Science:cot
|
1547
|
9506d59e15b84623aeac2ede1a2bf6ea
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Let $V_{T}=\left\{ \left. a \right., b \right\}, V_{N}=\left\{ \left. A \right., B, C \right\}, S$ be the starting symbol. The production rules are as follows:
$$
\begin{array} {l c} \\{{{S \xrightarrow[p1]{{\mathrm{\scriptsize~ 1 ~}}} A B}}} & {{{A \xrightarrow[p2]{{\mathrm{\scriptsize~ 0. 9 ~}}} a A B}}} & {{{A \xrightarrow[p3]{{\mathrm{\scriptsize~ 1 ~}}}} a}}
\\ \\{{{A \xrightarrow[p4]{{\mathrm{\scriptsize~ 0. 5 ~}}} a B}}} & {{{A \xrightarrow[p5]{{\mathrm{\scriptsize~ 0. 2 ~}}} B}}} & {{{A \xrightarrow[p6]{{\mathrm{\scriptsize~ 0. 5 ~}}} a C}}}
\\ \\{{{B \xrightarrow[p7]{{\mathrm{\scriptsize~ 1 ~}}} a b}}} & {{{C \xrightarrow[p8]{{\mathrm{\scriptsize~ 0. 5 ~}}} a}}} & {{{C \xrightarrow[p9]{{\mathrm{\scriptsize~ 0. 2 ~}}} a a}}} \\ \end{array}
$$
What is the membership degree of the terminal string " $a b$ " and "aaabbb"?
(A) $$G(ab)=0.9,G(aaabbb)=0.8$$
(B) $$G(ab)=0.8,G(aaabbb)=1$$
(C) $$G(ab)=0.7,G(aaabbb)=0.9$$
(D) $$G(ab)=1,G(aaabbb)=0.9$$
(E) $$G(ab)=0.9,G(aaabbb)=1$$
(F) $$G(ab)=0.8,G(aaabbb)=0.7$$
(G) $$G(ab)=1,G(aaabbb)=0.95$$
(H) $$G(ab)=0.85,G(aaabbb)=0.9$$
(I) $$G(ab)=1,G(aaabbb)=0.7$$
(J) $$G(ab)=1,G(aaabbb)=0.8$$
|
D
|
supergpqa_Science:cot
|
1303
|
16ddee8c1ace41b08cd1ea46fc4031c5
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Let $n$ represent the smallest integer that satisfies the following conditions:
$\frac n2$ is a perfect square.
$\frac n3$ is a perfect cube.
$\frac n5$ is a perfect fifth.
How many divisors does $n$ have that are not multiples of $10$ ?
(A) 242
(B) 248
(C) 244
(D) 241
(E) 243
(F) 245
(G) 249
(H) 240
(I) 246
(J) 247
|
A
|
supergpqa_Science:cot
|
3050
|
ea8ee1f301e24f2abef3454faa2bcad3
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: With 1 mol of an ideal gas ($N_{2}$) as the medium, the following cycle is formed: $A \to B$, an isothermal reversible process; $B \to C$, an isochoric process; $C \to A$, an adiabatic reversible process. It is known that $T_{A} = 1000 \ \mathrm{K}$, $V_{A} = 1 \ \mathrm{dm}^{3}$, and $V_{B} = 20 \ \mathrm{dm}^{3}$. Calculate the thermal efficiency $\eta$ of this cycle process and determine the ratio of this engine's $\eta$ to the Carnot cycle's efficiency $\eta_{\mathrm{c}}$ under the same high and low temperature reservoir conditions, $\eta/ \eta_{\mathrm{c}}$ is_____.
(A) 38. 50%,0.5821
(B) 42. 30%,0.6101
(C) 43. 10%,0.6250
(D) 41. 75%,0.5979
(E) 46. 75%,0.6667
(F) 47. 50%,0.6789
(G) 39. 20%,0.5687
(H) 40. 00%,0.5555
(I) 45. 00%,0.6520
(J) 44. 25%,0.6392
|
D
|
supergpqa_Science:cot
|
3525
|
3c63131ea4ef4fa3800eed9bd8990340
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Compute the integral:
$$
\int \frac{ \sqrt{25+x^2} }{ 5 \cdot x } \, dx
$$
(A) C + \frac{1}{2} \cdot \ln\left(\left|\frac{\sqrt{25+x^2}-5}{5+\sqrt{25+x^2}}\right|\right) + \frac{1}{5} \cdot \sqrt{25+x^2}
(B) C + \frac{1}{2} \cdot \ln\left(\left|\frac{\sqrt{25+x^2}+5}{5-\sqrt{25+x^2}}\right|\right) - \frac{1}{5} \cdot \sqrt{25+x^2}
(C) C + \frac{1}{2} \cdot \ln\left(\left|\frac{\sqrt{25+x^2}+5}{5+\sqrt{25+x^2}}\right|\right) + \frac{1}{5} \cdot \sqrt{25+x^2}
(D) C + \frac{1}{2} \cdot \ln\left(\left|\frac{\sqrt{25+x^2}-5}{5-\sqrt{25+x^2}}\right|\right) - \frac{1}{5} \cdot \sqrt{25+x^2}
(E) C + \frac{1}{2} \cdot \ln\left(\left|\frac{\sqrt{25+x^2}-5}{5-\sqrt{25+x^2}}\right|\right) + \frac{1}{5} \cdot \sqrt{25+x^2}
(F) C + \frac{1}{2} \cdot \ln\left(\left|\frac{\sqrt{25+x^2}+5}{5-\sqrt{25+x^2}}\right|\right) + \frac{1}{5} \cdot \sqrt{25+x^2}
|
A
|
supergpqa_Science:cot
|
150
|
ee60046a313643beb3b3e16bc447fcc6
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| false
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The heat capacity of copper between $20^{\circ} \ \mathrm{C}$ and its melting point can be expressed as $C_{\mathrm{p}} = 22.6 + 6.27 \times 10^{-3} \, T \mathrm{~ J / (mol \cdot K)}$. The heat of fusion for copper is $13,290 \, \mathrm{J/mol}$, and the equilibrium solidification temperature is $1356 \, \mathrm{K}$. Under adiabatic conditions, what supercooling is required for $1 \, \mathrm{mol}$ of copper to completely solidify without the temperature rising back to the melting point?
(A) $$
3 7 5 \ ( \mathrm{K} )
$$
(B) $$
5 1 5 \ ( \mathrm{K} )
$$
(C) $$
7 7 0 \ ( \mathrm{K} )
$$
(D) $$
4 4 8 \ ( \mathrm{K} )
$$
(E) $$
3 2 0 \ ( \mathrm{K} )
$$
(F) $$
2 9 0 \ ( \mathrm{K} )
$$
(G) $$
6 2 5 \ ( \mathrm{K} )
$$
(H) $$
8 4 0 \ ( \mathrm{K} )
$$
(I) $$
5 5 0 \ ( \mathrm{K} )
$$
(J) $$
6 6 5 \ ( \mathrm{K} )
$$
|
D
|
supergpqa_Science:cot
|
1577
|
9b3cd7b8b36e4cf38359a936cd5c54ca
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Statement 1 | S_n is non-Abelian for all n >= 3. Statement 2 | If a is a permutation that is an m-cycle and b is a permutation that is an n-cycle, then |ab| = lcm(m,n).
(A) True, False
(B) Depends on the values of n, True
(C) True, True
(D) False, Depends on the values of m and n
(E) False, False
(F) Depends on the values of m and n, False
(G) False, True
(H) True, Depends on the values of m and n
(I) Depends on the values of n, False
(J) Depends on the values of m and n, True
|
A
|
supergpqa_Science:cot
|
3394
|
357323fa8bf14291a49441895311da75
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: 1 mol of butanediol and 1 mol of adipic acid are used to synthesize a polyester where $\overline{{{{M_{\mathrm{n}}}}}} = 5000$. The amounts of the two difunctional substances are exactly the same, and the effect of the end groups on $\overline{{{M_{\mathrm{n}}}}}$ is ignored. Determine the degree of reaction $p$ at which the polycondensation reaction ends.
(A) 0.92
(B) 0.84
(C) 0.90
(D) 0.95
(E) 0.88
(F) 0.89
(G) 0.87
(H) 0.91
(I) 0.98
(J) 0.93
|
I
|
supergpqa_Science:cot
|
263
|
0f7e6ef8f49a465c8791fe211ff2fe38
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The cell $Pt|H_2(g, \space0.1\space bar)|H^+(aq), \space pH = X || Cl^-(aq, \space 1\space M)|Hg_2Cl_2|Hg|Pt$,
has e.m.f. of $0.5755\space V$ at $25^{\small\circ}C$. The SOP of calomel electrode is $-0.28\space V$, then $pH$ of the solution will be:
(A) $$4.5$$
(B) 5.7
(C) none of these
(D) 4.7
(E) 4.9
(F) $$11$$
(G) 5.3
(H) 4.8
(I) $$5.5$$
(J) $$5.0$$
|
I
|
supergpqa_Science:cot
|
3468
|
c87a6e12c409452d949226282d1f5dd6
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: An infinite set of balls numbered $1,2,3, \dots $ are placed in an infinite set of boxes numbered $1,2,3, \dots $ by repeating the following:
1. Flip a fair coin repeatedly until it lands on heads.
2. If the head was on flip $k,$ place the smallest-numbered ball not yet in a box into the $k$ th smallest-numbered box not yet with a ball.
The expected value of box $6$ 's ball is $\dfrac{a}{b}$ , where $a$ and $b$ are relatively prime positive integers. Find $a+b.$
(A) 152
(B) 143
(C) 147
(D) 157
(E) 145
(F) 159
(G) 153
(H) 151
(I) 149
(J) 155
|
I
|
supergpqa_Science:cot
|
89
|
b2f36902db37440eb6113eb87a23ca43
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Solution A is a monoprotic weak acid with $c \left( \mathrm{~ H ~}^{+} \right)=\mathrm{a} \, \mathrm{~ mol ~} \cdot\mathrm{~ dm}^{-3}$. Solution Z is a sodium salt solution of this monoprotic weak acid, with $c \, ( \mathrm{~ H^{+} ~} )=\mathrm{b} \; \mathrm{~ mol ~} \cdot\mathrm{~ dm^{-3} ~}$. When the aforementioned solution A and solution Z are mixed in equal volumes, the measured $c \left( \mathrm{~ H ~}^{+} \right)=\mathrm{c} \mathrm{~ mol ~} \cdot\mathrm{~ dm ~}^{-3}$. What is the dissociation equilibrium constant $K_{\mathrm{a}}^{\ominus}$ for this monoprotic weak acid?
(A) $$
K_{\mathrm{a}}^{\ominus}=\frac{b^{2} a^{2}} {c K_{\mathrm{w}} }
$$
(B) $$
K_{\mathrm{a}}^{\ominus}=\frac{a^{2} b^{2}} {c K_{\mathrm{w}}^{\ominus}}
$$
(C) $$
K_{\mathrm{a}}^{\ominus}=\frac{c^{2} a^{2}} {b K_{\mathrm{w}}^{\ominus}}
$$
(D) $$
K_{\mathrm{a}}^{\ominus}=\frac{a b c^{2}} {K_{\mathrm{w}}^{\ominus}}
$$
(E) $$
K_{\mathrm{a}}^{\ominus}=\frac{a b^{2}} {c^{2} K_{\mathrm{w}}^{\ominus}}
$$
(F) $$
K_{\mathrm{a}}^{\ominus}=\frac{a^{2} c^{2}} {b K_{\mathrm{w}}^{\ominus}}
$$
(G) $$
K_{\mathrm{a}}^{\ominus}=\frac{b^{2} c^{2}} {a K_{\mathrm{w}}^{\ominus}}
$$
(H) $$
K_{\mathrm{a}}^{\ominus}=\frac{a^{2} b} {c^{2} K_{\mathrm{w}}^{\ominus}}
$$
(I) $$
K_{\mathrm{a}}^{\ominus}=\frac{c a^{2}} {b^{2} K_{\mathrm{w}}^{\ominus}}
$$
(J) $$
K_{\mathrm{a}}^{\ominus}=\frac{b a^{2}} {c^{2} K_{\mathrm{w}}^{\ominus}}
$$
|
B
|
supergpqa_Science:cot
|
3522
|
9be95739512f4a49b0520bf557b5d910
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: A solid sphere, a cone and a cylinder are floating in water. All have same mass, density and radius. Let $ f_{1},f_{2}$ and $f_{3} $ are the fraction of their volumes inside the water and $h_{1}, h_{2} $ and $h _{3}$ depths inside water Then
(A) $$h_{2} < h_{1}$$
(B) $$h_{3}< h_{2}$$
(C) $$h_{3} > h_{1}$$
(D) $$h_{3} < h_{1}$$
(E) $$h_{3} = h_{2}$$
(F) $$f_{3} > f_{2} >f_{1}$$
(G) $$f_{1}=f_{2}=f_{3}$$
(H) $$h_{3} > h_{2}$$
(I) $$h_{2} < h_{3}$$
|
B
|
supergpqa_Science:cot
|
865
|
c5632825dac84046af5fb820a66ff3ea
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| false
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: We now define an algorithm: The definition of a(n) is the triangle T(n,k) where T(n,k) = phi(k) if k divides n, and T(n,k) = 0 otherwise (n >= 1, 1 <= k <= n). Phi(k) represents Euler's totient function. Additionally, T(n,k) represents the number of elements of order k in a cyclic group of order n. Given the input x_list (a series of values): [94, 95, 96, 97, 98, 99, 100, 101, 102, 103], determine the corresponding output sequence y_list.
