MikaStars39/nano-eval huggingface dataset:
We now define an algorithm: The definition of a(n) is: Shifts left two terms under the binomial transform, which is a linear transformation relevant in combinatorial mathematics. 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. [29551768, 152005634, 820518729, 4472244574, 25497104007, 149993156234, 909326652914, 5674422999544, 36408092349897, 239942657880360]
B. [29551768, 152005634, 810518729, 4472244574, 25497104007, 149993156234, 909326652914, 5674422994544, 36408092349897, 239942657880360]
C. [29551769, 152005634, 810518729, 4472244574, 25497102007, 149993156234, 909326652914, 5674422994544, 36408092349897, 239942657880360]
D. [29551768, 152005634, 810518729, 4272244574, 25497104007, 149993166234, 909326652914, 5674422994544, 36408092349897, 239942657880360]
E. [29551768, 152015634, 810518729, 4472244574, 25497104007, 149993156234, 909326652914, 5674422994544, 36408092349897, 239952657880360]
F. [29551768, 152005634, 810518729, 4472244573, 25497104007, 149993156234, 909326652914, 5674422994544, 36408092949897, 239942657880360]
G. [29551768, 152005634, 810528729, 4472244574, 25497104007, 149993156234, 909326652914, 5674422994544, 36408192349897, 239942657880360]
H. [29551768, 142006734, 810528729, 4472244574, 25497104007, 149993156234, 909327652914, 5674422994544, 36408192349897, 239942657880360]
I. [29551568, 152005634, 810518729, 4472244574, 25497104007, 149993156234, 909326662914, 5674422994544, 36408092349897, 239942657880360]
J. [29551768, 152005634, 810518729, 4672244574, 25497104007, 149993156234, 909326652914, 5674422994544, 36408092349898, 239942657880360]
Answer: B
We now define an algorithm: The definition of a(n) is the number of perfect riffle shuffles required to return a deck of 2n cards to its original order. Given the input x_list (a series of values): [58, 59, 60, 61, 62, 63, 64, 65, 66, 67], determine the corresponding output sequence y_list.

Options:
A. [44, 12, 24, 110, 20, 100, 14, 14, 130, 18]
B. [40, 12, 26, 110, 24, 98, 16, 14, 128, 20]
C. [44, 14, 24, 104, 20, 99, 14, 18, 130, 18]
D. [44, 10, 22, 120, 24, 100, 14, 16, 128, 18]
E. [44, 12, 26, 112, 22, 100, 14, 14, 126, 18]
F. [12, 24, 48, 10, 22, 18, 14, 56, 70, 130]
G. [46, 14, 22, 110, 20, 101, 14, 18, 130, 16]
H. [42, 16, 22, 108, 20, 100, 16, 12, 130, 18]
I. [48, 14, 24, 110, 20, 102, 14, 16, 128, 20]
J. [46, 12, 24, 112, 18, 100, 14, 14, 132, 20]
Answer: A
We now define an algorithm: The definition of a(n) is: Exchange the rightmost two binary digits of n for n > 1, otherwise a(0)=0 and a(1)=2. Given the input x_list (a series of values): [63, 64, 65, 66, 67, 68, 69, 70, 71, 72], determine the corresponding output sequence y_list.

Options:
A. [63, 64, 66, 65, 67, 69, 70, 71, 71, 72]
B. [62, 64, 66, 65, 67, 68, 70, 69, 71, 73]
C. [63, 64, 66, 65, 67, 68, 70, 69, 71, 72]
D. [63, 64, 66, 66, 67, 68, 70, 69, 71, 72]
E. [63, 64, 66, 65, 67, 68, 70, 69, 71, 73]
F. [63, 64, 65, 66, 67, 68, 69, 70, 71, 72]
G. [63, 64, 66, 65, 68, 68, 70, 69, 71, 72]
H. [63, 65, 66, 67, 68, 69, 70, 71, 72, 73]
I. [63, 64, 67, 65, 67, 68, 71, 69, 71, 72]
J. [63, 64, 66, 65, 67, 68, 70, 69, 72, 73]
Answer: C
We now define an algorithm: The definition of a(n) is the coefficients of the power series that satisfies A(x)^2 - 4*x*A(x)^3 = 1, with A(0) = 1. Given the input x_list (a series of values): [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], determine the corresponding output sequence y_list.

