MikaStars39/nano-eval huggingface dataset:
We now define an algorithm: The definition of a(n) is the number of ordered rooted trees with n edges such that the rightmost leaf of each subtree is at even level. Equivalently, it is the number of Dyck paths of semilength n with no return descents of odd length. The sequence starts with 1, 1, 4, 10, 32, 100, 329, 1101, 3761, 13035. Given the input x_list (a series of values): [17, 18, 19, 20, 21, 22, 23, 24, 25, 26], determine the corresponding output sequence y_list.

Options:
A. [27756630, 101888168, 375750540, 1391512658, 5172607770, 19293659258, 72188904390, 270870709268, 1019033438064, 3842912963396]
B. [27756625, 101888163, 375750535, 1391512653, 5172607765, 19293659253, 72188904385, 270870709263, 1019033438059, 3842912963391]
C. [27756623, 101888161, 375750533, 1391512651, 5172607763, 19293659251, 72188904383, 270870709261, 1019033438057, 3842912963389]
D. [27756628, 101888166, 375750538, 1391512656, 5172607768, 19293659256, 72188904388, 270870709266, 1019033438062, 3842912963394]
E. [27756626, 101888164, 375750536, 1391512654, 5172607766, 19293659254, 72188904386, 270870709264, 1019033438060, 3842912963392]
F. [27756624, 101888162, 375750534, 1391512652, 5172607764, 19293659252, 72188904384, 270870709262, 1019033438058, 3842912963390]
G. [27756622, 101888160, 375750532, 1391512650, 5172607762, 19293659250, 72188904382, 270870709260, 1019033438056, 3842912963388]
H. [27756621, 101888159, 375750531, 1391512649, 5172607761, 19293659249, 72188904381, 270870709259, 1019033438055, 3842912963387]
I. [27756627, 101888165, 375750537, 1391512655, 5172607767, 19293659255, 72188904387, 270870709265, 1019033438061, 3842912963393]
J. [27756629, 101888167, 375750539, 1391512657, 5172607769, 19293659257, 72188904389, 270870709267, 1019033438063, 3842912963395]
Answer: E
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.

Options:
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]
Answer: A
We now define an algorithm: The definition of a(n) is: Coefficients in the expansion of the Eisenstein series \\( E_2 \\) (also referred to as \\( E_1 \\) or \\( G_2 \\)) in number theory. This series is notable in the context of modular forms and plays a significant role in various mathematical fields, including elliptic functions and complex analysis. Given the input x_list (a series of values): [37, 38, 39, 40, 41, 42, 43, 44, 45, 46], determine the corresponding output sequence y_list.

Options:
A. [-805, -1250, -1194, -1990, -918, -2134, -966, -1846, -1702, -1558]
B. [-807, -1270, -1214, -2010, -938, -2154, -986, -1866, -1722, -1578]
C. [-809, -1290, -1234, -2030, -958, -2174, -1006, -1886, -1742, -1598]
D. [-810, -1300, -1244, -2040, -968, -2184, -1016, -1896, -1752, -1608]
E. [-808, -1280, -1224, -2020, -948, -2164, -996, -1876, -1732, -1588]
F. [-813, -1320, -1264, -2060, -988, -2204, -1036, -1916, -1772, -1628]
G. [-804, -1240, -1184, -1980, -908, -2124, -956, -1836, -1692, -1548]
H. [-806, -1260, -1204, -2000, -928, -2144, -976, -1856, -1712, -1568]
I. [-811, -1310, -1254, -2050, -978, -2194, -1026, -1906, -1762, -1618]
J. [-912, -1440, -1344, -2160, -1008, -2304, -1056, -2016, -1872, -1728]
Answer: J
We now define an algorithm: The definition of a(n) is the sequence which is the inverse of the 6th cyclotomic polynomial. This is a periodic sequence with period 6. Given the input x_list (a series of values): [92, 93, 94, 95, 96, 97, 98, 99, 100, 101], determine the corresponding output sequence y_list.

Options:
A. [0, 1, 1, 0, -1, -1, 0, 1, 1, 0]
B. [1, 0, 0, 1, -1, -1, 1, 0, 0, 1]
C. [1, 0, 0, 1, -1, -1, 0, 0, 1, 1]
D. [-1, 1, 1, -1, 0, 0, -1, 1, 1, -1]
E. [0, 1, 0, 1, -1, 1, 0, 1, 0, -1]
F. [0, -1, -1, 0, 1, 1, 0, -1, -1, 0]
G. [1, 1, -1, -1, 0, 0, 1, 1, -1, -1]
H. [-1, -1, 0, 1, 1, 0, -1, -1, 0, 1]
I. [0, 0, 1, 1, -1, 0, 0, 1, 1, -1]
J. [1, -1, -1, 1, 0, 0, 1, -1, -1, 1]
Answer: F
We now define an algorithm: The definition of a(n) is as follows:\n\nExpansion of $Product_{k>=0} (1 + x^{(2k+1)})$; number of partitions of n into distinct odd parts; number of self-conjugate partitions; number of symmetric Ferrers graphs with n nodes. Given the input x_list (a series of values): [60, 61, 62, 63, 64, 65, 66, 67, 68, 69], determine the corresponding output sequence y_list.

Options:
A. [214, 228, 241, 260, 281, 299, 317, 340, 366, 390]
B. [205, 219, 232, 251, 272, 290, 308, 331, 357, 381]
C. [209, 223, 236, 255, 276, 294, 312, 335, 361, 385]
D. [207, 221, 234, 253, 274, 292, 310, 333, 359, 383]
E. [213, 227, 240, 259, 280, 298, 316, 339, 365, 389]
F. [206, 220, 233, 252, 273, 291, 309, 332, 358, 382]
G. [210, 224, 237, 256, 277, 295, 313, 336, 362, 386]
H. [208, 222, 235, 254, 275, 293, 311, 334, 360, 384]
I. [211, 225, 238, 257, 278, 296, 314, 337, 363, 387]
J. [212, 226, 239, 258, 279, 297, 315, 338, 364, 388]
Answer: C
We now define an algorithm: The definition of a(n) is the numerator of the continued fraction expansion whose terms are the first-order differences of exponents in the binary representation of 4*n, with the exponents of 2 being listed in descending order. Given the input x_list (a series of values): [67, 68, 69, 70, 71, 72, 73, 74, 75, 76], determine the corresponding output sequence y_list.

Options:
A. [19, 16, 21, 20, 22, 17, 22, 25, 27, 19]
B. [16, 17, 21, 18, 24, 16, 23, 24, 28, 19]
C. [18, 18, 22, 20, 23, 15, 24, 22, 27, 17]
D. [17, 19, 22, 19, 24, 15, 23, 24, 26, 17]
E. [18, 16, 23, 18, 24, 17, 23, 23, 26, 20]
F. [19, 17, 22, 20, 23, 16, 22, 25, 27, 18]
G. [17, 17, 22, 19, 23, 16, 23, 24, 27, 19]
H. [18, 17, 21, 19, 24, 15, 24, 23, 28, 18]
I. [16, 18, 22, 20, 22, 17, 22, 25, 26, 20]
J. [17, 18, 23, 18, 23, 15, 22, 24, 26, 18]
Answer: G
We now define an algorithm: The definition of a(n) is: Factorial expansion of Gamma(1/4) = Sum_{n>=1} a(n)/n! with largest possible a(n), where Gamma is the Euler's gamma function. Given the input x_list (a series of values): [70, 71, 72, 73, 74, 75, 76, 77, 78, 79], determine the corresponding output sequence y_list.