(A) [0, 0, 0, 0, 0, 0, 0, 0, 6, 0]
(B) [0, 0, 0, 0, 6, 2, 0, 0, 0, 0]
(C) [0, 0, 0, 7, 0, 0, 0, 0, 0, 0]
(D) [0, 1, 0, 0, 6, 0, 0, 0, 0, 0]
(E) [1, 0, 0, 0, 6, 0, 0, 0, 0, 0]
(F) [0, 0, 0, 0, 6, 0, 1, 0, 0, 0]
(G) [0, 0, 0, 0, 5, 0, 0, 0, 0, 0]
(H) [0, 0, 0, 0, 6, 0, 0, 0, 1, 0]
(I) [0, 0, 1, 0, 6, 0, 0, 0, 0, 0]
(J) [0, 0, 0, 0, 6, 0, 0, 0, 0, 0]
|
J
|
supergpqa_Science:cot
|
1382
|
618aa8d4f6a449d2b813027eebee13c6
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Given positive integers $p$, define the sequence $d(p)$ by the following rules: $d(1) = 1$, $d(2p) = d(p)$, and $d(2p+1) = (-1)^p d(p)$. Find the value of \[ \sum_{p=1}^{3983} d(p) d(p+2). \]
(A) -1
(B) -6
(C) 0
(D) -5
(E) -3
(F) 2
(G) -4
(H) 1
(I) -7
(J) -2
|
A
|
supergpqa_Science:cot
|
2051
|
8949df8fe2c7467b8536e2a6e61bc0f0
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: \( \int_{-\sqrt{2}}^{\sqrt{2}}{\sqrt{8-2 { { y}^{2}}}dy} \) = ( )
(A) \\( 2\\sqrt{2}(\\pi - 1) \\)
(B) \( \sqrt{2}(\pi +2) \)
(C) \(\sqrt{2}(\pi + 3)\)
(D) \sqrt{2}(\pi - 1)
(E) \( \sqrt{2}(\pi -2) \)
(F) \sqrt{2}(\pi + 1)
(G) \( 2\sqrt{2}(\pi +2) \)
(H) \sqrt{2}(\pi - 3)
(I) \( 2\sqrt{2}(\pi -2) \)
(J) \sqrt{2}(\pi - 4)
|
B
|
supergpqa_Science:cot
|
2023
|
9a2c16b9edf647a08ecf5365d3c49f01
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Oxygen and carbon monoride compete for binding to hemoglobin. If enough CO binds to hemoglobin,
the ability of the blood to deliver oxygen is impaired, and carbon monoride poisoning ensues. Consider the hemoglobin molecule to be a two-state system: the heme group is bound either to $O_{2}$ or to CO. Calculate the probability of binding to CO is(). Let the $G$ factor of Eq. 3.25 be equal to the ratio of the concentrations of CO and $O_{2}$ . Assume CO is 100 times less abundant than $O_{2}$ . CO is more tightly bound than $O_{2}$ to the heme group by about $0. 1 5 \, \mathrm{e V}$ . Let $T=3 0 0 \, \mathrm{K}$ .
(A) 5.29
(B) 1.34
(C) 0.42
(D) 6.47
(E) 2.18
(F) 4.89
(G) 9.13
(H) 8.66
(I) 3.72
(J) 7.01
|
I
|
supergpqa_Science:cot
|
1302
|
f6cf214aa91d4bd39669d8d4447a2645
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| false
| false
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: A grasshopper starts at the origin in the coordinate plane and makes a sequence of hops. Each hop has length $5$, and after each hop the grasshopper is at a point whose coordinates are both integers; thus, there are $12$ possible locations for the grasshopper after the first hop. What is the smallest number of hops needed for the grasshopper to reach the point $(2021, 2021)$?
(A) 581
(B) 577
(C) 573
(D) 575
(E) 580
(F) 574
(G) 576
(H) 579
(I) 572
(J) 578
|
J
|
supergpqa_Science:cot
|
3056
|
c54fc23723184342bf6d1c6278f32b76
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The spectral line of yttrium atom (Y) with a wavelength of 407.7359 nm is emitted during the $\mathrm{^2 F}_{5 / 2} \rightarrow \mathrm{^2 D}_{3 / 2}$ transition. In a weak external magnetic field of 1T, this spectral line will undergo Zeeman splitting. How many spectral lines can be observed perpendicular to the direction of the magnetic field? How many spectral lines can be observed parallel to the direction of the magnetic field?
(A) 14 lines are observed perpendicular to the direction of the magnetic field, and 6 lines are observed parallel to the direction of the magnetic field.
(B) 12 lines are observed perpendicular to the direction of the magnetic field, and 10 lines are observed parallel to the direction of the magnetic field.
(C) 16 lines are observed perpendicular to the direction of the magnetic field, and 12 lines are observed parallel to the direction of the magnetic field.
(D) 10 lines are observed perpendicular to the direction of the magnetic field, and 12 lines are observed parallel to the direction of the magnetic field.
(E) 12 lines are observed perpendicular to the direction of the magnetic field, and 8 lines are observed parallel to the direction of the magnetic field.
(F) 10 lines are observed perpendicular to the direction of the magnetic field, and 8 lines are observed parallel to the direction of the magnetic field.
(G) 14 lines are observed perpendicular to the direction of the magnetic field, and 10 lines are observed parallel to the direction of the magnetic field.
(H) 8 lines are observed perpendicular to the direction of the magnetic field, and 6 lines are observed parallel to the direction of the magnetic field.
(I) 18 lines are observed perpendicular to the direction of the magnetic field, and 8 lines are observed parallel to the direction of the magnetic field.
(J) 10 lines are observed perpendicular to the direction of the magnetic field, and 6 lines are observed parallel to the direction of the magnetic field.
|
E
|
supergpqa_Science:cot
|
2304
|
1cd9225b1e9e4399bda795b2a67cdc4b
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Potassium chloride $(^{39} \mathrm{K}^{35} \mathrm{Cl})$ is a colorless and transparent ionic crystal with a density of $\rho = 2.0 \mathrm{g/cm}^{3}$: (1) calculate the nearest neighbor distance between $\mathrm{K^{+}}$ and $\mathrm{Cl^{-}}$ in this solid; (2) based on the given optical properties, derive the lower limit of the energy gap between the valence band and the conduction band; (3) provide the relationship between the specific heat capacity $c$ of solid KCl and the temperature $T$;
(A) $$
2. 9 \, \AA
$$
$$
1. 5 0 \times1 0^{-1 8} \mathrm{J}
$$
$$
\beta T^{2}
$$
(B) $$
5. 0 \, \AA
$$
$$
2. 0 0 \times1 0^{-1 9} \mathrm{J}
$$
$$
\beta T^{3}
$$
(C) $$
3. 3 \, \AA
$$
$$
1. 2 0 \times1 0^{-1 8} \mathrm{J}
$$
$$
\alpha T^{2}
$$
(D) $$
3. 6 \, \AA
$$
$$
1. 1 0 \times1 0^{-1 8} \mathrm{J}
$$
$$
\delta T^{2}
$$
(E) $$
4. 5 \, \AA
$$
$$
1. 9 0 \times1 0^{-1 9} \mathrm{J}
$$
$$
\gamma T^{3}
$$
(F) $$
4. 0 \, \AA
$$
$$
1. 7 0 \times1 0^{-1 9} \mathrm{J}
$$
$$
\gamma T^{2}
$$
(G) $$
4. 2 \, \AA
$$
$$
1. 8 0 \times1 0^{-1 8} \mathrm{J}
$$
$$
\alpha T^{2}
$$
(H) $$
3. 7 \, \AA
$$
$$
1. 0 0 \times1 0^{-1 9} \mathrm{J}
$$
$$
\alpha T^{4}
$$
(I) $$
3. 4 \, \AA
$$
$$
3.1 eV
$$
$$
c = \alpha T^{3}
$$
(J) $$
5. 1 \, \AA
$$
$$
1. 4 0 \times1 0^{-1 9} \mathrm{J}
$$
$$
\delta T^{3}
$$
|
I
|
supergpqa_Science:cot
|
1233
|
3fbbd6aff1d844e9938d0deb8aa6a056
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The State of Florida must make two types of ballots, A and B, using three types of materials: construction paper, tissue paper, and ink. Ballot A uses 210 cm² of construction paper, 35 cm² of tissue paper, and 3 tsp of ink, and generates 7 chads. Ballot B uses 190 cm² of construction paper, 55 cm² of tissue paper, and 2 tsp of ink, and generates 3 chads. The State must generate at least 70,000 chads, but only 2.8 million cm² of construction paper, 0.63 million cm² of tissue paper, and 35,000 tsp of ink are available. Construction paper costs 23 cents per 100 cm², tissue paper costs 2 cents per 100 cm², and ink costs 15 cents per tsp. How many units of ballots A and B should be produced to minimize cost?
(A) 10000 units of ballot A and 9000 units of ballot B
(B) 14000 units of ballot A and 6000 units of ballot B
(C) 15000 units of ballot A and 5000 units of ballot B
(D) 8000 units of ballot A and 12000 units of ballot B
(E) 9000 units of ballot A and 11000 units of ballot B
(F) 11000 units of ballot A and 9000 units of ballot B
(G) 10000 units of ballot A and 10000 units of ballot B
(H) 7000 units of ballot A and 14000 units of ballot B
(I) 13000 units of ballot A and 7000 units of ballot B
(J) 12000 units of ballot A and 8000 units of ballot B
|
G
|
supergpqa_Science:cot
|
2532
|
e631b53b61874ac2a2874575522f9cec
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: matrix $A=(\begin{array}{rrrr} -2 & -1 & -1 & -1 \ 2 & 1 & 3 & 2 \ 1 & 1 & 0 & 1 \ -1 & -1 & -2 & -2 \end{array})$. Suppose f is the minimal polynomial of A. What is f(99)? Return the numeric without explanation.
(A) 989000.0
(B) 980100.0
(C) 990000.0
(D) 1010000.0
(E) 980000.0
(F) 100000.0
(G) 980001.0
(H) 1000000.0
(I) 990100.0
(J) 999000.0
|
C
|
supergpqa_Science:cot
|
3393
|
286476b1da534a969d0a71cda4c5ec85
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Let $p$ , $q$ , $r$ , and $s$ be positive real numbers such that
$$\begin{align*}p+q+r+s&=15\\p^2+q^2+r^2+s^2&=n\end{align*}$$
and $p\ge q\ge r\ge s$ . Given that the minimum possible value of $pq-rs$ is $12$ for a choice of constant $n$ , the sum of the possible values of $n$ is $x$ . If $x$ is an integer, compute $x$ . If $x$ can be expressed as $\frac mn$ for relatively prime positive integers $m$ and $n\ne1$ , compute $m+n$ . If $x$ can be expressed as $\frac{a+b\sqrt c}d$ for positive integers $a$ , $b$ , $c$ , and $d$ such that $\gcd(a,b,d)=1$ and $c$ is not divisible by the square of any prime, compute $a+b+c+d$ .
(A) 46
(B) 39
(C) 42
(D) 44
(E) 41
(F) 40
(G) 45
(H) 47
(I) 38
(J) 43
|
B
|
supergpqa_Science:cot
|
44
|
c0db1ebbdc0a48c097284a4e4228a3f2
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Let $A$ be an $m \times n$ matrix, $B$ be an $n \times m$ matrix, and $AB$ equals the identity matrix. Then
(A) $A$'s column vector set is linearly independent, $B$'s row vector set is linearly dependent;
(B) $A$'s row vector set is linearly dependent, $B$'s column vector set is linearly independent;
(C) $A$'s row vector set is linearly independent, $B$'s column vector set is linearly independent;
(D) $A$'s row vector set is linearly dependent, $B$'s column vector set is linearly dependent;
(E) $A$'s row vector set is linearly dependent, $B$'s row vector set is linearly dependent;
(F) $A$'s column vector set is linearly independent, $B$'s row vector set is linearly independent;
(G) $A$'s column vector set is linearly independent, $B$'s column vector set is linearly independent.
(H) $A$'s column vector set is linearly dependent, $B$'s row vector set is linearly independent;
(I) $A$'s row vector set is linearly independent, $B$'s row vector set is linearly dependent;
(J) $A$'s row vector set is linearly independent, $B$'s row vector set is linearly independent;
|
C
|
supergpqa_Science:cot
|
1017
|
eb5f66b6a67a4746b11edd2181e07154
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The amount of $(NH_{4})_{2}SO_{4}$ having degree of dissocation 75% which should be dissolved in 1500 ml of 1 M $NH_{4}OH$ to decrease its degree of dissociation by 200 times, is [$k_{b}$ of $NH_{4}OH$ = $1.8$ $\times10^{-5}$]:
(A) 112.1gm
(B) 56.0gm
(C) 28.0gm
(D) 140.1gm
(E) 65.4gm
(F) 224.2 gm
(G) 112.2gm
|
A
|
supergpqa_Science:cot
|
1876
|
ef612ca7f0484df0abf766c80fa17cfc
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| false
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Adding zinc to copper causes some copper atoms to be replaced by zinc atoms. Using the free electron model, determine the ratio of zinc atoms to copper atoms at which the Fermi sphere contacts the first Brillouin zone boundary. (Copper has a face-centered cubic lattice and is monovalent, while zinc is divalent.)
$${\frac{n_{Zn}} {n_{Cu}}=}$$
(A) $$
{\frac{7} {1 3}}
$$
(B) $$
{\frac{5} {1 2}}
$$
(C) $$
{\frac{8} {1 5}}
$$
(D) $$
{\frac{9} {1 6}}
$$
(E) $$
{\frac{1 1} {1 8}}
$$
(F) $$
{\frac{1 3} {2 0}}
$$
(G) $$
{\frac{1 1} {1 5}}
$$
(H) $$
{\frac{1 4} {1 7}}
$$
(I) $$
{\frac{6} {1 9}}
$$
(J) $$
{\frac{5} {1 4}}
$$
|
D
|
supergpqa_Science:cot
|
208
|
480a1ce9bfc740a5a15caf6a5c50f938
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Try to find the pH of a mixture of 300mL of 0.50mo/L H3 PO4 and 500mL of 0.50mol/L NaOH is ____.