Options:
A. [168043986, 1526726662, 14025209106, 130056978438, 1215785268846, 11445014102022, 108401560073196, 1032295389593606, 9877854438949986, 94927710773575686]
B. [168043984, 1526726660, 14025209104, 130056978436, 1215785268844, 11445014102020, 108401560073194, 1032295389593604, 9877854438949984, 94927710773575684]
C. [168043988, 1526726664, 14025209108, 130056978440, 1215785268848, 11445014102024, 108401560073198, 1032295389593608, 9877854438949988, 94927710773575688]
D. [168043989, 1526726665, 14025209109, 130056978441, 1215785268849, 11445014102025, 108401560073199, 1032295389593609, 9877854438949989, 94927710773575689]
E. [168043982, 1526726658, 14025209102, 130056978434, 1215785268842, 11445014102018, 108401560073192, 1032295389593602, 9877854438949982, 94927710773575682]
F. [168043983, 1526726659, 14025209103, 130056978435, 1215785268843, 11445014102019, 108401560073193, 1032295389593603, 9877854438949983, 94927710773575683]
G. [168043981, 1526726657, 14025209101, 130056978433, 1215785268841, 11445014102017, 108401560073191, 1032295389593601, 9877854438949981, 94927710773575681]
H. [168043985, 1526726661, 14025209105, 130056978437, 1215785268845, 11445014102021, 108401560073195, 1032295389593605, 9877854438949985, 94927710773575685]
I. [168043987, 1526726663, 14025209107, 130056978439, 1215785268847, 11445014102023, 108401560073197, 1032295389593607, 9877854438949987, 94927710773575687]
J. [168043980, 1526726656, 14025209100, 130056978432, 1215785268840, 11445014102016, 108401560073190, 1032295389593600, 9877854438949980, 94927710773575680]
Answer: J
We now define an algorithm: The definition of a(n) is the sum of the n-th powers of the divisors of 6. 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. [2178317874, 13072296532, 78378963450, 470299366252, 2822153019714, 16936788715972, 101660344351050, 609460902796252, 3657161927895954, 21946961102828212]
B. [3177317874, 13062296534, 78368963450, 470299366251, 2822153019713, 16926788715974, 101660344351051, 609460902796253, 3657161927895955, 21946961102828216]
C. [2177317875, 13062296533, 78368963451, 470199366253, 2821153019715, 16926788715973, 101560344351051, 609360902796253, 3656161927895955, 21936961102828213]
D. [2177317875, 13062296531, 78368963451, 470199366253, 2821153019712, 16926788715974, 101560344351048, 609360902796251, 3656161927895952, 21936961102828214]
E. [2177317876, 13063296532, 78368963452, 470299366252, 2822153019715, 16936788715973, 101560344351052, 609360902796253, 3656161927895954, 21936961102828217]
F. [2177317873, 13062296532, 78378963451, 470199366252, 2821153019716, 16936788715972, 101660344351050, 609460902796252, 3656161927895956, 21936961102828215]
G. [2177317874, 13062296532, 78368963450, 470199366251, 2821153019715, 16926788715973, 101560344351049, 609360902796253, 3656161927895955, 21936961102828213]
H. [2177317873, 13062296531, 78368963449, 470199366251, 2821153019713, 16926788715971, 101560344351049, 609360902796251, 3656161927895953, 21936961102828211]
I. [3164846819, 13545605874, 54798473241, 472016499831, 3297473768442, 17273743786644, 93049105843015, 659719396729832, 3124691761583914, 23216491589043876]
J. [2177317874, 13062296532, 78368963450, 470199366252, 2821153019714, 16926788715972, 101560344351050, 609360902796252, 3656161927895954, 21936961102828212]
Answer: J
We now define an algorithm: The definition of a(n) is the real part of (1 + 2*i)^n, where i is sqrt(-1). Given the input x_list (a series of values): [19, 20, 21, 22, 23, 24, 25, 26, 27, 28], determine the corresponding output sequence y_list.

Options:
A. [-2521477, -9653200, -6699324, 34867791, 103232190, 32125399, -451910126, -1064447290, 130656250, 5583548862]
B. [-2521489, -9653210, -6699215, 34867911, 103232984, 32125402, -451910141, -1064447296, 130656245, 5583548887]
C. [-2521448, -9653269, -6699316, 34867892, 103232187, 32125383, -451910169, -1064447295, 130656240, 5583548802]
D. [-2521450, -9653275, -6699320, 34867822, 103232188, 32125414, -451910148, -1064447289, 130656226, 5583548888]
E. [-2521423, -9653282, -6699300, 34867814, 103232175, 32125388, -451910150, -1064447248, 130656262, 5583548819]
F. [-2521451, -9653287, -6699319, 34867797, 103232189, 32125393, -451910159, -1064447283, 130656229, 5583548873]
G. [-2521456, -9653281, -6699314, 34867815, 103232179, 32125390, -451910166, -1064447282, 130656204, 5583548891]
H. [-2521435, -9653264, -6699318, 34867883, 103232170, 32125381, -451910168, -1064447210, 130656228, 5583548892]
I. [-2521499, -9653283, -6699308, 34867865, 103232185, 32125394, -451910152, -1064447259, 130656235, 5583548825]
J. [-2521491, -9653284, -6699327, 34867879, 103232189, 32125357, -451910165, -1064447253, 130656202, 5583548844]
Answer: F
We now define an algorithm: The definition of a(n) is: From Euler's Pentagonal Theorem: coefficient of q^n in the infinite product representing the generating function Product_{m>=1} (1 - q^m), wherein each term corresponds to the count of distinct partitions of integer n into an even number of distinct parts minus the count of distinct partitions into an odd number of distinct parts. Given the input x_list (a series of values): [83, 84, 85, 86, 87, 88, 89, 90, 91, 92], determine the corresponding output sequence y_list.

Options:
A. [1, 0, 0, 0, 1, 0, 0, 0, 1, 0]
B. [1, 0, 0, 1, 1, 0, 1, 0, 0, 1]
C. [0, 0, 0, 1, 0, 0, 1, 0, 0, 0]
D. [0, 0, 1, 0, 0, 0, 0, 1, 0, 0]
E. [0, 1, 1, 0, 0, 1, 0, 1, 1, 0]
F. [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
G. [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
H. [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]
I. [1, 1, 0, 1, 0, 1, 0, 1, 0, 0]
J. [1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
Answer: F
We now define an algorithm: The definition of a(n) is the n-th Fourier coefficient of the Eisenstein series E_10(q) (alternate convention E_5(q)) for the modular form with weight 10. Given the input x_list (a series of values): [7, 8, 9, 10, 11, 12, 13, 14, 15, 16], determine the corresponding output sequence y_list.