Options:
A. [30, 51, 61, 8, 76, 75, 27, 58, 68, 58]
B. [25, 46, 56, 3, 71, 70, 22, 53, 63, 53]
C. [31, 52, 62, 9, 77, 76, 28, 59, 69, 59]
D. [29, 50, 60, 7, 75, 74, 26, 57, 67, 57]
E. [28, 49, 59, 6, 74, 73, 25, 56, 66, 56]
F. [26, 47, 57, 4, 72, 71, 23, 54, 64, 54]
G. [32, 53, 63, 10, 78, 77, 29, 60, 70, 60]
H. [24, 45, 55, 2, 70, 69, 21, 52, 62, 52]
I. [33, 54, 64, 11, 79, 78, 30, 61, 71, 61]
J. [27, 48, 58, 5, 73, 72, 24, 55, 65, 55]
Answer: B
We now define an algorithm: The definition of a(n) is the mean of leading digits in real-life sources of data, aligned with Benford's law (also known as the first-digit law), which states that in many naturally occurring collections of numbers, the leading digit is likely to be small. Given the input x_list (a series of values): [96, 97, 98, 99, 100, 101, 102, 103, 104, 105], determine the corresponding output sequence y_list.

Options:
A. [3, 7, 2, 8, 1, 6, 4, 3, 5, 9]
B. [1, 5, 7, 6, 4, 9, 8, 3, 2, 7]
C. [5, 8, 4, 3, 2, 9, 1, 6, 7, 5]
D. [4, 6, 2, 5, 7, 1, 9, 8, 3, 6]
E. [2, 9, 1, 8, 8, 3, 7, 2, 6, 1]
F. [7, 3, 9, 1, 6, 2, 8, 4, 5, 7]
G. [3, 9, 6, 4, 8, 5, 2, 7, 1, 9]
H. [6, 4, 8, 2, 5, 3, 9, 7, 1, 4]
I. [9, 1, 3, 7, 4, 8, 5, 6, 2, 8]
J. [8, 2, 5, 9, 3, 7, 6, 1, 4, 3]
Answer: E
We now define an algorithm: The definition of a(n) is numbers that cannot be expressed as m^k, where m > 0, k > 1, and m and k are integers. Given the input x_list (a series of values): [62, 63, 64, 65, 66, 67, 68, 69, 70, 71], determine the corresponding output sequence y_list.

Options:
A. [60, 61, 62, 63, 64, 66, 67, 68, 69, 71]
B. [63, 65, 67, 69, 71, 73, 75, 77, 79, 81]
C. [70, 71, 72, 73, 74, 75, 76, 77, 78, 79]
D. [83, 84, 85, 86, 87, 88, 89, 90, 91, 92]
E. [53, 54, 55, 56, 57, 58, 59, 60, 61, 62]
F. [72, 73, 75, 77, 78, 79, 81, 82, 84, 85]
G. [64, 65, 66, 67, 68, 69, 70, 71, 72, 73]
H. [74, 75, 76, 77, 78, 80, 81, 82, 84, 86]
I. [52, 64, 66, 68, 70, 72, 74, 76, 78, 80]
J. [73, 74, 75, 76, 77, 78, 79, 80, 82, 83]
Answer: J
We now define an algorithm: The definition of a(n) is the number of Baxter permutations of length n (Baxter numbers). Baxter permutations are permutations that avoid the patterns 2-14-3 and 3-41-2. Given the input x_list (a series of values): [15, 16, 17, 18, 19, 20, 21, 22, 23, 24], determine the corresponding output sequence y_list.

Options:
A. [2593341584, 16458756584, 105791986684, 687782586842, 4517543071922, 29949238543314, 200234184620734, 1349097425104917, 9154276618636013, 62522506583844269]
B. [2593341589, 16458756589, 105791986689, 687782586849, 4517543071929, 29949238543319, 200234184620739, 1349097425104919, 9154276618636019, 62522506583844279]
C. [2593341587, 16458756587, 105791986683, 687782586845, 4517543071925, 29949238543317, 200234184620737, 1349097425104913, 9154276618636017, 62522506583844273]
D. [2593341582, 16458756580, 105791986680, 687782586840, 4517543071920, 29949238543310, 200234184620730, 1349097425104915, 9154276618636010, 62522506583844270]
E. [2593341583, 16458756583, 105791986683, 687782586841, 4517543071921, 29949238543312, 200234184620732, 1349097425104918, 9154276618636012, 62522506583844275]
F. [2593341588, 16458756588, 105791986688, 687782586848, 4517543071928, 29949238543318, 200234184620738, 1349097425104912, 9154276618636020, 62522506583844278]
G. [2593341580, 16458756580, 105791986680, 687782586840, 4517543071919, 29949238543309, 200234184620729, 1349097425104911, 9154276618636009, 62522506583844268]
H. [2593341581, 16458756581, 105791986681, 687782586841, 4517543071921, 29949238543311, 200234184620731, 1349097425104914, 9154276618636014, 62522506583844274]
I. [2593341586, 16458756586, 105791986682, 687782586844, 4517543071924, 29949238543316, 200234184620736, 1349097425104912, 9154276618636016, 62522506583844272]
J. [2593341585, 16458756585, 105791986685, 687782586843, 4517543071923, 29949238543315, 200234184620735, 1349097425104916, 9154276618636015, 62522506583844271]
Answer: I
We now define an algorithm: The definition of a(n) is: Bisection (odd part) of Chebyshev sequence with Diophantine property. Chebyshev sequences are specific sequences derived from Chebyshev polynomials, which have applications in approximation theory and Diophantine equations. This specific subsequence takes only the odd-indexed terms of such a Chebyshev sequence. Given the input x_list (a series of values): [12, 13, 14, 15, 16, 17, 18, 19, 20, 21], determine the corresponding output sequence y_list.

Options:
A. [9725505567, 56684405277, 330380931085, 1925601180283, 11223226150563, 65413755723585, 381259308191437, 2222142093424987, 12951593252358435, 75487417420726113]
B. [9725506566, 56684406276, 330380931094, 1925601180292, 11223226150662, 65413755723684, 381259308191446, 2222142093424996, 12951593252358534, 75487417420726212]
C. [8734506567, 46574406277, 229280931095, 1814601180293, 10113226150663, 55303755723685, 280159308191447, 1211142093424997, 11841593252358535, 65377417420726213]
D. [9735506567, 56784406277, 331380931095, 1935601180293, 11323226150663, 65513755723685, 382259308191447, 2232142093424997, 13051593252358535, 75587417420726213]
E. [10725506567, 67684406277, 440380931095, 3025601180293, 12223226150663, 76413755723685, 481259308191447, 3222142093424997, 23951593252358535, 86487417420726213]
F. [9725506567, 56684406277, 330380931095, 1925601180293, 11223226150663, 65413755723685, 381259308191447, 2222142093424997, 12951593252358535, 75487417420726213]
G. [9724506567, 56674406277, 330280931095, 1924601180293, 11213226150663, 65403755723685, 381159308191447, 2221142093424997, 12941593252358535, 75477417420726213]
H. [8725506567, 46684406277, 230380931095, 1825601180293, 10223226150663, 55413755723685, 281259308191447, 1222142093424997, 11951593252358535, 65487417420726213]
I. [9725506568, 56684406278, 330380931096, 1925601180294, 11223226150664, 65413755723686, 381259308191448, 2222142093424998, 12951593252358536, 75487417420726214]
J. [9725506566, 56684406275, 330380931093, 1925601180291, 11223226150661, 65413755723683, 381259308191445, 2222142093424995, 12951593252358533, 75487417420726211]
Answer: F
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.