(A) 7.51
(B) 7.23
(C) 8.11
(D) 8.35
(E) 6.95
(F) 7.44
(G) 7.68
(H) 6.80
(I) 7.92
(J) 7.85
|
A
|
supergpqa_Science:cot
|
352
|
2d0ee334c1154c33ae7773177df5ce2f
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The conductivity of a saturated solution containing $ AgA(K_{sp} = 3\times 10^{-14}) $ and $ AgB (K_{sp} = 1\times 10^{-14}) $ is $ 3.75\times 10^{-8}\Omega ^{-1}cm^{-1} $. If the limiting molar conductivity of $ Ag^{+} $ and $ A^{-}$ ion is 60 and 80 $\Omega ^{-1} cm^{2} mol^{-1} $ respectively, the limiting molar conductivity of $ B^{-}$ (in$ \Omega ^{-1}cm^{2}mol^{-1}$) is
(A) 165
(B) 155
(C) 270
(D) 190
(E) 180
(F) 170
(G) 145
(H) 67.5
(I) 135
(J) 260
|
C
|
supergpqa_Science:cot
|
681
|
9beb8ab9dcfb43b18064c4ed7f25ccb0
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Circle $\omega_1$ is defined by the equation $(x-7)^2+(y-1)^2=k,$ where $k$ is a positive real number. Circle $\omega_2$ passes through the center of $\omega_1$ and its center lies on the line $7x+y=28.$ Suppose that one of the tangent lines from the origin to circles $\omega_1$ and $\omega_2$ meets $\omega_1$ and $\omega_2$ at $A_1,A_2$ respectively, that $OA_1=OA_2,$ where $O$ is the origin, and that the radius of $\omega_2$ is $\frac{2011} {211}$ . What is $k$ ?
(A) 42
(B) 44
(C) 47
(D) 48
(E) 46
(F) 43
(G) 45
(H) 49
(I) 40
(J) 41
|
B
|
supergpqa_Science:cot
|
2161
|
a2e2310b18a04d7786c32ba5e1599aed
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: 10.05 mL of 0.02000 mol/L EDTA solution is mixed with 10.00 mL of 0.02000 mol/L Pb(NO3)2 solution [lgK(PbY)=18.0, lgY(H)=6.5 at pH=5.0], and the concentration of uncomplexed Pb2+ is ( )mol/L.
(A) 10^-5.8
(B) 10^-9.0
(C) 10^-8.4
(D) 10^-8.9
(E) 10^-8.1
(F) 10^-9.2
(G) 10^-6.0
(H) 10^-7.3
(I) 10^-7.5
(J) 10^-6.5
|
F
|
supergpqa_Science:cot
|
1642
|
20fff2a5feb746d5a6614e360c9bec7d
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: After coating the surface of a steel needle with density $\rho=7.8 \times 10^{3} \ \mathrm{kg/m}^{3}$ with a thin layer of oil that cannot be wetted by water, it is gently placed horizontally on the surface of still water. To ensure that the needle does not sink into the water at 0°C, disregarding Archimedes' buoyancy, what is the maximum diameter the steel needle can have?
(A) $$ 0. 1 6 \times1 0^{-3} \mathrm{~ m}
$$
(B) $$
= 0. 0 9 \times1 0^{-3} \mathrm{~ m}
$$
(C) $$
= 0. 0 5 \times1 0^{-3} \mathrm{~ m}
$$
(D) $$
= 0. 2 8 \times1 0^{-3} \mathrm{~ m}
$$
(E) $$
= 0. 3 5 \times1 0^{-3} \mathrm{~ m}
$$
(F) $$
= 0. 1 9 \times1 0^{-3} \mathrm{~ m}
$$
(G) $$
= 0. 2 0 \times1 0^{-3} \mathrm{~ m}
$$
(H) $$
= 0. 3 1 \times1 0^{-3} \mathrm{~ m}
$$
(I) $$
= 0. 0 7 \times1 0^{-3} \mathrm{~ m}
$$
(J) $$
= 0. 2 4 \times1 0^{-3} \mathrm{~ m}
$$
|
A
|
supergpqa_Science:cot
|
1588
|
a31cdb23b7bb488bba1d7400a74b30fa
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: In the early days, semiconductor materials such as germanium and silicon were often assessed for purity by measuring their resistivity. If the resistivity measured at room temperature is 10Ω cm, estimate the purity of $N$-type germanium as ().
(Germanium electron mobility $\mu = 3900 \, \mathrm{cm}^{2} \mathrm{V}^{-1} \mathrm{s}^{-1}$, germanium atomic density $d = 4.42 \times 10^{22} \mathrm{cm}^{-3}$, electron charge $e = 1.6 \times 10^{-19} \mathrm{A} \cdot \mathrm{s}$)
(A) $$ 8 8. \ \underbrace{8 8 8 8 8 8}_{6 \uparrow8} 5 3 \ \% $$
(B) $$ 6 6. \ \underbrace{6 6 6 6 6 6}_{6 \uparrow6} 7 5 \ \% $$
(C) $$
9 9. \ \underbrace{9 9 9 9 9 9}_{6 \uparrow9} 6 4 \ \%
$$
(D) $$ 2 2. \ \underbrace{2 2 2 2 2 2}_{6 \uparrow2} 4 1 \ \% $$
(E) $$ 4 4. \ \underbrace{4 4 4 4 4 4}_{6 \uparrow4} 9 8 \ \% $$
(F) $$ 1 1. \ \underbrace{1 1 1 1 1 1}_{6 \uparrow1} 3 6 \ \% $$
(G) $$ 7 7. \ \underbrace{7 7 7 7 7 7}_{6 \uparrow7} 5 9 \ \% $$
(H) $$ 5 5. \ \underbrace{5 5 5 5 5 5}_{6 \uparrow5} 8 2 \ \% $$
(I) $$ 0 0. \ \underbrace{0 0 0 0 0 0}_{6 \uparrow0} 5 4 \ \% $$
(J) $$ 3 3. \ \underbrace{3 3 3 3 3 3}_{6 \uparrow3} 2 7 \ \% $$
|
C
|
supergpqa_Science:cot
|
2290
|
055c10d76c6b4e57aa738d8b13f7d04f
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: We now define an algorithm: The definition of a(n) is the expansion of (8 + 7 x - 7 x^2 - 7 x^3)/(1 - 6 x - 7 x^2 + 5 x^3 + 6 x^4). Given the input x_list (a series of values): [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], determine the corresponding output sequence y_list.
(A) [13298456487, 91648010583, 631647678777, 4353391555507, 30004193292643, 206794130187017, 1425270850320398, 9822478297435248, 67697525926163329, 466579244606302616]
(B) [13297456486, 91647010581, 631637678776, 4353291555505, 30003193292641, 206784130187015, 1425170850320396, 9822378297435246, 67696525926163327, 466569244606302614]
(C) [13296456486, 91646010581, 631627678776, 4353181555505, 30002193292641, 206774130187015, 1425070850320396, 9822278297435246, 67695525926163327, 466559244606302614]
(D) [13297456485, 91647010580, 631637678775, 4353291555504, 30003193292640, 206784130187014, 1425170850320395, 9822378297435245, 67696525926163326, 466569244606302613]
(E) [13296456485, 91646010580, 631627678775, 4353181555504, 30002193292640, 206774130187014, 1425070850320395, 9822278297435245, 67695525926163326, 466559244606302613]
(F) [13297456484, 91647010582, 631637678774, 4353291555506, 30003193292642, 206784130187016, 1425170850320397, 9822378297435247, 67696525926163328, 466569244606302615]
(G) [13296456484, 91646010582, 631627678774, 4353181555506, 30002193292642, 206774130187016, 1425070850320397, 9822278297435247, 67695525926163328, 466559244606302615]
(H) [13298456486, 91648010581, 631647678776, 4353391555505, 30004193292641, 206794130187015, 1425270850320396, 9822478297435246, 67697525926163327, 466579244606302614]
(I) [13297456487, 91647010583, 631637678777, 4353291555507, 30003193292643, 206784130187017, 1425170850320398, 9822378297435248, 67696525926163329, 466569244606302616]
|
B
|
supergpqa_Science:cot
|
2380
|
07bffa881c0e4bc69b927b1e467ff28a
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: When a medium is present, we introduce the electric displacement vector and magnetic field strength in addition to the original electric field strength and magnetic induction. Why was magnetic induction not initially called magnetic field strength? Besides historical reasons, can we see any clues from the equations of static magnetic fields?
(A) Yes, because the equations of static magnetic fields have the same structure as those of electrostatic fields.
(B) Yes, because magnetic induction is a vector source produced by charge density, which is different from the property of electric field strength being a scalar source produced by current density.
(C) Yes, because magnetic induction is a scalar source produced by current density, which is different from the property of electric field strength being a vector source produced by charge density.
(D) No
(E) Yes, because magnetic induction is a vector source produced by current density, which is different from the property of electric field strength being a scalar source produced by charge density.
(F) Yes, because the Maxwell's equations for magnetic media without conduction currents and residual magnetism only become equivalent to the Maxwell's equations for dielectric media when magnetic field strength, magnetic induction, and permeability are respectively replaced by electric field strength, electric displacement, and dielectric constant.
(G) Yes, because magnetic induction is a scalar source produced by charge density, which is different from the property of electric field strength being a vector source produced by current density.
|
E
|
supergpqa_Science:cot
|
3506
|
7820a0106f784c2786e372fb65ca972a
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The flat bottom of cylinder tank is silvered and water ($\mu=4/3$) is filled in the tank upto a height $h$. A small bird is hovering at a height $3h$ from the bottom of the tank. When a small hole is opened near the bottom of the tank, the water level falls at the rate of $1cm.s$. The bird will perceive that his image's velocity is:
(A) 0.75cm/s downward
(B) 0.25cm/s upward
(C) $0.5cm/s$ upward
(D) 1cm/s downward
(E) 1.25cm/s upward
(F) 0.75cm/s upward
(G) $0.5cm/s$ downwards
(H) $1m/s$ downwards
(I) none of these
(J) 1cm/s upward
|
C
|
supergpqa_Science:cot
|
3665
|
adb0c3dcb03042788d6b93cc32c16d54
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: A charge particle of charge $q$ and mass $m$ is clamped rigidly at the circumference of a ring with mass $m$ and radius $R$. Initially ring is in vertical plane resting on a sufficiently rough horizontal surface with charge $q$ at the same horizontal level as that of the center of the ring. There exist uniform horizontal electric fields as shown. At $ t = 0$ the system is let free. Given that $(qE = mg)$. Using the above information answer the following. (Assume there is no sliding at point of contact at any moment of time during motion).Work done by the electric field when the ring has rotated through $90^{\circ}$ (use $ \pi = \frac{22}{7}$)
(A) $$ \dfrac{4}{7} mgR$$
(B) $$ -mgR$$
(C) \dfrac{8}{7} mgR
(D) \dfrac{3}{7} mgR
(E) $$ mg \sqrt{2}R$$
(F) $$ \dfrac{2}{7} mgR$$
(G) \dfrac{5}{7} mgR
(H) \dfrac{6}{7} mgR
(I) \dfrac{1}{7} mgR
(J) \dfrac{9}{7} mgR
|
A
|
supergpqa_Science:cot
|
463
|
941e4b3e4f7c4594b486d26a76c7c26e
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Compute $\int_{0}^{\frac{ 1 }{ 5 }} e^{-2 \cdot x^2} \, dx$ with accuracy $0.00001$.