Options:
A. [-10653351512, -35502821640, -102284205672, -264515760412, -622498190688, -1364917062432, -2799587834736, -5465169838656, -10149567696576, -18177444679944]
B. [-10653352512, -35502821640, -102284205672, -264515760432, -622498190688, -1364917062432, -2799587834736, -5465169838656, -10149567696576, -18177444679944]
C. [-10653352552, -35502821640, -102284205672, -264515760432, -622498190688, -1364917062432, -2799587834736, -5465169838656, -10149567692576, -18177444679944]
D. [-10653352512, -35502821640, -102284205672, -264515760432, -622498190688, -1364917062432, -2799587834736, -5465169838656, -10149567696576, -18177444649944]
E. [-10653352612, -35502821640, -102284205672, -264515760432, -622498190688, -1364917062432, -2799587834736, -5465169838656, -10149567696576, -18177444679944]
F. [-10653352512, -35502821640, -102284205672, -264515760432, -622498190688, -1364917062432, -2799587834736, -5465169838656, -10149567696576, -18177444678944]
G. [-10653352012, -35502821640, -102284205652, -264515760432, -622498190688, -1364917062432, -2799587834736, -5465169838656, -10149567696576, -18177444679944]
H. [-10653352112, -35502821340, -102284205672, -264515760432, -622498190688, -1364917062432, -2799587834736, -5465169838656, -10149567696576, -18177444679944]
I. [-10653352512, -35502821640, -102284205672, -264515730432, -622498190688, -1364917062432, -2799587834736, -5465169818656, -10149567696576, -18177444679944]
J. [-10653352512, -35502821640, -102284205672, -264515760432, -622498170688, -1364917062432, -2799587834736, -5465169838656, -10149567696576, -18177444679944]
Answer: B
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.

Options:
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]
Answer: B
We now define an algorithm: The definition of a(n) is as follows: it is a characteristic function that indicates whether a number is relatively prime to 11. In other words, a(n) equals 1 if n is relatively prime (coprime) to 11, and 0 otherwise. Given the input x_list (a series of values): [95, 96, 97, 98, 99, 100, 101, 102, 103, 104], determine the corresponding output sequence y_list.

Options:
A. [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
B. [1, 0, 0, 1, 1, 0, 0, 1, 1, 0]
C. [1, 1, 0, 1, 0, 1, 0, 1, 0, 1]
D. [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
E. [1, 1, 1, 1, 0, 1, 1, 1, 1, 1]
F. [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]
G. [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]
H. [0, 0, 1, 0, 1, 1, 0, 0, 1, 1]
I. [1, 0, 1, 1, 0, 0, 1, 1, 0, 0]
J. [1, 1, 0, 0, 1, 1, 0, 0, 1, 1]
Answer: E
We now define an algorithm: The definition of a(n) is the canonical enumeration of integers where the sequence starts with zero and alternates between positive and negative integers. 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.

Options:
A. [27, -27, 29, -29, 31, -31, 33, -33, 35, -35]
B. [25, -25, 27, -27, 29, -29, 30, -30, 32, -32]
C. [26, -26, 28, -28, 29, -29, 31, -31, 32, -32]
D. [26, -26, 28, -28, 30, -30, 31, -31, 34, -34]
E. [27, -27, 28, -28, 29, -29, 30, -30, 31, -31]
F. [27, -27, 28, -28, 30, -30, 32, -32, 34, -34]
G. [28, -28, 29, -29, 30, -30, 32, -32, 34, -34]
H. [28, -28, 27, -27, 29, -29, 32, -32, 33, -33]
I. [26, -26, 27, -27, 30, -30, 32, -32, 33, -33]
J. [25, -25, 28, -28, 30, -30, 31, -31, 33, -33]
Answer: E
We now define an algorithm: The definition of a(n) is: In the prime factorization of n, for each prime factor, if its exponent is odd, increment it by 1; if its exponent is even, decrement it by 1. This transformation is multiplicative and self-inverse. Given the input x_list (a series of values): [48, 49, 50, 51, 52, 53, 54, 55, 56, 57], determine the corresponding output sequence y_list.

Options:
A. [74, 8, 19, 2599, 336, 2810, 322, 3020, 786, 3242]
B. [68, 12, 26, 2606, 332, 2808, 329, 3021, 787, 3252]
C. [69, 8, 25, 2598, 337, 2814, 327, 3019, 781, 3244]
D. [75, 10, 20, 2605, 334, 2811, 325, 3015, 789, 3246]
E. [72, 9, 18, 2601, 340, 2813, 320, 3030, 784, 3245]
F. [70, 7, 21, 2600, 339, 2805, 326, 3035, 782, 3243]
G. [71, 6, 23, 2602, 341, 2802, 328, 3023, 788, 3238]
H. [72, 7, 20, 2601, 338, 2809, 324, 3025, 784, 3249]
I. [76, 11, 24, 2604, 333, 2812, 321, 3033, 785, 3248]
J. [73, 5, 22, 2603, 335, 2806, 323, 3032, 783, 3250]
Answer: H
We now define an algorithm: The definition of a(n) is the number of inequivalent Gaussian primes (complex integers of form a+bi, where a and b are integers) whose norm is n. Given the input x_list (a series of values): [91, 92, 93, 94, 95, 96, 97, 98, 99, 100], determine the corresponding output sequence y_list.

Options:
A. [0, 0, 0, 0, 0, 0, 2, 0, 0, 0]
B. [1, 0, 0, 0, 0, 0, 1, 0, 0, 0]
C. [0, 0, 1, 0, 0, 0, 0, 0, 0, 0]
D. [0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
E. [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
F. [0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
G. [0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
H. [0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
I. [0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
J. [0, 0, 0, 0, 1, 0, 0, 0, 0, 0]
Answer: A
We now define an algorithm: The definition of a(n) is the irregularity index of the n-th prime: the number of integers k, where 1 <= k <= (p-3)/2 and p = prime(n), such that the prime p divides the numerator of the Bernoulli number B(2k). Given the input x_list (a series of values): [97, 98, 99, 100, 101, 102, 103, 104, 105, 106], determine the corresponding output sequence y_list.