Options:
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]
Answer: A
We now define an algorithm: The definition of a(n) is: If cards numbered 1 through n are "Down Two Table" shuffled (top two put on bottom one at a time, third from top card dealt to table) until all of the cards are placed on the table, a(n) is the number of the last card dealt. Given the input x_list (a series of values): [62, 63, 64, 65, 66, 67, 68, 69, 70, 71], determine the corresponding output sequence y_list.

Options:
A. [11, 52, 19, 55, 22, 58, 25, 61, 28, 64]
B. [16, 50, 21, 53, 24, 56, 27, 59, 30, 62]
C. [15, 53, 18, 56, 21, 59, 24, 62, 27, 65]
D. [10, 51, 20, 54, 23, 57, 26, 60, 29, 63]
E. [17, 47, 14, 50, 27, 53, 30, 56, 13, 59]
F. [18, 48, 13, 51, 26, 54, 29, 57, 12, 60]
G. [14, 56, 17, 57, 20, 62, 23, 65, 26, 68]
H. [19, 49, 12, 52, 25, 55, 28, 58, 11, 61]
I. [12, 54, 15, 59, 18, 60, 21, 63, 24, 66]
J. [13, 55, 16, 58, 19, 61, 22, 64, 25, 67]
Answer: J
We now define an algorithm: The definition of a(n) is "Fermi-Dirac primes": numbers of the form $p^{(2^k)}$ where p is a prime number and k is a non-negative integer. Given the input x_list (a series of values): [52, 53, 54, 55, 56, 57, 58, 59, 60, 61], determine the corresponding output sequence y_list.

Options:
A. [193, 197, 199, 211, 223, 227, 229, 233, 239, 241]
B. [196, 198, 204, 215, 221, 224, 227, 231, 239, 246]
C. [199, 195, 203, 207, 221, 228, 229, 234, 241, 243]
D. [197, 193, 201, 208, 217, 230, 234, 235, 238, 242]
E. [200, 202, 206, 212, 218, 221, 225, 230, 235, 240]
F. [192, 198, 205, 213, 219, 228, 231, 234, 237, 242]
G. [191, 196, 202, 210, 224, 225, 228, 236, 241, 245]
H. [194, 199, 203, 214, 222, 226, 230, 232, 238, 243]
I. [198, 200, 206, 211, 222, 223, 232, 233, 236, 244]
J. [195, 201, 207, 209, 220, 229, 233, 237, 240, 244]
Answer: A
We now define an algorithm: The definition of a(n) is "Brazilian" numbers: numbers n such that there is a natural number b with 1 < b < n-1 such that the representation of n in base b has all equal digits. "Les nombres brésiliens" in French. 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.

Options:
A. [78, 80, 81, 82, 84, 85, 86, 87, 88, 90]
B. [80, 81, 82, 84, 85, 86, 87, 89, 90, 92]
C. [77, 79, 81, 83, 84, 86, 87, 88, 90, 91]
D. [78, 81, 82, 83, 85, 86, 88, 89, 90, 91]
E. [78, 80, 82, 83, 85, 86, 88, 90, 91, 92]
F. [79, 81, 82, 84, 85, 87, 88, 89, 90, 91]
G. [77, 79, 81, 82, 83, 85, 87, 88, 89, 91]
H. [78, 80, 82, 84, 86, 87, 88, 89, 91, 92]
I. [78, 79, 80, 82, 83, 84, 86, 87, 89, 90]
J. [79, 80, 81, 83, 84, 85, 87, 88, 89, 90]
Answer: A
We now define an algorithm: The definition of a(n) is: Table T(n,k) = n OR k read by antidiagonals. The OR operation refers to the bitwise inclusive OR. Given the input x_list (a series of values): [84, 85, 86, 87, 88, 89, 90, 91, 92, 93], determine the corresponding output sequence y_list.

Options:
A. [5, 8, 12, 10, 9, 14, 13, 15, 14, 12]
B. [8, 7, 13, 11, 11, 12, 12, 15, 12, 11]
C. [6, 8, 12, 10, 11, 12, 11, 14, 14, 13]
D. [9, 6, 12, 13, 10, 12, 14, 12, 11, 14]
E. [6, 7, 12, 11, 10, 11, 12, 13, 13, 11]
F. [9, 7, 11, 13, 10, 14, 12, 12, 13, 12]
G. [7, 10, 11, 10, 14, 11, 13, 12, 13, 12]
H. [7, 9, 11, 12, 11, 10, 12, 14, 12, 10]
I. [8, 9, 12, 11, 12, 13, 11, 14, 13, 10]
J. [10, 6, 13, 10, 12, 11, 12, 14, 12, 13]
Answer: E
We now define an algorithm: The definition of a(n) is numbers n such that there are no carries when n is squared by "long multiplication" in base 10. Given the input x_list (a series of values): [44, 45, 46, 47, 48, 49, 50, 51, 52, 53], determine the corresponding output sequence y_list.

Options:
A. [1050, 1052, 1054, 1060, 1070, 1071, 1072, 1150, 1151, 1152]
B. [1023, 1025, 1026, 1034, 1035, 1040, 1041, 1110, 1112, 1113]
C. [1020, 1023, 1030, 1035, 1040, 1090, 1091, 1170, 1171, 1172]
D. [1031, 1032, 1033, 1045, 1050, 1060, 1061, 1140, 1141, 1142]
E. [1015, 1016, 1017, 1041, 1042, 1080, 1081, 1160, 1161, 1162]
F. [1003, 1005, 1024, 1025, 1026, 1040, 1045, 1120, 1121, 1122]
G. [1060, 1062, 1064, 1075, 1076, 1101, 1103, 1180, 1181, 1182]
H. [1011, 1014, 1015, 1032, 1033, 1050, 1051, 1130, 1131, 1132]
I. [1040, 1043, 1055, 1056, 1065, 1110, 1112, 1190, 1191, 1192]
J. [1012, 1013, 1020, 1021, 1022, 1030, 1031, 1100, 1101, 1102]
Answer: J
We now define an algorithm: The definition of a(n) is the number of terms in the simple continued fraction for the n-th harmonic number \\( H_n = \\sum_{k=1}^n \\frac{1}{k} \\). Given the input x_list (a series of values): [64, 65, 66, 67, 68, 69, 70, 71, 72, 73], determine the corresponding output sequence y_list.