(A) 0.1943
(B) 0.1949
(C) 0.1947
(D) 0.1945
(E) 0.1941
(F) 0.1944
(G) 0.1948
(H) 0.1946
(I) 0.1942
(J) 0.1950
|
G
|
supergpqa_Science:cot
|
3069
|
5c57d012bcac4b25a2a2d2e81563f9c5
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: A particle of mass $m$, carrying in a uniform magnetic field directed along $x-$axis. At the instant $t=0$ it is given a velocity $v_0$ at an angle $\theta$ with the $y-$axis, in the $x-y$ plane. The coordinates of the particle after one revolution will be :
(A) $$\left (\dfrac {2\pi m v_0 \cos \theta}{qB} 0, 2 \right)$$
(B) $$\left (\dfrac {2\pi m v_0 \sin \theta}{qB} 0, 4\right)$$
(C) $$\left (\dfrac {2\pi m v_0 \sin \theta}{qB} 0, 0\right)$$
(D) \left (\dfrac {2\pi m v_0 \sin \theta}{qB} 0, 2 \right)
(E) $$\left (\dfrac {2\pi m v_0 \cos \theta}{qB} 0, 4\right)$$
(F) $$\left (\dfrac {2\pi m v_0 \cos \theta}{qB} 0, 0 \right)$$
(G) $$\left (0,0 \dfrac {2\pi m v_0 \sin \theta}{qB}\right)$$
(H) $$(0,0,0)$$
|
C
|
supergpqa_Science:cot
|
2978
|
5eeae7acc4b941ea94a4725480ece259
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Compute the integral:
$$
\int \cos\left(\frac{ x }{ 2 }\right)^4 \, dx
$$
(A) \frac{\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)^3}{2}+\frac{3}{4}\cdot\left(\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)+\frac{x}{6}\right)+C
(B) \frac{\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)^3}{2}+\frac{3}{4}\cdot\left(\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)+\frac{x}{3}\right)+C
(C) \frac{\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)^3}{2}+\frac{3}{4}\cdot\left(\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)+\frac{x}{4}\right)+C
(D) \frac{\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)^3}{2}+\frac{3}{4}\cdot\left(\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)+\frac{x}{7}\right)+C
(E) \frac{\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)^3}{2}+\frac{3}{4}\cdot\left(\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)+\frac{x}{5}\right)+C
(F) \frac{\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)^3}{2}+\frac{3}{4}\cdot\left(\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)+\frac{x}{12}\right)+C
(G) \frac{\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)^3}{2}+\frac{3}{4}\cdot\left(\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)+\frac{x}{10}\right)+C
(H) \frac{\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)^3}{2}+\frac{3}{4}\cdot\left(\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)+\frac{x}{8}\right)+C
(I) \frac{\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)^3}{2}+\frac{3}{4}\cdot\left(\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)-\frac{x}{2}\right)+C
(J) \frac{\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)^3}{2}+\frac{3}{4}\cdot\left(\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)+\frac{x}{2}\right)+C
|
J
|
supergpqa_Science:cot
|
3109
|
80f71deefd6f4fe2868d702876493f01
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Evaluate \[ \lim_{x \to 1^-} \prod_{n=0}^\infty \left(\frac{1 + x^{n+1}}{1 + x^n}\right)^{x^n}. \]
(A) \frac{1}{2\sqrt{e}}
(B) \frac{1}{e}
(C) \frac{1}{2e}
(D) \frac{1}{\sqrt{e}}
(E) \frac{1}{2}
(F) \frac{1}{e^2}
(G) \frac{1}{2e^2}
(H) \frac{2}{e}
(I) \frac{1}{2} \cdot \frac{2}{e}
(J) \frac{e}{2}
|
H
|
supergpqa_Science:cot
|
3057
|
e381c92707814a44bb3afcf6c7460e7d
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Let $a_n$ be a recursively defined sequence such that $a_1 = 0$ , and for all integers $n > 1$ , we have
$$a_{n+1} = (2n+1)a_n + 2n.$$
Compute the last three digits of $a_{2019}$ .
(A) 377
(B) 374
(C) 375
(D) 373
(E) 378
(F) 371
(G) 379
(H) 370
(I) 372
(J) 376
|
B
|
supergpqa_Science:cot
|
2047
|
4031b1ea4c604b91b5715e832ec6f262
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Find the measure of the angle $\theta$ between the three-dimensional vectors $\vec{a}$ and $\vec{b}$, expressed in radians rounded to two decimal places, if it is not possible to express it exactly.
Given:
$\vec{a} = 3 \cdot \vec{i} - \vec{j} - 2 \cdot \vec{k}$
$\vec{b} = \vec{v} - \vec{w}$, where $\vec{v} = 2 \cdot \vec{i} + \vec{j} + 4 \cdot \vec{k}$ and $\vec{w} = 6 \cdot \vec{i} + \vec{j} + 2 \cdot \vec{k}$
(A) 2.79
(B) 2.54
(C) 2.64
(D) 2.49
(E) 2.84
(F) 2.44
(G) 2.69
(H) 2.94
(I) 2.59
(J) 2.74
|
E
|
supergpqa_Science:cot
|
3146
|
81c3b99b0d644075a57d4b1685f29033
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: In an infinitely long smooth-walled tube with a radius of 2 cm, a plane wave with a frequency of 300 Hz and a power of 0.1 $\mathbf{W}$ propagates along the axis of the tube. If there is a small hole with a radius of 0.5 cm on the tube wall, find: the reflected sound power; the transmitted sound power; and the sound power passing through the small hole.
(A) $$ 0. 0 2 8 8 \ {\bf w} ;0. 0 0 8 2 \ {\bf w} ;0 \ {\bf w} $$
(B) $$ 0. 0 5 9 8 \ {\bf w} ;0. 0 0 5 2 \ {\bf w} ;0 \ {\bf w} $$
(C) $$ 0. 0 7 9 8 \ {\bf w} ;0. 0 0 1 2 \ {\bf w} ;0 \ {\bf w} $$
(D) $$ 0. 0 3 9 8 \ {\bf w} ;0. 0 0 7 2 \ {\bf w} ;0 \ {\bf w} $$
(E) $$ 0. 0 1 9 8 \ {\bf w} ;0. 0 0 9 2 \ {\bf w} ;0 \ {\bf w} $$
(F) $$ 0. 0 6 9 8 \ {\bf w} ;0. 0 0 4 2 \ {\bf w} ;0 \ {\bf w} $$
(G) $$ 0. 0 4 7 8 \ {\bf w} ;0. 0 0 6 2 \ {\bf w} ;0 \ {\bf w} $$
(H) $$ 0. 0 0 5 8 \ {\bf w} ;0. 0 0 1 0 \ {\bf w} ;0 \ {\bf w} $$
(I) $$
0. 0 9 7 8 \ {\bf w} ;0. 0 0 2 2 \ {\bf w} ;0 \ {\bf w}
$$
(J) $$ 0. 0 8 7 8 \ {\bf w} ;0. 0 0 3 2 \ {\bf w} ;0 \ {\bf w} $$
|
I
|
supergpqa_Science:cot
|
2255
|
458772312d194dbaa5a9baa4ba172fe3
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: An infinitely long straight line is uniformly charged, with a charge per unit length of λ. Under the influence of its electric field, a particle with mass $m$ and charge $q$ performs uniform circular motion around it as its axis. What are the particle's speed $\upsilon$ and period $T$?
(A) $$
{\sqrt{\frac{q m} {2 \pi\varepsilon_{0} \lambda}}},~2 \pi r \sqrt{\frac{2 \varepsilon_{0} q} {-m \lambda}}
$$
(B) $$
{\sqrt{\frac{\varepsilon_{0} \lambda} {2 \pi q m}}},~2 r \pi \sqrt{\frac{-2 m \varepsilon_{0}} {q \lambda}}
$$
(C) $$
{\sqrt{\frac{\lambda q} {2 \pi m \varepsilon_{0}}}},~2 \pi r \sqrt{\frac{-2 \pi m} {q \lambda \varepsilon_{0}}}
$$
(D) $$
{\sqrt{\frac{-q \lambda} {2 \varepsilon_{0} \pi m}}},~2 r \pi \sqrt{\frac{\varepsilon_{0} m} {-q 2 \lambda}}
$$
(E) $$
{\sqrt{\frac{-q \lambda} {4 \varepsilon_{0} \pi m}}},~2 r \pi \sqrt{\frac{\varepsilon_{0} m} {-2 q \lambda}}
$$
(F) $$
{\sqrt{\frac{-\pi q} {2 \varepsilon_{0} m \lambda}}},~r \pi \sqrt{\frac{2 \pi m} {-q \lambda}}
$$
(G) $$
{\sqrt{\frac{q \lambda} {2 \pi\varepsilon_{0} m}}},~2 \pi r \sqrt{\frac{-2 \pi\varepsilon_{0} m} {q \lambda}}
$$
(H) $$
{\sqrt{\frac{-q \pi} {2 \lambda\varepsilon_{0} m}}},~r \sqrt{\frac{4 \pi\varepsilon_{0} m} {-q \lambda}}
$$
(I) $$
{\sqrt{\frac{-q \lambda} {2 \pi\varepsilon_{0} m}}},~2 \pi r \sqrt{\frac{2 \pi\varepsilon_{0} m} {-q \lambda}}
$$
(J) $$
{\sqrt{\frac{-\lambda q} {4 \pi\varepsilon_{0} m}}},~4 \pi r \sqrt{\frac{2 \varepsilon_{0} m} {q \lambda}}
$$
|
I
|
supergpqa_Science:cot
|
1223
|
1438eac39862499bb111d02699b7a83b
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: In corn, the number of double recessive types among the offspring of the AB/ab × AB/ab cross accounts for 16% of all progeny. What is the genetic map distance between these two genes?
(A) 50
(B) 45
(C) 30
(D) 10
(E) 15
(F) 20
(G) 35
(H) 40
(I) 60
(J) 25
|
F
|
supergpqa_Science:cot
|
391
|
c4989fc378654551b8ef93ad99fcf5bb
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| false
| false
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: We now define an algorithm: The definition of a(n) is: Abundant numbers (sum of divisors of m exceeds 2m). In number theory, the divisors of a positive integer m include all integers from 1 to m that divide m without leaving a remainder. The sum of these divisors should be greater than twice the number m itself. \n\nOutput the first n terms of this sequence. Given the input x_list (a series of values): [53, 54, 55, 56, 57, 58, 59, 60, 61, 62], determine the corresponding output sequence y_list.
(A) [212, 218, 230, 234, 240, 250, 252, 256, 268, 274]
(B) [218, 226, 232, 238, 244, 254, 260, 262, 270, 274]
(C) [210, 220, 226, 230, 236, 248, 256, 260, 266, 274]
(D) [210, 222, 228, 236, 244, 248, 258, 260, 266, 280]
(E) [208, 220, 224, 234, 242, 246, 250, 258, 266, 278]
(F) [214, 224, 230, 236, 242, 252, 256, 264, 268, 272]
(G) [214, 220, 226, 232, 248, 254, 256, 260, 266, 276]
(H) [224, 228, 234, 240, 246, 252, 258, 260, 264, 270]
(I) [212, 218, 222, 232, 238, 244, 248, 252, 260, 272]
(J) [216, 222, 228, 236, 240, 250, 254, 262, 268, 276]
|
H
|
supergpqa_Science:cot
|
3638
|
317a3c06808e402d89accf388904859f
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: $int x^2 sin x dx=$
(A) $-x^2 cos x + 2x sin x - 2 cos x +C$
(B) $2x cos{(x)} + (x^2 - 2) sin{(x)} + C$
(C) 2x sin{(x)} + (x^2 + 2) cos{(x)} + C
(D) 2x sin{(x)} + (x^2 - 2) cos{(x)} - C
(E) 0
(F) $2x cos{(x)} + (2 - x^2) sin{(x)} + C$
(G) $2x cos{(x)} + (x^2 + 2) sin{(x)} + C$
(H) $2x sin{(x)} + (2 - x^2) cos{(x)} + C$
(I) $x^2 cos x +C$
(J) 2x sin{(x)} + (x^2 - 2) cos{(x)} + C
|
H
|
supergpqa_Science:cot
|
3032
|
edd0e034a73c4dd3b278de507525b0fb
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The $K_{m} \!=\! 2.9 \times 10^{-4} M$ and $K_{i} \!=\! 2 \times 10^{-5} M$ for a certain enzyme. When $\left[ S \right]= 1.5 \times 10^{-3} M$, what concentration of a competitive inhibitor will result in 75% inhibition?
(A) $$
9. 4 \times 1 0^{-8} M
$$
(B) $$
8. 3 \times 1 0^{-3} M
$$
(C) $$
3. 7 \times1 0^{-4} M
$$
(D) $$
2. 6 \times 1 0^{-5} M
$$
(E) $$
2. 1 \times 1 0^{-4} M
$$
(F) $$
4. 5 \times 1 0^{-5} M
$$
(G) $$
1. 5 \times 1 0^{-7} M
$$
(H) $$
5. 9 \times 1 0^{-3} M
$$
(I) $$
7. 2 \times 1 0^{-6} M
$$
(J) $$
6. 8 \times 1 0^{-4} M
$$
|
C
|
supergpqa_Science:cot
|
1240
|
8f09ed9a7bfc429faf6e0ff6b84b43a0
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| false
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: When is the range of values for $a$ such that the quadratic form $f ( x_{1}, x_{2}, x_{3} )=x_{1}^{2}+x_{2}+5 x_{3}+2 a x_{1} x_{2}-2 x_{1} x_{3}+4 x_{2} x_{3}$ ?