Options:
A. [0, 0, 1, 1, 2, 1, 0, 1, 0, 0]
B. [0, 1, 1, 1, 1, 1, 0, 0, 0, 2]
C. [0, 0, 0, 1, 2, 2, 0, 0, 1, 1]
D. [0, 1, 1, 0, 1, 1, 0, 0, 0, 1]
E. [1, 0, 0, 1, 3, 1, 0, 0, 0, 1]
F. [0, 0, 1, 1, 2, 1, 0, 0, 0, 1]
G. [1, 0, 1, 0, 2, 1, 0, 0, 1, 0]
H. [0, 0, 0, 2, 2, 0, 0, 1, 1, 1]
I. [0, 0, 1, 2, 2, 1, 0, 0, 0, 1]
J. [0, 1, 1, 1, 2, 1, 1, 0, 0, 1]
Answer: F
We now define an algorithm: The definition of a(n) is the nth term in the triangle of numbers of Dyck paths, where each row corresponds to the number of Dyck paths of given length and each column corresponds to the number of distinct peak heights. The sequence is read by rows. Given the input x_list (a series of values): [45, 46, 47, 48, 49, 50, 51, 52, 53, 54], determine the corresponding output sequence y_list.

Options:
A. [3711916, 3711917, 2068560, 804440, 231868, 49689, 7644, 780, 48, 1]
B. [3711918, 3711914, 2068562, 804442, 231870, 49688, 7648, 782, 47, 9]
C. [3711920, 3711916, 2068570, 804450, 231878, 49690, 7650, 785, 50, 3]
D. [3711916, 3711916, 2068560, 804440, 231868, 49686, 7644, 780, 45, 1]
E. [3711919, 3711918, 2068563, 804432, 231868, 49680, 7647, 776, 43, 6]
F. [3711986, 3711986, 2068566, 804460, 231868, 49666, 7644, 770, 45, 5]
G. [3711906, 3711906, 2068556, 804446, 231860, 49668, 7642, 778, 41, 8]
H. [3711917, 3711916, 2068561, 804441, 231869, 49687, 7645, 781, 46, 2]
I. [3711916, 3711915, 2068559, 804439, 231867, 49685, 7643, 779, 44, 0]
J. [3711996, 3711936, 2068520, 804445, 231848, 49586, 7643, 760, 40, 4]
Answer: D
We now define an algorithm: The definition of a(n) is the sequence derived from iterating the process x := x - (sin(x) - cos(x)*x - Pi/2)/(sin(x)*x) with a given initial value, representing the number of digits of the exact value of π, determining the decimal places in the calculations. 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, 0, 4, 9, 7, 1, 5, 3, 9, 7]
B. [3, 0, 3, 9, 8, 1, 5, 3, 9, 7]
C. [3, 0, 3, 8, 7, 1, 5, 3, 8, 8]
D. [3, 0, 3, 9, 7, 1, 5, 3, 9, 8]
E. [3, 1, 3, 8, 7, 2, 5, 2, 9, 7]
F. [2, 0, 3, 9, 7, 1, 5, 3, 9, 9]
G. [3, 0, 2, 9, 7, 1, 6, 3, 8, 8]
H. [2, 0, 3, 9, 7, 0, 5, 3, 9, 8]
I. [3, 1, 3, 9, 7, 1, 5, 3, 9, 9]
J. [3, 0, 3, 9, 6, 1, 5, 4, 9, 8]
Answer: D
We now define an algorithm: The definition of a(n) is the smallest term in the Zeckendorf representation of n, where each positive integer is represented as the sum of one or more distinct, non-consecutive Fibonacci numbers. Given the input x_list (a series of values): [80, 81, 82, 83, 84, 85, 86, 87, 88, 89], determine the corresponding output sequence y_list.

Options:
A. [21, 34, 55, 89, 1, 5, 8, 2, 3, 13]
B. [2, 89, 3, 8, 1, 13, 21, 34, 55, 89]
C. [89, 5, 55, 21, 13, 8, 3, 2, 1, 34]
D. [13, 21, 34, 55, 89, 2, 3, 5, 1, 8]
E. [3, 2, 1, 89, 5, 8, 13, 21, 34, 55]
F. [34, 55, 89, 2, 3, 1, 8, 13, 21, 5]
G. [1, 5, 1, 2, 8, 1, 2, 3, 1, 89]
H. [55, 89, 2, 3, 1, 5, 8, 13, 34, 21]
I. [5, 8, 13, 21, 34, 55, 89, 2, 3, 1]
J. [8, 13, 21, 34, 55, 89, 2, 3, 1, 5]
Answer: G
We now define an algorithm: The definition of a(n) is the number of digits required to write the prime factors of n, including their multiplicities. For example, for n = 30, the prime factors are 2, 3, and 5, which require a total of 3 digits. Given the input x_list (a series of values): [97, 98, 99, 100, 101, 102, 103, 104, 105, 106], determine the corresponding output sequence y_list.

Options:
A. [3, 3, 4, 4, 4, 4, 3, 5, 3, 4]
B. [2, 3, 3, 4, 3, 5, 3, 5, 3, 4]
C. [2, 3, 5, 4, 3, 4, 4, 5, 4, 4]
D. [2, 4, 4, 5, 3, 5, 4, 5, 4, 3]
E. [3, 4, 4, 4, 3, 4, 4, 6, 3, 3]
F. [3, 3, 4, 5, 4, 5, 3, 5, 3, 4]
G. [3, 3, 4, 4, 4, 4, 3, 5, 4, 4]
H. [2, 3, 4, 4, 3, 4, 3, 5, 3, 3]
I. [3, 4, 4, 5, 4, 5, 4, 6, 4, 3]
J. [2, 3, 4, 5, 3, 4, 3, 6, 3, 3]
Answer: H
We now define an algorithm: The definition of a(n) is: Sums of distinct powers of 5, which are the numbers that can be represented as the sum of unique terms from the sequence 5^0, 5^1, 5^2, and so on. Given the input x_list (a series of values): [40, 41, 42, 43, 44, 45, 46, 47, 48, 49], determine the corresponding output sequence y_list.