Options:
A. [48, 58, 53, 45, 68, 51, 50, 58, 75, 76]
B. [46, 56, 51, 43, 66, 49, 48, 56, 73, 74]
C. [50, 60, 55, 47, 70, 53, 52, 60, 77, 78]
D. [44, 54, 49, 41, 64, 47, 46, 54, 71, 72]
E. [49, 59, 54, 46, 69, 52, 51, 59, 76, 77]
F. [52, 62, 57, 49, 72, 55, 54, 62, 79, 80]
G. [45, 55, 50, 42, 65, 48, 47, 55, 72, 73]
H. [43, 53, 48, 40, 63, 46, 45, 53, 70, 71]
I. [51, 61, 56, 48, 71, 54, 53, 61, 78, 79]
J. [47, 57, 52, 44, 67, 50, 49, 57, 74, 75]
Answer: D
We now define an algorithm: The definition of a(n) is: Periods of reciprocals of integers that are coprime with 10. Given the input x_list (a series of values): [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], determine the corresponding output sequence y_list.

Options:
A. [73, 18, 79, 14, 70, 82, 159, 76, 19, 46]
B. [78, 13, 74, 16, 69, 84, 167, 75, 22, 48]
C. [72, 14, 77, 12, 62, 83, 162, 77, 15, 45]
D. [77, 19, 80, 18, 64, 87, 163, 72, 23, 42]
E. [71, 17, 75, 15, 68, 85, 164, 74, 21, 47]
F. [74, 15, 76, 11, 65, 80, 160, 79, 17, 44]
G. [79, 11, 81, 19, 63, 88, 165, 71, 24, 41]
H. [70, 21, 72, 20, 61, 89, 168, 70, 25, 40]
I. [76, 12, 73, 17, 67, 86, 161, 73, 20, 49]
J. [75, 16, 78, 13, 66, 81, 166, 78, 18, 43]
Answer: J
We now define an algorithm: The definition of a(n) is the sequence of numbers formed by using the formulas k*(5*k+1)/2 or k*(5*k-1)/2, where k is an integer. Given the input x_list (a series of values): [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], determine the corresponding output sequence y_list.

Options:
A. [1008, 1090, 1111, 1198, 1220, 1310, 1333, 1427, 1451, 1549]
B. [1018, 1100, 1121, 1207, 1229, 1319, 1342, 1436, 1460, 1558]
C. [1014, 1096, 1117, 1205, 1227, 1317, 1340, 1434, 1458, 1556]
D. [1010, 1092, 1113, 1199, 1221, 1311, 1334, 1428, 1452, 1550]
E. [1016, 1098, 1119, 1201, 1223, 1313, 1336, 1430, 1454, 1552]
F. [1012, 1094, 1115, 1203, 1225, 1315, 1338, 1432, 1456, 1554]
G. [1003, 1083, 1103, 1189, 1211, 1301, 1324, 1418, 1442, 1540]
H. [1005, 1085, 1105, 1191, 1213, 1303, 1326, 1420, 1444, 1542]
I. [1007, 1087, 1110, 1194, 1216, 1306, 1330, 1424, 1448, 1546]
J. [1020, 1102, 1123, 1209, 1231, 1321, 1344, 1438, 1462, 1560]
Answer: D
We now define an algorithm: The definition of a(n) is: Triangle T from the array A(x, y) = gcd(x,y), for x >= 1, y >= 1, read by antidiagonals. Given the input x_list (a series of values): [99, 100, 101, 102, 103, 104, 105, 106, 107, 108], determine the corresponding output sequence y_list.

Options:
A. [1, 1, 3, 3, 5, 5, 7, 7, 9, 9]
B. [7, 6, 9, 5, 6, 5, 5, 5, 5, 2]
C. [6, 3, 8, 2, 5, 3, 9, 4, 6, 7]
D. [1, 3, 5, 1, 3, 1, 1, 1, 2, 1]
E. [3, 1, 4, 5, 1, 2, 2, 3, 1, 4]
F. [5, 2, 6, 3, 2, 3, 5, 2, 3, 4]
G. [3, 1, 1, 4, 3, 2, 2, 4, 1, 1]
H. [2, 4, 6, 2, 4, 2, 2, 2, 3, 2]
I. [4, 5, 6, 2, 3, 1, 1, 5, 3, 4]
J. [2, 5, 1, 4, 3, 3, 4, 5, 2, 3]
Answer: D
We now define an algorithm: The definition of a(n) is: Numbers k such that the binomial coefficient C(2^k, k) is divisible by the binomial coefficient C(2^k, 2). Given the input x_list (a series of values): [59, 60, 61, 62, 63, 64, 65, 66, 67, 68], determine the corresponding output sequence y_list.

Options:
A. [56, 57, 58, 60, 61, 62, 65, 66, 68, 70]
B. [62, 63, 64, 66, 67, 68, 71, 72, 74, 76]
C. [66, 67, 68, 70, 71, 72, 75, 76, 78, 80]
D. [69, 70, 71, 73, 74, 75, 78, 79, 81, 83]
E. [78, 79, 80, 82, 83, 84, 87, 88, 90, 92]
F. [88, 89, 90, 92, 93, 94, 97, 98, 100, 102]
G. [97, 98, 99, 101, 102, 103, 106, 107, 109, 111]
H. [53, 54, 55, 57, 58, 59, 62, 63, 65, 67]
I. [81, 82, 83, 85, 86, 87, 90, 91, 93, 95]
J. [70, 71, 72, 74, 75, 76, 79, 80, 82, 84]
Answer: G
We now define an algorithm: The definition of a(n) is: Integers \\( n > 0 \\) such that \\( n \\) XOR \\( 20n = 21n \\). Given the input x_list (a series of values): [50, 51, 52, 53, 54, 55, 56, 57, 58, 59], determine the corresponding output sequence y_list.

Options:
A. [387, 388, 389, 391, 513, 514, 515, 516, 517, 519]
B. [388, 389, 390, 392, 514, 515, 516, 517, 518, 520]
C. [390, 391, 392, 394, 518, 519, 520, 521, 522, 524]
D. [385, 386, 387, 389, 511, 512, 513, 514, 515, 517]
E. [389, 390, 391, 393, 515, 516, 517, 518, 519, 521]
F. [382, 383, 384, 386, 508, 509, 510, 511, 512, 514]
G. [384, 385, 386, 388, 510, 511, 512, 513, 514, 516]
H. [386, 387, 388, 390, 512, 513, 514, 515, 516, 518]
I. [391, 392, 393, 395, 519, 520, 521, 522, 523, 525]
J. [383, 384, 385, 387, 509, 510, 511, 512, 513, 515]
Answer: H
We now define an algorithm: The definition of a(n) is: Numbers whose multiplicative digital root value equals 3. The multiplicative digital root of a number is obtained by multiplying its digits together, continuing this process iteratively until a single-digit number is obtained. Given the input x_list (a series of values): [23, 24, 25, 26, 27, 28, 29, 30, 31, 32], determine the corresponding output sequence y_list.