(A) $$
- \frac{1} {5} < a < \frac{1} {5}
$$
(B) $$
- 2 < a < 2
$$
(C) $$
- 1< a < 1
$$
(D) $$
- \frac{4} {5} < a < \frac{4} {5}
$$
(E) $$
- \frac{3} {5} < a < \frac{3} {5}
$$
(F) $$
- \frac{2} {5} < a < \frac{2} {5}
$$
(G) $$
- \frac{4} {9} < a < 0
$$
(H) $$
- \frac{4} {3} < a < 0
$$
(I) $$
- \frac{4} {7} < a < 0
$$
(J) $$
- \frac{4} {5} < a < 0
$$
|
J
|
supergpqa_Science:cot
|
2354
|
f01f5f7f44e1480f812ee7045ff5e797
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: A uniform circular wire loop is connected to the terminals of a battery. The magnetic field induction at the centre due to ABC portion of the wire will be (length of ABC = ${ l }_{ 1 }$, length of ADC = ${ l }_{ 2 }$)
(A) $$\dfrac { { \mu }_{ 0 } { il }_{ 1 } {l}_{2}}{ 8\pi R^{ 2 }(l_{ 1 }+{ l }_{ 2 }{ ) } }$$
(B) $$\dfrac { { \mu }_{ 0 } { il }_{ 1 } {l}_{2}}{ 5\pi R^{ 2 }(l_{ 1 }+{ l }_{ 2 }{ ) } }$$
(C) $$\dfrac { { \mu }_{ 0 }{ il }_{ 1 }{ l }_{ 2 } }{ 2R(l_{ 1 }+{ l }_{ 2 }{ ) }^{ 2 } } $$
(D) $$\dfrac { { \mu }_{ 0 } { il }_{ 1 } {l}_{2}}{ 4\pi R^{ 2 }(l_{ 1 }+{ l }_{ 2 }{ ) } } $$
(E) $$\dfrac { { \mu }_{ 0 } { il }_{ 1 } {l}_{2}}{ 3\pi R^{ 2 }(l_{ 1 }+{ l }_{ 2 }{ ) } }$$
(F) $$\dfrac { { \mu }_{ 0 } { il }_{ 1 } {l}_{2}}{ 7\pi R^{ 2 }(l_{ 1 }+{ l }_{ 2 }{ ) } }$$
(G) $$Zero$$
(H) $$\dfrac { { \mu }_{ 0 } { il }_{ 1 } {l}_{2}}{ 6\pi R^{ 2 }(l_{ 1 }+{ l }_{ 2 }{ ) } }$$
(I) $$\dfrac { { \mu }_{ 0 } i(l_{ 1 }+{ l }_{ 2 }{ ) }\quad }{ 2\pi R\quad l_{ 1 }{ l }_{ 2 } } $$
(J) $$\dfrac { { \mu }_{ 0 } { il }_{ 1 } {l}_{2}}{ 2\pi R^{ 2 }(l_{ 1 }+{ l }_{ 2 }{ ) } }$$
|
D
|
supergpqa_Science:cot
|
870
|
322eeef653964174a164866cce151781
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: 10 mole of $N{H}_{3}$ is heated at 15 atm from $27$ to $347$ assuming volume constant. The pressure at equilibrium is found to be 50 atm. The equilibrium constant for dissociation of $N{H}_{3} : 2N{H}_{3} \rightleftharpoons {N}_{2} + 3{H}_{2}$; $\Delta H = 91.94 kJ$ can be written as; ${K}_{p} = \displaystyle\frac{{P}_{{N}_{2}} \times {\left({P}_{{H}_{2}}\right)}^{3}}{{\left({P}_{N{H}_{3}}\right)}^{2}} {\left(atm\right)}^{2}$The degree of dissociation of $N{H}_{3}$ is :
(A) 20%
(B) 46%
(C) 58.3%
(D) 55%
(E) 59.3%
(F) 56.3%
(G) 63.3%
(H) 61.3%
(I) 48%
(J) none of these
|
H
|
supergpqa_Science:cot
|
743
|
904a4aeefbb644f684bed204a8647109
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Equation $( x^{2} y+x \mathrm{s i n} x ) \mathrm{d} x+x N ( x, y ) \mathrm{d} y=0$ have integral factor $\mu( x, y )={\frac{1} {x^{2}}}$. Then ().
(A) $N (x, y)=x [2x+\varphi(y)]$, where $\varphi(x)$ is any continuously differentiable function
(B) $N (x, y)= 2x+\varphi(y)$, where $\varphi(x)$ is any continuously differentiable function
(C) $N (x, y)= 2x+3\varphi(y)$, where $\varphi(x)$ is any continuously differentiable function
(D) $N (x, y)=x [x+\varphi(y)]$, where $\varphi(x)$ is any continuously differentiable function
(E) $N (x, y)=2x [x+\varphi(y)]$, where $\varphi(x)$ is any continuously differentiable function
(F) $N (x, y)=3x [x+2\varphi(y)]$, where $\varphi(x)$ is any continuously differentiable function
(G) $N (x, y)=3x [2x+\varphi(y)]$, where $\varphi(x)$ is any continuously differentiable function
(H) $N (x, y)= x+\varphi(y)$, where $\varphi(x)$ is any continuously differentiable function
(I) $N (x, y)= x+2\varphi(y)$, where $\varphi(x)$ is any continuously differentiable function
(J) $N (x, y)=x [x+2\varphi(y)]$, where $\varphi(x)$ is any continuously differentiable function
|
D
|
supergpqa_Science:cot
|
2345
|
5a85bf30979846bdb004ae14828b491d
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The electromotive force of the battery Zn|ZnCl(0.05 mol/dm$^{3}$), AgCl(solid)|Ag at 25°C is 1.015 V, and the temperature coefficient of the electromotive force is $- 4.92 \times 10^{-4}$ V/K. The change in Gibbs free energy, the heat effect of the reaction, and the change in entropy for the battery reaction is().
(A) $$
=-2 3 5. 1 ~ \mathrm{k J} / \mathrm{m o l}
$$
(B) $$
=-2 2 8. 5 ~ \mathrm{k J} / \mathrm{m o l}
$$
(C) $$
=-2 3 1. 8 ~ \mathrm{k J} / \mathrm{m o l}
$$
(D) $$
=-2 3 2. 4 ~ \mathrm{k J} / \mathrm{m o l}
$$
(E) $$
=-2 4 0. 0 ~ \mathrm{k J} / \mathrm{m o l}
$$
(F) $$
=-2 2 9. 3 ~ \mathrm{k J} / \mathrm{m o l}
$$
(G) $$
=-2 1 5. 9 ~ \mathrm{k J} / \mathrm{m o l}
$$
(H) $$
=-2 2 4. 2 ~ \mathrm{k J} / \mathrm{m o l}
$$
(I) $$
=-2 3 0. 6 ~ \mathrm{k J} / \mathrm{m o l}
$$
(J) $$
=-2 1 6. 7 ~ \mathrm{k J} / \mathrm{m o l}
$$
|
H
|
supergpqa_Science:cot
|
2623
|
128ffff5854845708805580c2ee5b215
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: We now define an algorithm: The definition of a(n) is Bertrand primes: a(n) is largest prime < 2*a(n-1) for n > 1, with a(1) = 2. Bertrand's postulate states that for any integer n > 1, there is always at least one prime p such that n < p < 2n. This sequence constructs a list of primes based on this principle. Given the input x_list (a series of values): [24, 25, 26, 27, 28, 29, 30, 31, 32, 33], determine the corresponding output sequence y_list.
(A) [5099891, 10199759, 20399545, 40799055, 81598081, 163196143, 326392263, 652784487, 1305568933, 2611137839]
(B) [5099897, 10199765, 20399539, 40799049, 81598075, 163196135, 326392257, 652784477, 1305568927, 2611137825]
(C) [5099901, 10199757, 20399529, 40799057, 81598083, 163196145, 326392265, 652784485, 1305568935, 2611137835]
(D) [5099889, 10199763, 20399541, 40799051, 81598077, 163196139, 326392259, 652784479, 1305568929, 2611137831]
(E) [5099899, 10199771, 20399533, 40799043, 81598071, 163196131, 326392255, 652784475, 1305568923, 2611137821]
(F) [5099895, 10199761, 20399543, 40799053, 81598079, 163196141, 326392261, 652784483, 1305568931, 2611137833]
(G) [5099885, 10199769, 20399535, 40799045, 81598073, 163196133, 326392253, 652784473, 1305568925, 2611137819]
(H) [5099887, 10199773, 20399537, 40799047, 81598069, 163196137, 326392251, 652784481, 1305568921, 2611137823]
(I) [5099893, 10199767, 20399531, 40799041, 81598067, 163196129, 326392249, 652784471, 1305568919, 2611137817]
(J) [5099879, 10199775, 20399527, 40799059, 81598085, 163196147, 326392267, 652784489, 1305568937, 2611137841]
|
I
|
supergpqa_Science:cot
|
3640
|
706a9cd31ff740ad9da1c5e18947abf2
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Compute the length of the arc $y = 2 \cdot \ln(3 \cdot x)$ between the points $x = \sqrt{5}$ and $x = 2 \cdot \sqrt{3}$.
(A) 1+ln(15/3)
(B) 1+ln(3/5)
(C) 1+ln(3/15)
(D) 1+ln(9/5)
(E) 1+ln(15/9)
(F) 1+ln(15/5)
(G) 1+ln(5/3)
|
G
|
supergpqa_Science:cot
|
2148
|
3d9b50103322447e9139541267c392ed
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Use the following table to calculate the enthalpy of propane at 25° C and at oneatmassuming the enthalpy of solid carbon and hydrogen gas to be zero at that temperature and pressure. Bond Energy Bond Energy H - H 104.2 H - l 71.4 C - C 83.1 C - N 69.7 Cl -Cl 58.0 C - O 84.0 Br - Br 46.1 C -Cl 78.5 I - I 36.1 C - Br 65.9 C - H 98.8 C - I 57.4 N - H 93.4 O - O 33.2 O - H 110.6 N \equiv N 226 H -Cl 103.2 C = C 147 H - Br 87.5 C \equiv C 194 C = O 164 in formaldehyde 171 in otheraldehydes 174 inketones, Resonance energy in kcal/g mole Benzene ring = 37 Naphthalene= 75 Carboxylic acids = 28 Esters= 24 The heat of vaporization for carbon(s) to carbon(g) = 171.70 kcal/mole.
(A) 527.8 kcal
(B) -24.7 kcal
(C) -101.3 kcal
(D) 956.6 kcal
(E) 416.8 kcal
(F) -200.1 kcal
(G) 515.10 kcal
(H) 689.4 kcal
(I) 842.2 kcal
(J) 302.5 kcal
|
B
|
supergpqa_Science:cot
|
3656
|
3812456a7da343cab626ecb50ef8e308
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Anhydrous calcium chloride is often used as a dessicant. In the presence of excess of $CaCl_2$, the amount of the water taken up is governed by $K_p = 6.4 \times 10^{85}$ for the following reaction at room temperature, $CaCl_2 (s) + 6H_2O (g)\rightleftharpoons CaCl_2 \cdot 6H_2O (s)$. What is the equilibrium vapour pressure of water in a closed vessel that contains $CaCl_2 (s)$?
(A) $$P_{H_2O} = 3.5 \times 10^{-15}atm$$
(B) $$P_{H_2O} = 7.5 \times 10^{-14}atm$$
(C) $$P_{H_2O} = 7.5 \times 10^{-15}atm$$
(D) $$P_{H_2O} = 10 \times 10^{17}atm$$
(E) $$P_{H_2O} = 2.5 \times 10^{-15}atm$$
(F) None of these
(G) $$P_{H_2O} = 1.5 \times 10^{-15}atm$$
(H) $$P_{H_2O} = 5 \times 10^{-15}atm$$
(I) $$P_{H_2O} = 6.5 \times 10^{-15}atm$$
(J) $$P_{H_2O} = 7.5 \times 10^{-16}atm$$
|
H
|
supergpqa_Science:cot
|
2931
|
4f92ece51ef248b6b4864bb47137a512
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: If given
① $\mathbf{C}_{6} \mathbf{H}_{1 2} \mathbf{O}_{6}$ → $2CH_{3}CHOHCOOH$, $\Delta G^{\circ} = -52000 \mathrm{cal}$
② $\mathbf{C}_{6} \mathbf{H}_{1 2} \mathbf{O}_{6} + 6 \mathbf{O}_{2} \longrightarrow 6 \mathbf{C} \mathbf{O}_{2} + 6 \mathbf{H}_{2} \mathbf{O}$, $\Delta G^{\circ} = -68600 \mathrm{cal}$
Find the $\Delta G^{\circ}$ for the complete oxidation of lactic acid to $CO_{2}$ and $H_{2}O$, and when the energy conversion efficiency to ATP is 40%, how many $\mathrm{ATP}$ can be produced in this process?
(A) $$
- 2 5 0 0 0 0 \mathrm{c a l} \cdot\mathrm{m o l}^{-1},12.5
$$
(B) $$
- 3 5 0 0 0 0 \mathrm{c a l} \cdot\mathrm{m o l}^{-1},20.0
$$
(C) $$
- 3 1 0 0 0 0 \mathrm{c a l} \cdot\mathrm{m o l}^{-1},16.9
$$
(D) $$
- 3 2 0 0 0 0 \mathrm{c a l} \cdot\mathrm{m o l}^{-1},18.1
$$
(E) $$
- 3 6 0 0 0 0 \mathrm{c a l} \cdot\mathrm{m o l}^{-1},20.7
$$
(F) $$
- 3 4 0 0 0 0 \mathrm{c a l} \cdot\mathrm{m o l}^{-1},19.2
$$
(G) $$
- 2 8 0 0 0 0 \mathrm{c a l} \cdot\mathrm{m o l}^{-1},15.7
$$
(H) $$
- 2 9 0 0 0 0 \mathrm{c a l} \cdot\mathrm{m o l}^{-1},16.3
$$
(I) $$
- 3 8 0 0 0 0 \mathrm{c a l} \cdot\mathrm{m o l}^{-1},21.7
$$
(J) $$
- 3 1 7 0 0 0 \mathrm{c a l} \cdot\mathrm{m o l}^{-1},17.4
$$
|
J
|
supergpqa_Science:cot
|
2258
|
03317480f2c54f5993075514222c25fc
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: A charged particle is released from origin with initial velocity $V = V_0\hat{i} $ in a magnetic field $\vec{B}=\dfrac{\sqrt{3}}{2}B_0\hat{i}+\dfrac{B_0}{2}\hat{j}$. The charge and mass of the particle are $q$ and $m$ respectively. Choose the correct option(s):
(A) velocity \(\dfrac{ V_0\sqrt{3}}{3}\) is responsible for circular motion of particle in helix
(B) velocity \(\dfrac{ V_0\sqrt{3}}{2}\) is responsible for circular motion of particle in helix
(C) the velocity $\dfrac{ V_0\sqrt{3}}{2}$ is responsible for progress of particle in direction of magnetic field
(D) velocity \(\dfrac{ V_0\sqrt{3}}{6}\) is responsible for circular motion of particle in helix
(E) velocity \(\dfrac{ V_0}{\sqrt{2}}\) is responsible for circular motion of particle in helix
(F) velocity \(\dfrac{ V_0\sqrt{2}}{2}\) is responsible for circular motion of particle in helix
(G) velocity $\dfrac{ V_0}{2}$ is responsible for circular motion of particle in helix
(H) velocity \(\dfrac{ V_0\sqrt{3}}{4}\) is responsible for circular motion of particle in helix
(I) the pitch of the helical path described by the particle is $\dfrac{2\pi mV_0}{B_0q}$
|
G
|
supergpqa_Science:cot
|
1746
|
42218a1a88e144cda0a439614e5ed37a
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The conc. of ${Fe}^{3+}$ ions in a sample of water is found to be $50\times {10}^{-5}M$. Calculate the $pH$ at which $99$% of ${Fe}^{3+}$ will be precipitated. ${ K }_{ { sp }_{ Fe{ \left( OH \right) }_{ 3 } }\quad }={10}^{-36}$.