Options:
A. [3200, 3201, 3215, 3216, 3225, 3226, 3230, 3231, 3700, 3701]
B. [3500, 3501, 3515, 3516, 3525, 3526, 3530, 3531, 3600, 3601]
C. [3350, 3351, 3365, 3366, 3375, 3376, 3380, 3381, 3850, 3851]
D. [3600, 3601, 3625, 3626, 3635, 3636, 3640, 3641, 3950, 3951]
E. [3450, 3451, 3465, 3466, 3475, 3476, 3480, 3481, 3650, 3651]
F. [3300, 3301, 3325, 3326, 3335, 3336, 3340, 3341, 3800, 3801]
G. [3100, 3101, 3115, 3116, 3125, 3126, 3130, 3131, 3500, 3501]
H. [3550, 3551, 3565, 3566, 3575, 3576, 3580, 3581, 3950, 3951]
I. [3400, 3401, 3415, 3416, 3425, 3426, 3430, 3431, 3900, 3901]
J. [3250, 3251, 3255, 3256, 3275, 3276, 3280, 3281, 3750, 3751]
Answer: J
We now define an algorithm: The definition of a(n) is the result of the generalized nim sum of n and n, where nim sum is analogous to bitwise XOR operation but performed in base 5. Given the input x_list (a series of values): [46, 47, 48, 49, 50, 51, 52, 53, 54, 55], determine the corresponding output sequence y_list.

Options:
A. [66, 70, 65, 69, 99, 103, 105, 99, 105, 108]
B. [68, 69, 66, 68, 101, 102, 105, 100, 103, 109]
C. [66, 70, 67, 69, 100, 103, 105, 101, 102, 108]
D. [67, 69, 67, 68, 100, 102, 103, 102, 103, 111]
E. [68, 69, 67, 67, 101, 102, 103, 102, 104, 111]
F. [68, 70, 66, 70, 101, 103, 104, 101, 105, 112]
G. [67, 70, 66, 69, 101, 102, 106, 102, 105, 109]
H. [67, 69, 67, 68, 101, 103, 104, 101, 104, 110]
I. [67, 68, 67, 69, 100, 101, 104, 100, 102, 109]
J. [67, 69, 66, 68, 100, 102, 104, 101, 103, 110]
Answer: J
We now define an algorithm: The definition of a(n) is k appears 2k-1 times in the sequence and each number is the square root of its position in the sequence, rounded up. Given the input x_list (a series of values): [87, 88, 89, 90, 91, 92, 93, 94, 95, 96], determine the corresponding output sequence y_list.

Options:
A. [15, 15, 15, 15, 15, 15, 15, 15, 15, 15]
B. [8, 8, 8, 8, 8, 8, 8, 8, 8, 8]
C. [13, 13, 13, 13, 13, 13, 13, 13, 13, 13]
D. [7, 7, 7, 7, 7, 7, 7, 7, 7, 7]
E. [14, 14, 14, 14, 14, 14, 14, 14, 14, 14]
F. [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]
G. [11, 11, 11, 11, 11, 11, 11, 11, 11, 11]
H. [9, 9, 9, 9, 9, 9, 9, 9, 9, 9]
I. [16, 16, 16, 16, 16, 16, 16, 16, 16, 16]
J. [12, 12, 12, 12, 12, 12, 12, 12, 12, 12]
Answer: F
We now define an algorithm: The definition of a(n) is the number of distinct positive braids that can be formed with exactly n crossings using 5 strands. Given the input x_list (a series of values): [18, 19, 20, 21, 22, 23, 24, 25, 26, 27], determine the corresponding output sequence y_list.

Options:
A. [24492094, 58662208, 140498977, 336491069, 805872327, 1929982878, 4622081068, 11069299411, 26508431448, 63486323364]
B. [24092034, 58932298, 141498877, 338491169, 808372377, 1939983778, 4621083068, 11089289411, 26509421448, 63686333364]
C. [24492034, 58662298, 140498877, 336491169, 805872377, 1929983778, 4622083068, 11069289411, 26509431448, 63486333364]
D. [24592034, 58662288, 140498877, 336491269, 805872377, 1929984783, 4621083068, 11069299411, 26509432448, 63486343364]
E. [24892034, 58662298, 140598877, 336491169, 805872177, 1929983978, 4622085068, 11069289421, 26509433448, 63486333464]
F. [13979204, 47682918, 123492857, 312438169, 775872367, 1839984768, 4542084068, 10768289412, 25309431448, 61586333364]
G. [24493034, 58672398, 140498977, 336591169, 805972377, 1930983778, 4623083068, 11060289411, 26519431448, 63586333364]
H. [24492534, 58662198, 140498877, 336491179, 805872357, 1929984778, 4622083068, 11079289421, 26509431448, 63486333164]
I. [24492134, 58672298, 140498187, 336491179, 805872387, 1922978778, 4622083068, 11069289401, 26509434448, 63486335364]
J. [24492004, 58661298, 140499877, 336481169, 805872877, 1928983778, 4622082068, 11060289411, 26509431438, 63486333344]
Answer: C
We now define an algorithm: The definition of a(n) is: the minimum distance between n and the nearest product of two consecutive integers (also known as promic or heteromecic numbers). 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.