Options:
A. [2345678, 3456789, 4567890, 5678901, 6789012, 7890123, 8901234, 9012345, 1234567, 2345678]
B. [987654, 876543, 765432, 654321, 543210, 432109, 321098, 210987, 109876, 987650]
C. [7614576, 1764190, 8416729, 1053467, 2758931, 6537049, 2091482, 3634710, 5810934, 7429158]
D. [1212121, 2121212, 1212122, 2121221, 1212123, 2121232, 1212131, 2121312, 1213141, 2131412]
E. [1111131, 1111311, 1113111, 1131111, 1311111, 3111111, 11111113, 11111131, 11111311, 11113111]
F. [2222222, 3333333, 4444444, 5555555, 6666666, 7777777, 8888888, 9999999, 1111111, 1122334]
G. [123456, 654321, 456789, 987654, 321654, 789123, 951357, 357159, 753951, 159357]
H. [3141592, 2653589, 7932384, 6264338, 3279502, 8841971, 6939937, 5105820, 9749445, 9230781]
I. [123451, 234512, 345123, 451234, 512345, 614235, 723516, 835167, 941235, 257134]
J. [1123581, 1321345, 6891542, 9864597, 5712395, 3467591, 8679125, 4561782, 9023546, 1854762]
Answer: E
We now define an algorithm: The definition of a(n) is a sequence where each term is obtained by reversing the digits of the previous term and adding it to the previous term, starting with 196. Given the input x_list (a series of values): [17, 18, 19, 20, 21, 22, 23, 24, 25, 26], determine the corresponding output sequence y_list.

Options:
A. [1794102589, 8746117559, 16403234039, 70446464498, 130992928907, 450822227927, 900544455975, 1800098900975, 8801197801075, 17602285712105]
B. [1794102600, 8746117570, 16403234050, 70446464510, 130992928920, 450822227950, 900544456010, 1800098901010, 8801197801098, 17602285712140]
C. [1794102597, 8746117568, 16403234046, 70446464507, 130992928914, 450822227945, 900544455999, 1800098901008, 8801197801089, 17602285712177]
D. [1794102590, 8746117565, 16403234042, 70446464500, 130992928910, 450822227940, 900544455990, 1800098901002, 8801197801082, 17602285712172]
E. [1794102595, 8746117566, 16403234043, 70446464505, 130992928913, 450822227941, 900544455996, 1800098901005, 8801197801085, 17602285712175]
F. [1794102596, 8746117567, 16403234045, 70446464506, 130992928913, 450822227944, 900544455998, 1800098901007, 8801197801088, 17602285712176]
G. [1794102601, 8746117574, 16403234051, 70446464515, 130992928924, 450822227960, 900544456015, 1800098901025, 8801197801095, 17602285712195]
H. [1794102598, 8746117569, 16403234047, 70446464508, 130992928915, 450822227946, 900544456000, 1800098901009, 8801197801090, 17602285712178]
I. [1794102585, 8746117540, 16403234015, 70446464550, 130992928905, 450822227930, 900544455970, 1800098901200, 8801197801040, 17602285712130]
J. [1794102592, 8746117563, 16403234040, 70446464502, 130992928912, 450822227942, 900544455994, 1800098901004, 8801197801084, 17602285712174]
Answer: F
We now define an algorithm: The definition of a(n) is numbers n such that every group of order n is a nilpotent group. Given the input x_list (a series of values): [57, 58, 59, 60, 61, 62, 63, 64, 65, 66], determine the corresponding output sequence y_list.

Options:
A. [116, 119, 121, 123, 125, 128, 130, 132, 134, 136]
B. [118, 121, 122, 124, 126, 130, 132, 134, 136, 138]
C. [121, 123, 125, 127, 128, 131, 133, 135, 137, 139]
D. [110, 113, 114, 116, 119, 122, 124, 126, 129, 132]
E. [105, 108, 110, 112, 114, 118, 120, 122, 125, 127]
F. [108, 111, 113, 115, 117, 120, 122, 124, 126, 128]
G. [109, 112, 115, 117, 120, 123, 126, 128, 130, 133]
H. [112, 114, 117, 119, 123, 126, 128, 130, 133, 135]
I. [111, 115, 117, 120, 122, 125, 127, 130, 132, 134]
J. [115, 117, 119, 121, 124, 129, 131, 133, 135, 137]
Answer: C
We now define an algorithm: The definition of a(n) is Jablonski table T(n,k) read by antidiagonals: T(n,k) = number of distinct arrangements (necklaces) that can be formed using n beads of k different colors, accounting for rotations as identical. Given the input x_list (a series of values): [57, 58, 59, 60, 61, 62, 63, 64, 65, 66], determine the corresponding output sequence y_list.

Options:
A. [59, 253, 1048, 3371, 7830, 11169, 8234, 2199, 112, 7]
B. [57, 251, 1046, 3369, 7828, 11167, 8232, 2197, 110, 3]
C. [52, 246, 1041, 3364, 7823, 11162, 8227, 2192, 105, 6]
D. [60, 254, 1049, 3372, 7831, 11170, 8235, 2200, 113, 9]
E. [58, 252, 1047, 3370, 7829, 11168, 8233, 2198, 111, 5]
F. [55, 249, 1044, 3367, 7826, 11165, 8230, 2195, 108, 1]
G. [54, 248, 1043, 3366, 7825, 11164, 8229, 2194, 107, 0]
H. [51, 245, 1040, 3363, 7822, 11161, 8226, 2191, 104, 8]
I. [53, 247, 1042, 3365, 7824, 11163, 8228, 2193, 106, 4]
J. [56, 250, 1045, 3368, 7827, 11166, 8231, 2196, 109, 2]
Answer: F
We now define an algorithm: The definition of a(n) is the coordination sequence for the 2D periodic tiling 3.6.3.6, representing the number of vertices at distance n from a given vertex in a specified planar net structure. This sequence also corresponds to the spherical growth function for a certain reflection group in the Euclidean plane. Given the input x_list (a series of values): [47, 48, 49, 50, 51, 52, 53, 54, 55, 56], determine the corresponding output sequence y_list.

Options:
A. [186, 242, 204, 244, 200, 254, 218, 272, 216, 282]
B. [186, 234, 200, 246, 206, 260, 212, 268, 222, 272]
C. [192, 236, 200, 246, 208, 256, 212, 268, 220, 276]
D. [190, 236, 198, 250, 206, 262, 216, 270, 220, 274]
E. [194, 234, 194, 252, 202, 262, 210, 270, 218, 274]
F. [188, 240, 196, 250, 204, 260, 216, 266, 224, 280]
G. [192, 238, 196, 248, 204, 256, 214, 266, 222, 270]
H. [188, 230, 202, 254, 210, 264, 212, 272, 224, 276]
I. [190, 238, 198, 248, 206, 258, 214, 268, 222, 278]
J. [192, 240, 194, 248, 202, 258, 214, 270, 218, 278]
Answer: I
We now define an algorithm: The definition of a(n) is the q-expansion coefficients of the character of the vertex-operator superalgebra of rank 23.5, on which the Baby Monster group acts. Given the input x_list (a series of values): [9, 10, 11, 12, 13, 14, 15, 16, 17, 18], determine the corresponding output sequence y_list.