(A) 4.4
(B) none of these
(C) 5.9
(D) 4.2
(E) 4.1
(F) 4.0
(G) 4.3
(H) 5.8
(I) 3.7
(J) 4.5
|
I
|
supergpqa_Science:cot
|
937
|
1bcdfc904e89419ba9ec65b68b9c1b41
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Define the sequence of integers $V_n$ such that $V_1 = 5000, V_2 = 4999,$ and
$$$V_n = \lfloor (V_{n-1})^{\frac{2}{3}} \cdot \lfloor(V_{n-2})^{\frac{1}{3}}\rfloor \rfloor$$$
for all integers $n > 2.$ Find the last three digits of $V_{1000}.$
(A) 914
(B) 910
(C) 912
(D) 915
(E) 919
(F) 918
(G) 916
(H) 911
(I) 917
(J) 913
|
J
|
supergpqa_Science:cot
|
1027
|
7d85a045dee34fa1a349411dfbaea92f
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| false
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: At $298$K, the equilibrium constant for the reaction$Zn^{2+}+4NH_3\rightleftharpoons [Zn(NH_3)_4]^{2+}$ is $10^9$.If $E^o_{[Zn(NH_3)_4]^{2+}/[Zn^{2+}+4NH_3]}=-1.03$V then the value of $E^o_{Zn/Zn^{2+}}$ will be:
(A) -0.9545 V
(B) $+1.1$V
(C) $-1.1$V
(D) -0.7745 V
(E) none of these
(F) -0.7445 V
(G) -0.8245 V
(H) $-0.7645$V
(I) -0.7845 V
(J) -0.9245 V
|
H
|
supergpqa_Science:cot
|
1983
|
f3ecae66a41c499a994a86f1ec3dad45
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Calculation of real number integral
$$
I = \int_{0}^{2 \pi} \sin^{2n} x \, \mathrm{d}x \, (n \text{ is a natural number})
$$
(A) $$
\frac{2 \pi (n!) n (n + 2)}{2^{2n - 1}}
$$
(B) $$
\frac{\pi (2n + 1)!}{2^{2n + 1} (n!)^2}
$$
(C) $$
\frac{4 \pi n! (n - 1)!}{2^{2n + 2}}
$$
(D) $$
\frac{2 \pi\cdot2 n ( n-1 ) \cdots( n+1 )} {2^{2 n} n!}
$$
(E) $$
\frac{4 \pi (2n)!}{(n!) 2^{2n + 1}}
$$
(F) $$
\frac{2 \pi n! (n - 1) (2n)}{2^{2n} (n!)}
$$
(G) $$
\frac{\pi (2n - 1)!}{2^{2n} (n + 1)(n!)^2}
$$
(H) $$
\frac{2 \pi (n - 1)! n (n + 3)}{2^{n}}
$$
(I) $$
\frac{\pi n (n - 1) (n + 1)}{2^{n} (n!)^2}
$$
(J) $$
\frac{\pi n (n + 1) (n - 1)!}{2^{2n - 2}}
$$
|
D
|
supergpqa_Science:cot
|
1286
|
b577f124a6c54808b2a4101634356962
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The mass of a deuteron is twice that of a proton, and its charge is the same as that of a proton; the mass of an α particle is four times that of a proton, and its charge is twice that of a proton. When they are accelerated and enter the same uniform magnetic field, they both move in circular paths. It is measured that the radius of the proton's circular path is 10 cm. What are the radii of the paths for the deuteron and the α particle?
(A) $$
1 0 \, \mathrm{c m},~2 0 \, \mathrm{c m}
$$
(B) $$
1 5 \, \mathrm{c m},~2 0 \, \mathrm{c m}
$$
(C) $$
1 2 \, \mathrm{c m},~1 2 \, \mathrm{c m}
$$
(D) $$
1 8 \, \mathrm{c m},~1 8 \, \mathrm{c m}
$$
(E) $$
1 5 \, \mathrm{c m},~1 5 \, \mathrm{c m}
$$
(F) $$
2 0 \, \mathrm{c m},~2 0 \, \mathrm{c m}
$$
(G) $$
2 2 \, \mathrm{c m},~1 0 \, \mathrm{c m}
$$
(H) $$
1 4 \, \mathrm{c m},~1 4 \, \mathrm{c m}
$$
(I) $$
1 6 \, \mathrm{c m},~1 6 \, \mathrm{c m}
$$
(J) $$
1 0 \, \mathrm{c m},~1 5 \, \mathrm{c m}
$$
|
H
|
supergpqa_Science:cot
|
3228
|
157f398921704fbebb615e238a67e093
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: We now define an algorithm: The definition of a(n) is: Multiplication table {0..i} X {0..j} of binary polynomials (polynomials over GF(2)) interpreted as binary vectors, then written in base 10, or binary multiplication without carries. Note that this involves understanding binary polynomial arithmetic over the finite field GF(2), where addition and multiplication are performed modulo 2. Given the input x_list (a series of values): [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], determine the corresponding output sequence y_list.
(A) [27, 32, 27, 20, 27, 32, 27, 20, 11, 0]
(B) [24, 29, 24, 17, 24, 29, 24, 17, 8, 5]
(C) [22, 27, 22, 15, 22, 27, 22, 15, 6, 3]
(D) [29, 34, 29, 22, 29, 34, 29, 22, 13, 2]
(E) [28, 33, 28, 21, 28, 33, 28, 21, 12, 1]
(F) [31, 36, 31, 24, 31, 36, 31, 24, 15, 4]
(G) [30, 35, 30, 23, 30, 35, 30, 23, 14, 3]
(H) [26, 31, 26, 19, 26, 31, 26, 19, 10, 7]
(I) [23, 28, 23, 16, 23, 28, 23, 16, 7, 4]
(J) [25, 30, 25, 18, 25, 30, 25, 18, 9, 6]
|
A
|
supergpqa_Science:cot
|
2668
|
903eca94594a4fc28b84560c4ddf2caa
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| false
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Adam converts a base $10$ positive integer $n$ to base $3$ , and writes it down. Ben sees Adam's result, but interprets it in base $4$ , and converts it to base $10$ to give an integer $m$ . Find the number of possible values of $m-n$ that are at most $2000.$
(A) 246
(B) 244
(C) 239
(D) 241
(E) 247
(F) 245
(G) 243
(H) 242
(I) 238
(J) 240
|
D
|
supergpqa_Science:cot
|
2048
|
ecb6fa432e3f4f5da67ff8d24fbd45a6
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Another association: 150 lamps are on, each controlled by a pull switch (each pull changes the state of the corresponding lamp), numbered sequentially as 1, 2, 3, 4, ..., 150. If the pull switches of lamps numbered as multiples of 3 are pulled once, and then the pull switches of lamps numbered as multiples of 5 are pulled once, how many lamps will be on after all the pulls?
(A) 82
(B) 80
(C) 100
(D) 88
(E) 87
(F) 70
(G) 85
(H) 95
(I) 90
(J) 75
|
I
|
supergpqa_Science:cot
|
2995
|
701898aad61a489886c2eb8f4db59cdd
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Compute the area of the figure bounded by curves $y = 8 \cdot x^2$, $y = 4 + 4 \cdot x^2$, lines $x = 3$, $x = -2$, and the $x$-axis.
(A) 183/3
(B) 181/3
(C) 182/3
(D) 188/3
(E) 189/3
(F) 184/3
(G) 185/3
(H) 180/3
(I) 187/3
(J) 186/3
|
F
|
supergpqa_Science:cot
|
3067
|
8c5446b27c394fabbe0b7a9854905822
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Determine resonance energy of benzene $[{C}_{6}{H}_{6}(l)]$ from the following information:$\Delta {H}_{f}^{o}$ of ${C}_{6}{H}_{6}(l)=+49kJ$;$\Delta {H}_{f}^{o}$ of ${C}_{2}{H}_{2}(g)=+75kJ;$ $\Delta {H}_{v}^{o}$ of ${C}_{6}{H}_{6}(l)=+45kJ$$B.E$ of $C\equiv C=930kJ/mol$; $C=C=615kJ/mol$; $C-C=348kJ/mol$
(A) $$R.E=-32kJ/mol$$
(B) R.E=+160kJ/mol
(C) $$R.E=-230kJ/mol$$
(D) R.E=+230kJ/mol
(E) None of these
(F) $$R.E=+130kJ/mol$$
(G) $$R.E=+32kJ/mol$$
(H) $$R.E=+150kJ/mol$$
(I) R.E=-130kJ/mol
|
A
|
supergpqa_Science:cot
|
1934
|
635d752febee4c159c6c7b640f91afee
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Find the volume of the region of points $(x,y,z)$ such that \[ (x^2 + y^2 + z^2 + 8)^2 \leq 36(x^2 + y^2). \]
(A) 12 \pi^2 - 36 \pi
(B) 12 \pi^2 - 18 \pi
(C) 12 \pi
(D) 12 \pi^2 - 12 \pi
(E) 12 \pi^2 - 24 \pi
(F) 12 \pi^2 - 6 \pi
(G) 18 \pi
(H) 6 \pi^2
(I) 18 \pi^2
(J) 12 \pi^2
|
H
|
supergpqa_Science:cot
|
1055
|
4d7716b3582f480ab52401f4f555119e
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| false
| false
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: A charged object of mass $1\ kg$ is projected at $t = 0$ from ground with a velocity of $10 \sqrt{2}\ m/s$ making an angle $45^o$ with horizontal. In the entire region, an electric field is applied at $t = 0$, due to which a time varying force $F= 12t\ N$, where $t$ is in seconds acts on the object in horizontally forward direction. At how much distance from the starting point, the object strikes the ground? ($g = 10\ m/s^2$)
(A) $$88\ m$$
(B) $$80\ m$$
(C) $$96\ m$$
(D) $$72\ m$$
(E) $$68\ m$$
(F) $$60\ m$$
(G) $$64\ m$$
(H) $$10\ m$$
(I) $$48\ m$$
(J) $$20\ m$$
|
E
|
supergpqa_Science:cot
|
3833
|
19e08e9d421c4811aaf6e8c4f4afbef3
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: We now define an algorithm: The definition of a(n) is hypotenuse numbers (numbers that can be expressed as the square root of the sum of the squares of two non-zero integers). Given the input x_list (a series of values): [55, 56, 57, 58, 59, 60, 61, 62, 63, 64], determine the corresponding output sequence y_list.
(A) [119, 120, 122, 123, 125, 130, 135, 136, 137, 140]
(B) [115, 118, 120, 127, 129, 134, 138, 139, 144, 146]
(C) [114, 118, 121, 126, 129, 133, 137, 141, 142, 148]
(D) [118, 121, 124, 129, 131, 135, 136, 138, 143, 145]
(E) [116, 119, 120, 121, 123, 126, 131, 133, 135, 138]
(F) [122, 124, 125, 127, 131, 132, 138, 140, 141, 145]
(G) [121, 122, 124, 126, 128, 132, 136, 139, 140, 142]
(H) [124, 128, 130, 134, 137, 143, 147, 149, 150, 157]
(I) [120, 125, 127, 131, 135, 136, 139, 141, 142, 149]
(J) [117, 123, 126, 128, 133, 137, 139, 141, 143, 147]
|
A
|
supergpqa_Science:cot
|
2674
|
a0300a8a486b4ceeb8a3ee2034f5dadf
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| false
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Treating the conduction electrons in a metal as free electrons may seem simplistic, yet it often proves successful. For instance, it yields good results for the compressibility of certain metals. Given the electron density $a$ and the Fermi energy $\varepsilon_{\boldsymbol{r}}$, try to determine the isothermal compressibility when $K = -\ {\frac{1}{V}} \Big( {\frac{\partial V}{\partial p}} \Big)_{\mathrm{T}}$ at $T=0 \ \mathbf{K}$, where $V$ is the volume and $p$ is the pressure. (Hint: Use $pV = {\frac{2}{3}} E$, where $E$ is the total energy.)