Options:
A. [2, 3, 4, 5, 6, 7, 8, 9, 10, 9]
B. [6, 7, 8, 9, 10, 11, 12, 11, 10, 9]
C. [3, 2, 1, 0, 1, 2, 3, 4, 5, 6]
D. [5, 4, 5, 6, 7, 8, 9, 10, 11, 12]
E. [4, 5, 6, 7, 8, 9, 10, 9, 8, 7]
F. [5, 6, 7, 8, 9, 10, 11, 10, 9, 8]
G. [3, 4, 5, 6, 7, 8, 9, 10, 9, 8]
H. [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
I. [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
J. [3, 5, 7, 9, 11, 13, 15, 17, 19, 21]
Answer: E
We now define an algorithm: The definition of a(n) is the output image of n after one application of the "5x+1" transformation, which maps an integer n to 5n + 1. 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. [306, 31, 21, 32, 362, 33, 336, 34, 326, 35]
B. [306, 31, 211, 32, 326, 33, 326, 34, 25, 35]
C. [306, 31, 21, 32, 326, 33, 336, 34, 23, 35]
D. [361, 31, 21, 32, 326, 33, 633, 34, 23, 35]
E. [31, 306, 21, 32, 326, 33, 36, 34, 23, 335]
F. [306, 31, 210, 32, 326, 331, 336, 34, 23, 35]
G. [306, 31, 21, 32, 326, 33, 336, 43, 23, 305]
H. [36, 31, 21, 32, 326, 33, 336, 34, 230, 35]
I. [306, 31, 211, 32, 326, 33, 336, 34, 233, 35]
J. [306, 301, 310, 321, 326, 331, 336, 341, 326, 351]
Answer: C
We now define an algorithm: The definition of a(n) is the characteristic function of natural numbers whose number of divisors is a Lucas number. 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.

Options:
A. [0, 0, 1, 0, 0, 1, 0, 0, 1, 0]
B. [1, 1, 1, 0, 0, 0, 0, 1, 1, 0]
C. [1, 0, 1, 1, 0, 0, 1, 0, 1, 0]
D. [1, 1, 0, 1, 0, 0, 0, 1, 0, 1]
E. [1, 0, 0, 0, 1, 0, 0, 1, 0, 0]
F. [0, 0, 0, 0, 1, 1, 0, 0, 0, 1]
G. [0, 1, 0, 1, 1, 0, 1, 0, 0, 0]
H. [1, 0, 0, 1, 0, 1, 0, 1, 0, 0]
I. [0, 1, 1, 0, 0, 0, 1, 0, 0, 1]
J. [0, 1, 0, 0, 1, 0, 0, 1, 1, 0]
Answer: D
We now define an algorithm: The definition of a(n) is the Moser-de Bruijn sequence: sums of distinct powers of 4. Given the input x_list (a series of values): [42, 43, 44, 45, 46, 47, 48, 49, 50, 51], determine the corresponding output sequence y_list.

Options:
A. [1152, 1153, 1164, 1165, 1168, 1169, 1360, 1361, 1364, 1365]
B. [1002, 1003, 1024, 1025, 1028, 1029, 1260, 1261, 1264, 1265]
C. [1102, 1103, 1124, 1125, 1128, 1129, 1320, 1321, 1324, 1325]
D. [1082, 1083, 1114, 1115, 1118, 1119, 1340, 1341, 1344, 1345]
E. [1042, 1043, 1064, 1065, 1068, 1069, 1240, 1241, 1244, 1245]
F. [1092, 1093, 1104, 1105, 1108, 1109, 1280, 1281, 1284, 1285]
G. [1142, 1143, 1154, 1155, 1158, 1159, 1290, 1291, 1294, 1295]
H. [1192, 1193, 1204, 1205, 1208, 1209, 1380, 1381, 1384, 1385]
I. [1052, 1053, 1074, 1075, 1078, 1079, 1300, 1301, 1304, 1305]
J. [1022, 1023, 1094, 1095, 1098, 1099, 1220, 1221, 1224, 1225]
Answer: F
We now define an algorithm: The definition of a(n) is: Let n be a positive integer. For each prime divisor p of n, consider the highest power of p which does not exceed n. The sum a(n) of these powers is defined as the power-sum of n. For example, for n=10, the prime divisors are 2 and 5. The highest power of 2 that does not exceed 10 is 8 (2^3), and the highest power of 5 that does not exceed 10 is 5 (5^1). Therefore, a(10) = 8 + 5 = 13. 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. [59, 84, 60, 63, 76, 64, 37, 102, 67, 81]
B. [59, 84, 61, 63, 76, 64, 38, 102, 67, 81]
C. [59, 84, 61, 63, 77, 64, 38, 102, 67, 81]
D. [59, 85, 61, 63, 77, 64, 38, 102, 67, 82]
E. [60, 84, 61, 63, 76, 64, 38, 101, 67, 81]
F. [59, 84, 61, 62, 76, 64, 38, 102, 67, 80]
G. [59, 84, 62, 63, 76, 64, 38, 102, 67, 81]
H. [58, 84, 61, 63, 76, 65, 38, 102, 67, 81]
I. [59, 84, 61, 64, 76, 64, 38, 103, 67, 81]
J. [59, 83, 61, 63, 76, 64, 38, 102, 68, 81]
Answer: B
We now define an algorithm: The definition of a(n) is: Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives r values. Note that a Gaussian integer is a complex number of the form z = a+bi, where both a and b are integers, and the first-quadrant Gaussian integers have both a and b non-negative. 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. [184, 88, 159, 68, 380, 81, 136, 112, 198, 184]
B. [180, 84, 155, 64, 376, 77, 132, 108, 194, 180]
C. [175, 79, 150, 59, 371, 72, 127, 103, 189, 175]
D. [178, 82, 153, 62, 374, 75, 130, 106, 192, 178]
E. [182, 86, 157, 66, 378, 79, 134, 110, 196, 182]
F. [179, 83, 154, 63, 375, 76, 131, 107, 193, 179]
G. [177, 81, 152, 61, 373, 74, 129, 105, 191, 177]
H. [181, 85, 156, 65, 377, 78, 133, 109, 195, 181]
I. [176, 80, 151, 60, 372, 73, 128, 104, 190, 176]
J. [183, 87, 158, 67, 379, 80, 135, 111, 197, 183]
Answer: I
We now define an algorithm: The definition of a(n) is the smallest semiperimeter of an integral rectangle (a rectangle with integer side lengths) with area n. 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. [18, 60, 34, 18, 18, 20, 19, 67, 23, 27]
B. [18, 64, 31, 18, 18, 20, 19, 70, 23, 28]
C. [19, 65, 30, 19, 18, 21, 20, 71, 24, 29]
D. [17, 62, 33, 17, 16, 20, 18, 66, 21, 26]
E. [16, 61, 35, 16, 17, 19, 17, 65, 20, 24]
F. [15, 63, 32, 15, 15, 17, 16, 68, 20, 25]
G. [16, 62, 33, 16, 16, 18, 17, 68, 21, 26]
H. [15, 60, 34, 17, 15, 17, 16, 67, 20, 25]
I. [17, 63, 32, 15, 17, 19, 18, 69, 22, 27]
J. [16, 64, 31, 16, 16, 18, 17, 69, 21, 28]
Answer: G
We now define an algorithm: The definition of a(n) is the initial digit of the n-th Mersenne number, where a Mersenne number is defined as a number of the form 2^p - 1, with p itself being a prime number. Given the input x_list (a series of values): [91, 92, 93, 94, 95, 96, 97, 98, 99, 100], determine the corresponding output sequence y_list.