Options:
A. [1829005618, 8223700033, 33950840612, 130416170629, 470887671184, 1610882889453, 5254605009303, 16428803075150, 49446546607294, 143782211788209]
B. [1829005612, 8223700028, 33950840618, 130416170628, 470887671188, 1610882889458, 5254605009308, 16428803075154, 49446546607299, 143782211788219]
C. [1829005617, 8223700032, 33950840616, 130416170622, 470887671182, 1610882889451, 5254605009301, 16428803075157, 49446546607293, 143782211788207]
D. [1829005610, 8223700025, 33950840615, 130416170625, 470887671185, 1610882889455, 5254605009305, 16428803075151, 49446546607296, 143782211788216]
E. [1829005613, 8223700026, 33950840619, 130416170629, 470887671189, 1610882889459, 5254605009309, 16428803075155, 49446546607297, 143782211788217]
F. [1829005615, 8223700030, 33950840613, 130416170623, 470887671183, 1610882889456, 5254605009306, 16428803075156, 49446546607295, 143782211788211]
G. [1729005611, 8123700027, 32950840617, 120416170627, 460887671187, 1510882889457, 5154605009307, 15428803075153, 48446546607298, 133782211788218]
H. [1829005616, 8223700031, 33950840614, 130416170619, 470887671190, 1610882889460, 5254605009310, 16428803075158, 49446546607291, 143782211788200]
I. [1829005611, 8223700027, 33950840617, 130416170627, 470887671187, 1610882889457, 5254605009307, 16428803075153, 49446546607298, 143782211788218]
J. [1829005614, 8223700029, 33950840611, 130416170621, 470887671181, 1610882889452, 5254605009302, 16428803075152, 49446546607292, 143782211788212]
Answer: I
We now define an algorithm: The definition of a(n) is the number of distinct unlabeled connected graphs with exactly n nodes and one cycle of length 3. Given the input x_list (a series of values): [23, 24, 25, 26, 27, 28, 29, 30, 31, 32], determine the corresponding output sequence y_list.

Options:
A. [133606943, 372430476, 1040426154, 2912415527, 8167992598, 22947778342, 64577555147, 182009003773, 513729375064, 1452007713130]
B. [123606943, 362430476, 1000426154, 2812415527, 8067992598, 21947778342, 63577555147, 172009003773, 503729375064, 1352007713130]
C. [153606943, 402430476, 1200426154, 3212415527, 8467992598, 24947778342, 67577555147, 202009003773, 533729375064, 1652007713130]
D. [193606943, 442430476, 1600426154, 3612415527, 8867992598, 28947778342, 71577555147, 242009003773, 573729375064, 2052007713130]
E. [143606943, 392430476, 1100426154, 3112415527, 8367992598, 23947778342, 66577555147, 192009003773, 523729375064, 1552007713130]
F. [103606943, 352430476, 900426154, 2712415527, 7067992598, 20947778342, 62577555147, 162009003773, 493729375064, 1252007713130]
G. [163606943, 412430476, 1300426154, 3312415527, 8567992598, 25947778342, 68577555147, 212009003773, 543729375064, 1752007713130]
H. [183606943, 432430476, 1500426154, 3512415527, 8767992598, 27947778342, 70577555147, 232009003773, 563729375064, 1952007713130]
I. [173606943, 422430476, 1400426154, 3412415527, 8667992598, 26947778342, 69577555147, 222009003773, 553729375064, 1852007713130]
J. [233606943, 472430476, 1140426154, 3912415527, 9167992598, 32947778342, 74577555147, 282009003773, 613729375064, 2452007713130]
Answer: A
We now define an algorithm: The definition of a(n) is the number of spanning trees in a Moebius ladder \\( M_n \\) with \\( 2n \\) vertices. The sequence starts from \\( n = 0 \\). Given the input x_list (a series of values): [15, 16, 17, 18, 19, 20, 21, 22, 23, 24], determine the corresponding output sequence y_list.

Options:
A. [2846000000, 11330000000, 44920000000, 177500000000, 699400000000, 2747500000000, 10766000000000, 42095000000000, 164240000000000, 639600000000000]
B. [2846259350, 11330543600, 44929049070, 177540870736, 699402223737, 2747583822767, 10766828545740, 42095796462000, 164244726238329, 639620518110448]
C. [2846259390, 11330543620, 44929049780, 177540878700, 699402223100, 2747583822700, 10766828545700, 42095796462000, 164244726230000, 639620518110000]
D. [2846259406, 11330543649, 44929049812, 177540878737, 699402223138, 2747583822761, 10766828545768, 42095796462897, 164244726238390, 639620518118449]
E. [2846259405, 11330543648, 44929049811, 177540878736, 699402223137, 2747583822760, 10766828545767, 42095796462896, 164244726238389, 639620518118448]
F. [2846259404, 11330543647, 44929049810, 177540878735, 699402223136, 2747583822759, 10766828545766, 42095796462895, 164244726238388, 639620518118447]
G. [2846259407, 11330543639, 44929049803, 177540878721, 699402223122, 2747583822768, 10766828545780, 42095796462900, 164244726240000, 639620518119000]
H. [2846259460, 11330543660, 44929049850, 177540878790, 699402223190, 2747583822790, 10766828545900, 42095796463000, 164244726238500, 639620518118500]
I. [2846259300, 11330543000, 44929049000, 177540870000, 699402220000, 2747583800000, 10766828545000, 42095796460000, 164244726200000, 639620518100000]
J. [2846259410, 11330543650, 44929049815, 177540878740, 699402223142, 2747583822765, 10766828545770, 42095796462898, 164244726238391, 639620518118452]
Answer: E
We now define an algorithm: The definition of a(n) is the number of different candle trees having a total of n edges. Given the input x_list (a series of values): [16, 17, 18, 19, 20, 21, 22, 23, 24, 25], determine the corresponding output sequence y_list.

Options:
A. [67088378, 215535903, 663763424, 2034122936, 6295072048, 19386276329, 59601891739, 183857684500, 566207320100, 1743689586400]
B. [69988000, 215530000, 663764424, 2044122900, 6295072048, 19386276300, 59701891739, 183857600000, 565207300000, 1743689500000]
C. [69988378, 215535903, 663763424, 2044122936, 6292072048, 19386276329, 59701891739, 183857684500, 566207320575, 1743689586400]
D. [69988378, 215530000, 663000000, 2040000000, 6200000000, 19380000000, 59000000000, 183800000000, 560000000000, 1743000000000]
E. [59382718, 212765903, 664863424, 2033122936, 6284072048, 19486276329, 59601891739, 184857684514, 565207320575, 1733689586432]
F. [70000000, 215530000, 663700000, 2044000000, 6295000000, 19386000000, 59000000000, 183800000000, 565200000000, 1743600000000]
G. [69988000, 215535500, 663763424, 2040000000, 6295072000, 19386000000, 59001891739, 183857600000, 566200000000, 1743000000000]
H. [69988378, 215535903, 663763424, 2044122936, 6295072048, 19386276329, 59701891739, 183857684514, 566207320575, 1743689586432]
I. [69988000, 215535903, 664763424, 2044122000, 6290072048, 19386276000, 59701891000, 183857684500, 566207320500, 1743689586430]
J. [69988378, 215535903, 663763999, 2044122936, 6295072048, 19386276329, 59701891739, 183857684514, 566207320575, 1743689586000]
Answer: H
We now define an algorithm: The definition of a(n) is an upper bound on the biplanar crossing number of the complete graph on n nodes, which represents the minimum number of edge crossings required when the graph is drawn on two planes combined. Given the input x_list (a series of values): [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], determine the corresponding output sequence y_list.