(A) $$
\frac{3} {5 n \varepsilon_{r}}, \qquad( T=0 \mathrm{K} )
$$
(B) $$
\frac{1} {2 n \varepsilon_{r}}, \qquad( T=0 \mathrm{K} )
$$
(C) $$
\frac{7} {2 n \varepsilon_{r}}, \qquad( T=0 \mathrm{K} )
$$
(D) $$
\frac{7} {9 n \varepsilon_{r}}, \qquad( T=0 \mathrm{K} )
$$
(E) $$
\frac{3} {2 n \varepsilon_{r}}, \qquad( T=0 \mathrm{K} )
$$
(F) $$
\frac{3} {4 n \varepsilon_{r}}, \qquad( T=0 \mathrm{K} )
$$
(G) $$
\frac{3} {10 n \varepsilon_{r}}, \qquad( T=0 \mathrm{K} )
$$
(H) $$
\frac{3} {7 n \varepsilon_{r}}, \qquad( T=0 \mathrm{K} )
$$
(I) $$
\frac{9} {2 n \varepsilon_{r}}, \qquad( T=0 \mathrm{K} )
$$
(J) $$
\frac{7} {5 n \varepsilon_{r}}, \qquad( T=0 \mathrm{K} )
$$
|
E
|
supergpqa_Science:cot
|
2222
|
e706ab8388c24f29b19b738be024aabf
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: At 25 °C and 101,325 Pa, what is the collision frequency between $\mathrm{N_{2}}$ molecules and $\mathrm{O_{2}}$ molecules in the air? What is the average time for each collision?
(A) $$
1. \, 2 9 5 \, \times\, 1 0^{3 2} \mathrm{~ m^{-3} ~} \cdot\mathrm{~ s^{-1} ~},
$$
$$
8 \, \times\, 1 0^{-3 4} \mathrm{~ s}
$$
(B) $$
3. \, 9 4 0 \, \times\, 1 0^{3 3} \mathrm{~ m^{-3} ~} \cdot\mathrm{~ s^{-1} ~},
$$
$$
3 \, \times\, 1 0^{-3 5} \mathrm{~ s}
$$
(C) $$
2. \, 3 8 0 \, \times\, 1 0^{3 2} \mathrm{~ m^{-3} ~} \cdot\mathrm{~ s^{-1} ~},
$$
$$
5 \, ×\, 1 0^{-3 6} \mathrm{~ s}
$$
(D) $$
4. \, 3 5 7 \, \times\, 1 0^{3 4} \mathrm{~ m^{-3} ~} \cdot\mathrm{~ s^{-1} ~},
$$
$$
6 \, \times\, 1 0^{-3 6} \mathrm{~ s}
$$
(E) $$
2. \, 7 1 8 \, \times\, 1 0^{3 4} \mathrm{~ m^{-3} ~} \cdot\mathrm{~ s^{-1} ~},
$$
$$
9 \, \times\, 1 0^{-3 6} \mathrm{~ s}
$$
(F) $$
4. \, 1 4 5 \, \times\, 1 0^{3 5} \mathrm{~ m^{-3} ~} \cdot\mathrm{~ s^{-1} ~},
$$
$$
1 \, \times\, 1 0^{-3 4} \mathrm{~ s}
$$
(G) $$
2. \, 6 0 0 \, \times\, 1 0^{3 5} \mathrm{~ m^{-3} ~} \cdot\mathrm{~ s^{-1} ~},
$$
$$
2 \, \times\, 1 0^{-3 5} \mathrm{~ s}
$$
(H) $$
1. \, 8 5 0 \, \times\, 1 0^{3 3} \mathrm{~ m^{-3} ~} \cdot\mathrm{~ s^{-1} ~},
$$
$$
5 \, \times\, 1 0^{-3 5} \mathrm{~ s}
$$
(I) $$
3. \, 1 0 2 \, \times\, 1 0^{3 2} \mathrm{~ m^{-3} ~} \cdot\mathrm{~ s^{-1} ~},
$$
$$
7 \, \times\, 1 0^{-3 4} \mathrm{~ s}
$$
(J) $$
2. \, 4 9 5 \, \times\, 1 0^{3 4} \mathrm{~ m^{-3} ~} \cdot\mathrm{~ s^{-1} ~},
$$
$$
4 \, \times\, 1 0^{-3 5} \mathrm{~ s}
$$
|
J
|
supergpqa_Science:cot
|
3199
|
dee8e7c3b8314400bb56fdfb702d19e3
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Minimum distance between the parabola $4x={y}^{2}-8y+40$ and $4y={x}^{2}-8x+40$ is
(A) $$\sqrt{2}$$
(B) \sqrt{8}
(C) \sqrt{4}
(D) $$\sqrt{10}$$
(E) $$0$$
(F) \sqrt{6}
(G) $$\sqrt{3}$$
(H) \sqrt{5}
(I) \sqrt{7}
(J) $$2\sqrt{2}$$
|
A
|
supergpqa_Science:cot
|
3415
|
a0b73b031c0a41f68a6a1444736e45c3
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: A particle $P$ is sliding down a frictionless hemi-spherical howl. It passes the point $A$ at $t=0$. At this instant of time, the horizontal component of its velocity is $V$ A bead $Q$ of the same mass as $P$ is ejected from $A$ at $t=0$ along the horizontal string $AB$ with speed $v$. Friction between the bead and the string may be neglected. Let $t_{P}$ and $t_{Q}$ be the respective times taken by $P$ and $Q$ to reach the point $B$. Then
(A) $$t_P = t_Q$$
(B) $$t_P = \dfrac{1}{3} t_Q$$
(C) $$t_P = \dfrac{1}{2} t_Q$$
(D) $$t_P < t_Q$$
(E) $$\dfrac {t_P}{t_Q}=\dfrac {Length\ of\ arc\ ACB}{Length\ of\ AB} $$
(F) $$t_P > t_Q$$
(G) $$t_P = 2t_Q$$
(H) $$t_P = \dfrac{3}{2} t_Q$$
(I) $$t_P = \dfrac{2}{3} t_Q$$
|
D
|
supergpqa_Science:cot
|
787
|
731a0d1792c94eb696716015f6c617f1
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Using chemical methods to analyze uranium-containing ores, it is pointed out: at equilibrium, there is 3.59 × 10^7 grams of radium in 1 U^{238}. Try to find the decay constant $\lambda$ of uranium. The half-life of radium is equal to 1617 years.
(A) $$
\sim7.11 \cdot 10^{-17} \text{ seconds}^{-1}
$$
(B) $$
\sim4.88 \cdot 10^{-18} \text{ seconds}^{-1}
$$
(C) $$
\sim9.76 \cdot 10^{-19} \text{ seconds}^{-1}
$$
(D) $$
\sim1.13 \cdot 10^{-18} \text{ seconds}^{-1}
$$
(E) $$
\sim6.22 \cdot 10^{-19} \text{ seconds}^{-1}
$$
(F) $$
\sim8.01 \cdot 10^{-19} \text{ seconds}^{-1}
$$
(G) $$
\sim5.29 \cdot 10^{-17} \text{ seconds}^{-1}
$$
(H) $$
\sim2.54 \cdot 10^{-18} \text{ seconds}^{-1}
$$
(I) $$
\sim1.97 \cdot 10^{-17} \text{ seconds}^{-1}
$$
(J) $$
\sim3.45 \cdot 10^{-18} \text{ seconds}^{-1}
$$
|
B
|
supergpqa_Science:cot
|
3233
|
64dad03b2e5b4e4daa88802620e6f6e7
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The linear polycondensation of hydroxy acid $\mathrm{HO}(\mathrm{CH}_2)_4\mathrm{COOH}$ was performed, and the weight-average relative molecular mass of the product was measured to be 18,400. What are the percentage of esterified hydroxyl groups, the number-average relative molecular mass, and the number of structural units $X_n$?
(A) $98.9\%,\ 9251,\ 92.51$
(B) $97.8\%,\ 9000,\ 90.00$
(C) $92.5\%,\ 8600,\ 86.00$
(D) $96.6\%,\ 8800,\ 88.00$
(E) $99.1\%,\ 9200,\ 92.00$
(F) $95.0\%,\ 8051,\ 80.51$
(G) $97.3\%,\ 8900,\ 89.00$
(H) $94.7\%,\ 8400,\ 84.00$
(I) $96.0\%,\ 8950,\ 89.50$
(J) $93.9\%,\ 8150,\ 81.50$
|
A
|
supergpqa_Science:cot
|
224
|
bfefd58e83ec46a9ad184baa46c2dc89
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Acetylene gas, $\mathrm{C_{2} H_{2}} ( g ),$ can be prepared by the reaction of calcium carbide with water.
$$
\mathrm{C a C}_{2} ( s ) \,+\, 2 \ \mathrm{H}_{2} \mathrm{O} ( l ) \, \longrightarrow\, \mathrm{C a} ( \mathrm{O H} )_{2} ( s ) \,+\, C_{2} \mathrm{H}_{2} ( g )
$$
The volume of $C_{2}H_{2}$, that is collected over water at 23°C by reaction of 0.752 $g$ of $\mathsf{C a C}_{2}$ if the total pressure of the gas is 745 torr is____.
(A) $0. 3 0 8 \mathrm{L C}_{2} \mathrm{H}_{2}$
(B) $0. 2 6 7 \mathrm{L C}_{2} \mathrm{H}_{2}$
(C) $0. 3 1 5 \mathrm{L C}_{2} \mathrm{H}_{2}$
(D) $0. 2 8 5 \mathrm{L C}_{2} \mathrm{H}_{2}$
(E) $0. 3 1 0 \mathrm{L C}_{2} \mathrm{H}_{2}$
(F) $0. 2 9 9 \mathrm{L C}_{2} \mathrm{H}_{2}$
(G) $0. 3 0 2 \mathrm{L C}_{2} \mathrm{H}_{2}$
(H) $0. 2 9 0 \mathrm{L C}_{2} \mathrm{H}_{2}$
(I) $0. 2 7 3 \mathrm{L C}_{2} \mathrm{H}_{2}$
(J) $0. 3 2 4 \mathrm{L C}_{2} \mathrm{H}_{2}$
|
F
|
supergpqa_Science:cot
|
1632
|
7b5631946778488daddd46adda42092d
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: A solution contains a mixture of $\displaystyle Na_{2}CO_{3}$ and $NaOH$. Using phenolpthalein as indicator, $25$ mL of mixture required $19.5$ mL of $0.995\ N\ HCl$ for the end point. With methyl orange, $25$ mL of the solution required $25$ mL of the same $HCI$ for the end point. Calculate g/L of each substance in the mixture.
(A) $Na_{2}CO_{3}=23.2$ g/L, $NaOH= 22.3$ g/L
(B) $Na_{2}CO_{3}=23.2$ g/L, $NaOH= 21.3$ g/L
(C) Na_{2}CO_{3}=22.2 g/L, NaOH= 23.2 g/L
(D) Na_{2}CO_{3}=24.2 g/L, NaOH= 23.2 g/L
(E) $Na_{2}CO_{3}=22.3$ g/L, $NaOH= 23.2$ g/L
(F) Na_{2}CO_{3}=22.3 g/L, NaOH= 21.2 g/L
(G) None of the above
(H) $Na_{2}CO_{3}=24.2$ g/L, $NaOH= 21.2$ g/L
(I) $Na_{2}CO_{3}=20$ g/L, $NaOH= 25$ g/L
(J) Na_{2}CO_{3}=23.2 g/L, NaOH= 21.2 g/L
|
A
|
supergpqa_Science:cot
|
2900
|
97e08662b9b44cee8eefefa2a1b22763
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Molecular weight of solids. For $\mathbf{H}_{2}$, the Lennard-Jones parameters obtained from gas measurements are $\varepsilon\ =50 \times10^{-16} \ \mathrm{erg}, \ \ \sigma=2.96 \ \mathrm{Å}$ . Calculate the binding energy of $\mathbf{H}_{2}$ in fcc structure (in KJ/mol), treating each hydrogen molecule as spherical. The experimental value of the binding energy is 0.751 KJ/mol. Please compare the experimental value of the binding energy with the calculated value.
(A) $$
U_{t o t}
\approx-1. 4 8 \mathrm{K J / m o l}
$$
(B) $$
U_{t o t}
\approx-0. 9 5 \mathrm{K J / m o l}
$$
(C) $$
U_{t o t}
\approx-0. 6 3 \mathrm{K J / m o l}
$$
(D) $$
U_{t o t}
\approx-3. 9 1 \mathrm{K J / m o l}
$$
(E) $$
U_{t o t}
\approx-1. 1 0 \mathrm{K J / m o l}
$$
(F) $$
U_{t o t}
\approx-4. 0 2 \mathrm{K J / m o l}
$$
(G) $$
U_{t o t}
\approx-3. 2 5 \mathrm{K J / m o l}
$$
(H) $$
U_{t o t}
\approx-1. 7 6 \mathrm{K J / m o l}
$$
(I) $$
U_{t o t}
\approx-2. 8 7 \mathrm{K J / m o l}
$$
(J) $$
U_{t o t}
\approx-2. 5 5 \mathrm{K J / m o l}
$$
|
J
|
supergpqa_Science:cot
|
204
|
3897ab262fe9400da64efe756bb06bac
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: A spherical container with a radius of 10 cm is maintained at a temperature of $\mathbf{t}=27^{\circ} \, \mathbf{C}$, but there is a 1 $\operatorname{cm}^{2}$ area on the container wall that is kept at an extremely low temperature. The container is filled with water vapor, with an initial pressure of $\mathbf{p}_{0}=10 \mathrm{mm} \mathbf{Hg}$. Assuming that every water molecule condenses upon impacting the cold surface and deposits on this cold surface, how long is it will take for the vapor pressure in the container to drop to $\mathbf{p}=10^{-4} \mathrm{mm} \mathbf{Hg}$ ?.