Options:
A. [3, 1, 4, 6, 2, 2, 1, 5, 2, 7]
B. [3, 2, 3, 5, 1, 2, 1, 6, 2, 8]
C. [3, 1, 3, 6, 2, 2, 1, 5, 2, 6]
D. [3, 1, 2, 5, 1, 2, 1, 6, 3, 7]
E. [3, 2, 2, 6, 1, 2, 2, 6, 3, 7]
F. [4, 1, 3, 6, 1, 3, 1, 6, 2, 9]
G. [3, 1, 3, 6, 1, 2, 1, 6, 2, 7]
H. [3, 1, 3, 6, 1, 2, 1, 6, 3, 6]
I. [2, 1, 3, 7, 1, 2, 1, 6, 2, 7]
J. [4, 1, 3, 5, 1, 2, 1, 6, 2, 8]
Answer: G
We now define an algorithm: The definition of a(n) is numbers that are divisible by 5 and are the difference between two different positive cubes in at least one way. Given the input x_list (a series of values): [34, 35, 36, 37, 38, 39, 40, 41, 42, 43], determine the corresponding output sequence y_list.

Options:
A. [7630, 7890, 7950, 8325, 8940, 9050, 9060, 9280, 9800, 9990]
B. [7640, 7900, 7960, 8330, 8950, 9060, 9070, 9290, 9810, 10000]
C. [7620, 7880, 7940, 8320, 8930, 9040, 9050, 9270, 9790, 9980]
D. [7610, 7860, 7915, 8305, 8910, 9025, 9035, 9250, 9775, 9960]
E. [7625, 7875, 7930, 8315, 8920, 9035, 9045, 9260, 9785, 9970]
F. [7605, 7855, 7910, 8300, 8905, 9020, 9030, 9245, 9770, 9955]
G. [7615, 7865, 7925, 8310, 8915, 9030, 9040, 9255, 9780, 9965]
H. [7645, 7905, 7965, 8340, 8955, 9065, 9075, 9295, 9815, 10005]
I. [7650, 7910, 7970, 8345, 8960, 9070, 9080, 9300, 9820, 10010]
J. [7635, 7895, 7955, 8335, 8945, 9055, 9065, 9285, 9805, 9995]
Answer: E
We now define an algorithm: The definition of a(n) is the number of times one must divide n by 2 to reach 1 in the context of the '3x+1' problem, also known as the Collatz conjecture, or -1 if this never happens. 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. [17, 9, 9, 9, 63, 14, 71, 14, 9, 14]
B. [20, 12, 12, 12, 66, 17, 74, 17, 12, 17]
C. [19, 11, 11, 11, 65, 16, 73, 16, 11, 16]
D. [18, 10, 10, 10, 64, 15, 72, 15, 10, 15]
E. [22, 14, 14, 14, 68, 19, 76, 19, 14, 19]
F. [24, 16, 16, 16, 70, 21, 78, 21, 16, 21]
G. [21, 13, 13, 13, 67, 18, 75, 18, 13, 18]
H. [23, 15, 15, 15, 69, 20, 77, 20, 15, 20]
I. [16, 8, 8, 8, 62, 13, 70, 13, 8, 13]
J. [25, 17, 17, 17, 71, 22, 79, 22, 17, 22]
Answer: C
We now define an algorithm: The definition of a(n) is the multiplicative order of 3 modulo the nth positive integer m that is coprime with 3 (i.e., gcd(m, 3) = 1). Given the input x_list (a series of values): [68, 69, 70, 71, 72, 73, 74, 75, 76, 77], determine the corresponding output sequence y_list.