Options:
A. [9060, 10035, 11100, 12210, 13585, 14905, 16335, 17820, 19624, 21362]
B. [9058, 10032, 11105, 12215, 13588, 14902, 16338, 17828, 19626, 21368]
C. [9068, 10042, 11108, 12218, 13582, 14912, 16332, 17822, 19622, 21364]
D. [9062, 10028, 11112, 12212, 13600, 14910, 16325, 17818, 19630, 21365]
E. [9065, 10040, 11105, 12205, 13580, 14900, 16330, 17830, 19625, 21370]
F. [9050, 10025, 11090, 12200, 13675, 14895, 16325, 17810, 19614, 21352]
G. [9070, 10045, 11110, 12220, 13575, 14915, 16305, 17810, 19620, 21360]
H. [9060, 10030, 11110, 12215, 13595, 14910, 16345, 17825, 19620, 21350]
I. [9072, 10037, 11103, 12208, 13597, 14917, 16337, 17817, 19617, 21357]
J. [9055, 10020, 11115, 12225, 13590, 14920, 16320, 17815, 19619, 21355]
Answer: A
We now define an algorithm: The definition of a(n) is: Arkons: number of elementary maps with n-1 nodes in the context of graph theory and cartographic map coloring. Given the input x_list (a series of values): [17, 18, 19, 20, 21, 22, 23, 24, 25, 26], determine the corresponding output sequence y_list.

Options:
A. [80343445, 328159601, 1347699906, 5561774999, 23052871229, 95926831442, 400587408251, 1678251696379, 7051768702245, 29710764875014]
B. [80343451, 328159603, 1347699904, 5561774964, 23052871223, 95926831452, 400587408281, 1678251696379, 7051768702240, 29710764875013]
C. [80343447, 328159621, 1347699926, 5561774999, 23052870229, 95926833442, 400587438251, 1678251496379, 7051768702243, 29710764875016]
D. [80343444, 328159641, 1347699901, 5561775029, 23052874229, 95926833452, 400587408251, 1678251696379, 7051768702249, 29710764875012]
E. [80343449, 328159651, 1347699806, 5561774993, 23052873229, 95926832442, 400587408251, 1678251696379, 7051768702241, 29710764875018]
F. [80343440, 328159631, 1347699876, 5561774989, 23052871239, 95926830542, 400587408251, 1678251696379, 7051768702247, 29710764875017]
G. [80343455, 328156601, 1347691006, 5561774909, 23052871329, 95926831542, 400587408251, 1678251696379, 7051768702246, 29710764875015]
H. [80343448, 328159611, 1347699816, 5561774985, 23052871219, 95926836442, 400587448251, 1678251596379, 7051768702242, 29710764875019]
I. [80343446, 328159602, 1347699801, 5561774929, 23052871224, 95926831432, 400587408221, 1678251996379, 7051768702244, 29710764875021]
J. [80343450, 328159699, 1347699976, 5561774959, 23052871209, 95926831532, 400587488251, 1678251696379, 7051768702248, 29710764875011]
Answer: A
In paleontological research, skeletal fossils are the most discovered and studied component. Based on the following skeletal descriptions, please determine which type of living organism is most similar to the organism possessing this kind of skeleton.
1) The spine is differentiated into cervical vertebrae, thoracic vertebrae, lumbar vertebrae, sacral vertebrae, and caudal vertebrae.
2) The thoracic cage is formed by the thoracic vertebrae, ribs, and sternum.
3) Each side of the skull has two temporal fossae.
4) The oral cavity has widely distributed teeth.

Options:
A. Mollusks
B. Reptilia
C. Birds
D. Arthropods
E. Amphibians
F. Fish
G. Primates
H. Cetaceans
I. Invertebrates
J. Mammals
Answer: B
Escherichia coli is a facultative anaerobic intestinal bacterium. Which of the following components is not found in Escherichia coli?

Options:
A. Cellulose
B. Peptidoglycan
C. Keratin
D. Starch
E. Lipopolysaccharide
F. Cholesterol
G. N-acetylmuramic acid
H. Ergosterol
I. Hemoglobin
J. Phosphatidic acid
Answer: J
In the intertidal zone along the seashore, chitons and sandworms are often spotted. Which of the following is not one of their shared characteristics?

Options:
A. Feeding by External Enzyme Release
B. Having a trochophore larval stage
C. Formation of a True Coelom via Schizocoely
D. Developing Radially Symmetric Larvae
E. Using Ciliary Gliding for Movement
F. Metanephric Excretory System
G. Open-Tube Circulation System
H. Lacking Segmentation in Body Plan
I. Presence of Chitinous Exoskeleton
J. Possessing a Dorsal Nerve Cord
Answer: G
The saying "After a major disaster comes a major epidemic" refers to the occurrence of widespread infectious diseases often following flood disasters. Which of the following explanations do you think is the most accurate?

Options:
A. Flooding leads to immediate dry conditions, preventing any spread of parasites in affected areas.
B. Floods can spread parasites or co-hosts originally located in a certain area to a larger region.
C. The severe drought following a flood ensures rapid evaporation, reducing infection risks significantly.
D. After flooding disasters, the marshy ground provides excellent conditions for the mass reproduction of parasites' hosts.
E. Floods inherently introduce saline conditions, halting the spread of waterborne pathogens effectively.
F. During flooding disasters, the water cleanses the area, reducing the presence of parasites greatly.
G. After a flood disaster, since there is extensive stagnant water, people often walk barefoot on the ground, which may lead to infection by schistosome larvae.
H. Post-flood, the cooler temperatures inhibit the growth of disease-causing microorganisms entirely.
I. After the flood, people's immunity decreases, making them a susceptible population.
J. With floods, increased evaporation rates result in dry lands, eliminating breeding grounds for parasites.
Answer: D
Which description of the characteristics of farmland ecosystems is the most accurate?

Options:
A. The farmland ecosystem is a self-regulating system with no dependence on external human inputs.
B. Farmland ecosystems have minimal interaction with human activities and are considered purely natural systems.
C. The farmland ecosystem is a type of terrestrial ecosystem with high stability.
D. The primary role of the farmland ecosystem is maintaining ecological balance without human interference.
E. Farmland ecosystems lack specific goals and operate solely based on natural ecological processes.
F. The functions of the farmland ecosystem are strongly goal-oriented, making it a semi-artificial ecosystem.
G. Compared to natural ecosystems, the overall biodiversity level of farmland ecosystems is the lowest.
H. The biodiversity of farmland ecosystems is the highest among all terrestrial ecosystems due to abundant species diversity.
I. Farmland ecosystems function similarly to forests, providing extensive carbon sequestration and habitat diversity.
J. The functions of the farmland ecosystem are primarily reflected in agricultural production and its services to the natural environment.
Answer: F
There are three species of fruit doves that all feed on the fruits of a certain plant, but they consume fruits from different parts of the plant. What is the most reasonable explanation for this phenomenon?

Options:
A. Dietary Convergence
B. Habitat differentiation
C. Symbiotic Cooperation
D. Competitive Exclusion
E. Habitat Specialization
F. Niche Differentiation
G. Foraging Coexistence
H. Mutual Interference and Competition
I. Food Differentiation
J. Resource Partitioning
Answer: F
A large portion of the energy flow in a certain ecosystem is directed toward the predation food chain. What is this ecosystem most likely to be?