(A) Approximately 4.00 seconds
(B) Approximately 2.25 seconds
(C) Approximately 3.25 seconds
(D) Approximately 3.75 seconds
(E) Approximately 5.65 seconds
(F) Approximately 2.75 seconds
(G) Approximately 4.50 seconds
(H) Approximately 3.00 seconds
(I) Approximately 5.20 seconds
(J) Approximately 6.10 seconds
|
C
|
supergpqa_Science:cot
|
2297
|
a60fb94c2ad848febc5004fa5175db3d
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: We now define an algorithm: The definition of a(n) is the sequence derived from the Molien series for the 6-dimensional complex representation of the double cover of the second Janko group (J2), which is an important object in the study of finite simple groups and modular forms. Given the input x_list (a series of values): [56, 57, 58, 59, 60, 61, 62, 63, 64, 65], determine the corresponding output sequence y_list.
(A) [314, 335, 372, 381, 445, 462, 500, 538, 598, 622]
(B) [322, 340, 377, 390, 446, 453, 507, 539, 596, 615]
(C) [317, 331, 370, 383, 440, 459, 510, 535, 590, 614]
(D) [316, 333, 373, 384, 441, 458, 506, 532, 590, 613]
(E) [315, 334, 374, 386, 442, 455, 503, 530, 592, 614]
(F) [313, 332, 371, 385, 448, 461, 502, 536, 593, 616]
(G) [318, 336, 375, 382, 443, 460, 508, 533, 595, 618]
(H) [321, 338, 379, 387, 444, 457, 504, 529, 589, 612]
(I) [320, 339, 380, 391, 450, 467, 515, 541, 601, 625]
(J) [319, 337, 378, 388, 447, 456, 501, 534, 597, 620]
|
D
|
supergpqa_Science:cot
|
1993
|
4acbc51b8b16421898cfa7ff0aa38931
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: If we know that matrix $\left( \begin{matrix} {{{2 2}}} & {{{3 0}}} \\ {{{-1 2}}} & {{{a}}} \\ \end{matrix} \right)$ has an eigenvector $\left( \begin{matrix} {{-5}} \\ {{3}} \\ \end{matrix} \right)$, what is the value of $a$ ?
(A) $$
- 1
$$
(B) $$
- 4
$$
(C) $$
- 1 8
$$
(D) $$
- 8
$$
(E) $$
- 1 6
$$
(F) $$
- 1 0
$$
(G) $$
- 1 2
$$
(H) $$
- 20
$$
(I) $$
- 6
$$
(J) $$
- 1 4
$$
|
E
|
supergpqa_Science:cot
|
346
|
dd4fb79355254476aa2040547726ddc3
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: When a plant's genotype is aab6, the height of the plant is 40 cm, and when the genotype is AABB, the height is 60 cm. Assume that each dominant allele contributes additively to the height. In the F2 generation produced by self-crossing of F1, what proportion of the plants have a height of 50 cm?
(A) 3/16
(B) 4/16
(C) 6/16
(D) 2/16
(E) 12/16
(F) 5/16
(G) 7/16
(H) 9/16
(I) 10/16
(J) 8/16
|
C
|
supergpqa_Science:cot
|
1221
|
890117a942344f0cb306a9723181b888
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Let $D$ be a circular sheet of radius $R$, $L$be a tangent line of $D$, the point density of any point $P$ of $D$ is proportional to the square of the distance $d$from $P$ to $L$, the scaling coefficient $k > 0$, and the position of the mass center of the sheet is ().
(A) $$ (R, 0 ) $$
(B) $$ ( \frac{3} {4} R, 0 ) $$
(C) $$ ( \frac{1} {3} R, 0 ) $$
(D) $$ ( \frac{2} {5} R, 0 ) $$
(E) $$ ( \frac{2} {3} R, 0 ) $$
(F) $$ ( \frac{3} {5} R, 0 ) $$
(G) $$ ( \frac{1} {4} R, 0 ) $$
(H) $$ ( \frac{4} {5} R, 0 ) $$
(I) $$ ( \frac{1} {2} R, 0 ) $$
(J) $$ ( \frac{1} {5} R, 0 ) $$
|
D
|
supergpqa_Science:cot
|
332
|
fa5ce65587834156a20ffa002484968f
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Place $0.10\ \text{mol} \ \text{C}_2\text{H}_2$ gas in a sealed container filled with $1.00\ \text{mol} \ \text{O}_2$ with a volume of $10.0 \ \text{dm}^3$, allowing it to completely combust to produce $\text{CO}_2$ and $\text{H}_2\text{O}$. What is the pressure inside the container when the reaction is complete and the temperature is 150°C?
(A) $$
4. 0 8 \times1 0^{2} \mathrm{~ k P a}
$$
(B) $$
5. 2 7 \times1 0^{2} \mathrm{~ k P a}
$$
(C) $$
4. 1 2 \times1 0^{2} \mathrm{~ k P a}
$$
(D) $$
2. 9 4 \times1 0^{2} \mathrm{~ k P a}
$$
(E) $$
3. 1 8 \times1 0^{2} \mathrm{~ k P a}
$$
(F) $$
2. 4 5 \times1 0^{2} \mathrm{~ k P a}
$$
(G) $$
2. 7 6 \times1 0^{2} \mathrm{~ k P a}
$$
(H) $$
3. 9 5 \times1 0^{2} \mathrm{~ k P a}
$$
(I) $$
3. 6 9 \times1 0^{2} \mathrm{~ k P a}
$$
(J) $$
3. 3 3 \times1 0^{2} \mathrm{~ k P a}
$$
|
I
|
supergpqa_Science:cot
|
194
|
e48f0f199575410fa5ab4576d76164bf
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: The standard enthalpy of combustion of solid phenol, CgH5OH, is -3054 kJ mol-1 at 298 K and its standard molar entropy is 144.0 J $\mathrm{K}^{-1}$ mol1. Calculate the standard Gibbs energy of formation of phenol at 298 K.
(A) $$
{-5 1. 0 \mathrm{~ k J ~ m o l^{-1}}}
$$
(B) $$
{-4 7. 1 \mathrm{~ k J ~ m o l^{-1}}}
$$
(C) $$
{-2 8. 7 \mathrm{~ k J ~ m o l^{-1}}}
$$
(D) $$
{-7 0. 2 \mathrm{~ k J ~ m o l^{-1}}}
$$
(E) $$
{-5 4. 3 \mathrm{~ k J ~ m o l^{-1}}}
$$
(F) $$
{-4 9. 8 \mathrm{~ k J ~ m o l^{-1}}}
$$
(G) $$
{-6 0. 4 \mathrm{~ k J ~ m o l^{-1}}}
$$
(H) $$
{-4 3. 6 \mathrm{~ k J ~ m o l^{-1}}}
$$
(I) $$
{-3 0. 2 \mathrm{~ k J ~ m o l^{-1}}}
$$
(J) $$
{-3 5. 5 \mathrm{~ k J ~ m o l^{-1}}}
$$
|
F
|
supergpqa_Science:cot
|
617
|
af70e3a6c0404028aaab7fc58365ae31
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| false
| false
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: For positive integers $n$ , let $f(n)$ denote the number of integers $1 \leq a \leq 130$ for which there exists some integer $b$ such that $a^b-n$ is divisible by $131$ , and let $g(n)$ denote the sum of all such $a$ . Find the remainder when
$$$\sum_{n = 1}^{130} [f(n) \cdot g(n)]$$$
is divided by $131$ .
(A) 56
(B) 58
(C) 52
(D) 55
(E) 50
(F) 53
(G) 59
(H) 54
(I) 57
(J) 51
|
H
|
supergpqa_Science:cot
|
83
|
d0af43cbc530401f88b4f9233181b4ee
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: What is the inverse ordinal of permutation $1 \; ( k+1 ) \; 2 \; ( k+2 ) \; \cdots\; ( k-1 ) \; ( 2 k-1 ) \; k \; ( 2 k )$ ?
(A) $$
\frac{1} {2} k ( k-1 )
$$
(B) $$
\frac{1} {2} k ( k+1 )
$$
(C) $$
\frac{1} {4} k ( k-1 )
$$
(D) $$
\frac{1} {4} k ( k+1 )
$$
(E) $$
\frac{1} {4} k ( k-2 )
$$
(F) $$
\frac{1} {8} k ( k+1 )
$$
(G) $$
\frac{1} {2} k ( k-2 )
$$
(H) $$
\frac{1} {8} k ( k-1 )
$$
(I) $$
\frac{3} {8} k ( k+1 )
$$
(J) $$
\frac{3} {8} k ( k-1 )
$$
|
A
|
supergpqa_Science:cot
|
341
|
32222513af354bf7ad7a9e47730d8119
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| true
| true
| true
| false
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Find the area of the region bounded by $|x - |y|| + |y - |x|| + |y| = 9$ in the Cartesian plane.
(A) 57
(B) 60
(C) 72
(D) 56
(E) 63
(F) 54
(G) 58
(H) 65
(I) 69
(J) 66
|
E
|
supergpqa_Science:cot
|
3095
|
65445991cb244277a318a86c5d6ab3c9
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Franklyn chooses a random positive divisor of 2016, and calls it $x$ . Then, Franklyn randomly chooses a positive divisor of $x$ , and calls it $y$ . The probability that $y = 42$ can be expressed as $\dfrac{m}{n}$ , where $\gcd(m, n) = 1$ . Find $m$ .
(A) 37
(B) 29
(C) 31
(D) 33
(E) 35
|
B
|
supergpqa_Science:cot
|
3073
|
9ea72bef219b4a30a342965ec257fe8e
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| null | null |
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Ratio of n$^{th}$ to m$^{th}$ wavelength of Lyman series in $H$ - atom is equal to:
(A) \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2-2}{(n+1)^2-2}\right\}
(B) $$\displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\displaystyle\left\{\frac{(m+1)^2-1}{(n+1)^2-1}\right\}$$
(C) \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2+1}{(n+1)^2-1}\right\}
(D) \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2-1}{(n+1)^2+1}\right\}
(E) \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2-3}{(n+1)^2-3}\right\}
(F) $$\displaystyle\frac{\lambda_n}{\lambda_m}=\frac{(m^2-1)\times n^2}{(n^2-1)\times m^2}$$
(G) $$\displaystyle\frac{\lambda_n}{\lambda_m}=\frac{(n^2-1)\times m^2}{(m^2-1)\times n^2}$$
(H) \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2+2}{(n+1)^2+2}\right\}
(I) \displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(n+1)}{(m+1)}\right\}^2\left\{\frac{(m+1)^2+1}{(n+1)^2+1}\right\}
(J) $$\displaystyle\frac{\lambda_n}{\lambda_m}=\left\{\frac{(m+1)}{(n+1)}\right\}^2\displaystyle\left\{\frac{(n+1)^2-1}{(m+1)^2-1}\right\}$$
|
B
|
supergpqa_Science:cot
|
480
|
d61c9289910f4b08a7a78abf1c7d8aa1
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: Compute the derivative $y^{(5)}$ of the function $y = 2 \cdot e^{3 \cdot x} \cdot \sin(2 \cdot x)$.
(A) 2 * e^(3 * x) * (122 * cos(2 * x) - 599 * sin(2 * x))
(B) 2 * e^(3 * x) * (122 * cos(2 * x) - 590 * sin(2 * x))
(C) 2 * e^(3 * x) * (122 * cos(2 * x) - 594 * sin(2 * x))
(D) 2 * e^(3 * x) * (122 * cos(2 * x) - 596 * sin(2 * x))
(E) 2 * e^(3 * x) * (122 * cos(2 * x) - 598 * sin(2 * x))
(F) 2 * e^(3 * x) * (122 * cos(2 * x) - 595 * sin(2 * x))
(G) 2 * e^(3 * x) * (122 * cos(2 * x) - 593 * sin(2 * x))
(H) 2 * e^(3 * x) * (122 * cos(2 * x) - 591 * sin(2 * x))
(I) 2 * e^(3 * x) * (122 * cos(2 * x) - 597 * sin(2 * x))
(J) 2 * e^(3 * x) * (122 * cos(2 * x) - 592 * sin(2 * x))
|
I
|
supergpqa_Science:cot
|
1131
|
8094b8c4ea1e43719628f404b9a93086
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| true
| true
| true
|
Answer the following multiple-choice question by giving the correct answer letter in parentheses. Provide CONCISE reasoning for the answer, and make sure to finish the response with "ANSWER: X" where X is one of (A), (B), (C), (D), etc.
Question: $ABC$ is a scalene triangle. Points $D$ , $E$ , and $F$ are selected on sides $BC$ , $CA$ , and $AB$ respectively. The cevians $AD$ , $BE$ , and $CF$ concur at point $P$ . If $ [AFP] = 126$ , $[FBP] = 63$ , and $[CEP] = 24$ , determine the area of triangle $ABC$ .
(A) 336
(B) 357
(C) 350
(D) 345
(E) 342
(F) 348
(G) 363
(H) 360
(I) 354
(J) 351
|
J
|
supergpqa_Science:cot
|
3134
|
c9f109d5271741138de3255ec1f9204c
|
supergpqa
|
supergpqa_Science:cot
| false
| true
| false
| false
| null | null |
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