Options:
A. Grassland Ecosystem
B. Coastal Ecosystem
C. Wetland Ecosystem
D. Lake Ecosystems
E. Urban Ecosystem
F. Forest Ecosystem
G. River Ecosystem
H. Mountain Ecosystem
I. Desert Ecosystem
J. Tundra Ecosystem
Answer: D
In mosses, which of the following structures belong to the gametophyte generation?

Options:
A. Capsular teeth
B. Capsular peduncle
C. Calyptra cover
D. Capsule cap
E. Operculum top
F. Capsule lid
G. Spore stalk
H. Sporophyte stem
I. Peristome layer
J. Seta vessel
Answer: D
When identifying IAA using the wheat germ sheath section method, which of the following precautions is incorrect?

Options:
A. The experimental material should have the roots trimmed first.
B. You need to select uniformly sized wheat seeds, and they must be germinated into seedlings before conducting the experiment.
C. Ensure the apex of the root cap is removed before analysis.
D. The sections must be rinsed in water before measurement.
E. Experimental operations should be conducted under low light conditions.
F. The sections should be dried completely before measurement.
Answer: D
Regarding the tolerance limits of animals to high and low temperatures, which of the following characteristics does not belong to the causes of heat-induced death?

Options:
A. Rapid fat oxidation increases thermal stress.
B. Dehydration causes protein precipitation.
C. Nervous System Paralysis
D. Blood pH stabilizes under extreme heat conditions.
E. Elevated heat reduces blood circulation rates.
F. High temperatures enhance metabolic equilibrium.
G. Insufficient oxygen supply and impaired excretory function
H. Enzyme activity is disrupted.
I. Excessive water intake dilutes body fluids.
J. Heat induces muscle over-contraction damage.
Answer: B
Sometimes a quantity of interest is the Helmholtz Free Energy $F ( T, V, N )$ divided by $T$. (For example, this quantity is proportional to the logarithms of equilibrium constants or solubilities.) Suppose $F(T)$ depends on temperature in the following way: $F ( T )=2 a T^{2}+b T$ (so $F / T=2 a T+b )$ . $S ( T )$ is () .

Options:
A. $$
5 a T + b
$$
B. $$
3 a T - b
$$
C. $$
4 a T - b
$$
D. $$
a T^2 + b
$$
E. $$
6 a T + b
$$
F. $$
4 a T+b
$$
G. $$
3 a T + 2 b
$$
H. $$
2 a T - b
$$
I. $$
2 a T^2 + b
$$
J. $$
4 a T + 2 b
$$
Answer: F
What is the dissociation constant $K_{p}$ for iodine, $I_{2} \to2 I,$ at $T=3 0 0 \, \mathrm{K}$ ?

Options:
A. $$
8. 2 \times1 0^{-2 1} \mathrm{~ a t m}
$$
B. $$
8. 5 \times1 0^{-2 2} \mathrm{~ a t m}
$$
C. $$
6. 5 \times1 0^{-2 2} \mathrm{~ a t m}
$$
D. $$
9. 1 \times1 0^{-2 2} \mathrm{~ a t m}
$$
E. $$
10. 0 \times1 0^{-2 2} \mathrm{~ a t m}
$$
F. $$
8. 7 \times1 0^{-2 0} \mathrm{~ a t m}
$$
G. $$
8. 9 \times1 0^{-2 4} \mathrm{~ a t m}
$$
H. $$
8. 4 \times1 0^{-2 5} \mathrm{~ a t m}
$$
I. $$
5. 3 \times1 0^{-2 3} \mathrm{~ a t m}
$$
J. $$
7. 4 \times1 0^{-2 3} \mathrm{~ a t m}
$$
Answer: B
Convert the atom percent composition in Problem 4. 18 to weight percent.id().

Options:
A. $$
4. 0 \mathrm{~ w t}^{0} /_{0}
$$
B. $$
8. 5 \mathrm{~ w t}^{0} /_{0}
$$
C. $$
7. 4 \mathrm{~ w t}^{0} /_{0}
$$
D. $$
3. 8 \mathrm{~ w t}^{0} /_{0}
$$
E. $$
6. 1 \mathrm{~ w t}^{0} /_{0}
$$
F. $$
9. 7 \mathrm{~ w t}^{0} /_{0}
$$
G. $$
1. 5 \mathrm{~ w t}^{0} /_{0}
$$
H. $$
0. 9 \mathrm{~ w t}^{0} /_{0}
$$
I. $$
5. 2 \mathrm{~ w t}^{0} /_{0}
$$
J. $$
2. 9 \mathrm{~ w t}^{0} /_{0}
$$
Answer: A
The difference benveen the specific heats at constant pressure and constant volume is described by the expression
$$
c_{p}-c_{\nu}=\frac{\alpha_{\nu}^{2} \nu_{0} T} {\beta}
$$
where $\alpha$ is the volume coefficient of thermal expansion, $v_{o}$ is the specific volume (i.e, olume per unit mass, or the reciprocal of density), is the compressibility, and $T$ is the absolute temperature. Compute the values of $c_{\nu}$ at room temperature (293 K) for aluminum and iron using the data in Table 19 1, assuming that $\alpha_{v}=3 \alpha_{l}$ and given that the wales of orA adFear $I. 7 7 \times I 0^{-I I}$ and $2. 6 5 \times1 0^{-1 2} \, ( P a )^{-1}$ respectvel,

Options:
A. $$
4 2 5 \; \mathrm{J / k g-K}
$$
B. $$
3 8 0 \; \mathrm{J / k g-K}
$$
C. $$
4 1 0 \; \mathrm{J / k g-K}
$$
D. $$
4 6 0 \; \mathrm{J / k g-K}
$$
E. $$
4 5 0 \; \mathrm{J / k g-K}
$$
F. $$
3 7 0 \; \mathrm{J / k g-K}
$$
G. $$
4 7 0 \; \mathrm{J / k g-K}
$$
H. $$
4 4 0 \; \mathrm{J / k g-K}
$$
I. $$
3 9 0 \; \mathrm{J / k g-K}
$$
J. $$
4 3 0 \; \mathrm{J / k g-K}
$$
Answer: J
The pyramid model of balance and blend in a vocal ensemble refers to what theory?

Options:
A. Taller singers should stand behind shorter singers.
B. Higher-pitched singers should sing softer than the lowest pitched singers.
C. Melodic singers should sing louder than accompanying singers.
D. Louder singers should sing at the same level as softer singers.
Answer: B
Which of the following statements about the theme, answer, and countersubject in a fugue is incorrect?

Options:
A. The relationship between the theme and answer is one of contrasting polyphony
B. A free countersubject can be developed using motivic expansion techniques
C. If the countersubject always has the same melody, it is called a fixed countersubject
D. In the exposition, the theme and answer usually appear in the tonic and dominant keys
Answer: A
Concerning the musical genre of fugue, which of the following statements is incorrect?

Options:
A. The fugue genre reached its peak during the Baroque period
B. In Baroque fugues, the subject and answer usually appear in the same tonality
C. After the Baroque period, fugue sometimes appears in a movement of a sonata or suite
D. Fugue structure includes exposition, development, and recapitulation
Answer: B
In the Western music system, the 'middle C' is

Options:
A. Small letter group C
B. Small letter first group C
C. Small letter second group C
D. Big letter group C
Answer: B