Options:
A. [102, 33, 7, 51, 54, 26, 21, 13, 110, 45]
B. [100, 34, 6, 52, 53, 27, 20, 12, 112, 44]
C. [105, 38, 3, 55, 60, 31, 24, 17, 117, 40]
D. [103, 36, 9, 54, 57, 29, 22, 15, 115, 43]
E. [98, 37, 10, 48, 59, 24, 17, 16, 111, 41]
F. [99, 35, 5, 50, 55, 28, 19, 11, 113, 46]
G. [101, 32, 8, 53, 56, 25, 18, 14, 114, 47]
H. [97, 39, 2, 47, 61, 32, 25, 18, 118, 39]
I. [106, 40, 1, 46, 62, 33, 26, 19, 119, 38]
J. [104, 31, 4, 49, 58, 30, 23, 10, 116, 42]
Answer: B
We now define an algorithm: The definition of a(n) is: Numbers m such that there are precisely 4 groups of finite order m in group theory. 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. [428, 430, 432, 435, 442, 465, 470, 493, 495, 497]
B. [425, 427, 431, 435, 441, 464, 469, 493, 495, 497]
C. [426, 428, 430, 434, 442, 465, 470, 494, 495, 498]
D. [427, 429, 433, 434, 443, 467, 473, 497, 498, 502]
E. [426, 429, 433, 436, 444, 467, 472, 496, 497, 501]
F. [427, 429, 431, 434, 443, 465, 469, 494, 497, 500]
G. [426, 428, 432, 435, 443, 466, 471, 495, 496, 499]
H. [427, 428, 430, 436, 443, 466, 471, 494, 496, 498]
I. [429, 431, 433, 437, 445, 468, 473, 498, 499, 503]
J. [428, 430, 432, 436, 444, 467, 472, 495, 499, 501]
Answer: C
We now define an algorithm: The definition of a(n) is the number of aperiodic necklaces composed of n beads, each of which can be one of 6 different colors. This sequence also represents the dimensions of free Lie algebras. 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.

Options:
A. [32982550, 181394536, 1034668770, 5577420295, 31145665106, 178319264240, 997685849690, 5622219252460, 32271565263710, 180807918979777]
B. [32781550, 180384535, 1054668770, 5557420295, 31545665106, 173319264240, 992685849690, 5662219252460, 31871565263710, 178807918979777]
C. [32881550, 180394535, 1024668770, 5587420295, 31245665106, 175319264240, 994685849690, 5632219252460, 31971565263710, 181807918979777]
D. [33081550, 181404535, 1044668770, 5567420295, 31045665106, 174319264240, 993685849690, 5612219252460, 32171565263711, 179807918979777]
E. [32981550, 181394535, 1004668770, 5597420295, 31345665106, 176319264240, 995685849690, 5642219252460, 32071565263710, 182807918979777]
F. [32581550, 183394535, 1074668770, 5537420295, 30945665106, 179319264240, 998685849690, 5652219252460, 32271565263712, 176807918979777]
G. [33181550, 182394535, 1014668770, 5607420295, 31445665106, 177319264240, 996685849690, 5652219252460, 32171565263710, 183807918979777]
H. [32481550, 184394535, 1084668770, 5527420295, 30845665106, 171319264240, 999685849690, 5642219252461, 32371565263710, 175807918979777]
I. [32681550, 182384535, 1064668770, 5547420295, 31645665106, 172319264240, 991685849690, 5632219252460, 31771565263710, 177807918979777]
J. [32381550, 185394535, 1094668770, 5517420295, 30745665106, 170319264240, 990685849690, 5612219252460, 32471565263710, 174807918979777]
Answer: E
We now define an algorithm: The definition of a(n) is the number of series-reduced planted trees with n leaves. Also, it represents the number of essentially series series-parallel networks with n edges, and the number of essentially parallel series-parallel networks with n edges. In graph theory, "series-reduced" typically refers to a graph where no series reductions can be applied, and "planted trees" are rooted trees rooted at a specific "plant" node. Given the input x_list (a series of values): [19, 20, 21, 22, 23, 24, 25, 26, 27, 28], determine the corresponding output sequence y_list.

Options:
A. [78023602, 256738751, 848152864, 2811996971, 9353366564, 31204088381, 104384620070, 350064856815, 1176693361957, 3963752002320]
B. [78023602, 256738751, 848152863, 2811996972, 9353366564, 31204088380, 104384620070, 350064856815, 1176693361956, 3963752002320]
C. [78023601, 256738751, 848152864, 2811996973, 9353366564, 31204088381, 104384620070, 350064856814, 1176693361956, 3963752002320]
D. [78023602, 256738750, 848152864, 2811996973, 9353366564, 31204088381, 104384620069, 350064856815, 1176693361956, 3963752002320]
E. [78023602, 256738752, 848152864, 2811996972, 9353366564, 31204088381, 104384620071, 350064856815, 1176693361955, 3963752002320]
F. [78023602, 256738751, 848152865, 2811996972, 9353366563, 31204088381, 104384620070, 350064856815, 1176693361956, 3963752002321]
G. [78023602, 256738751, 848152864, 2811996972, 9353366564, 31204088381, 104384620069, 350064856816, 1176693361956, 3963752002320]
H. [78023603, 256738751, 848152864, 2811996972, 9353366564, 31204088381, 104384620070, 350064856816, 1176693361956, 3963752002320]
I. [78023602, 256738751, 848152865, 2811996972, 9353366565, 31204088381, 104384620070, 350064856815, 1176693361956, 3963752002319]
J. [78023602, 256738751, 848152864, 2811996972, 9353366564, 31204088381, 104384620070, 350064856815, 1176693361956, 3963752002320]
Answer: J
When using an ordinary optical microscope with an oil immersion objective, where should the immersion oil be applied?

Options:
A. Between the specimen and the objective lens
B. Behind the objective turret
C. On top of the specimen
D. On the light source
E. Specimen
F. Between the condenser and the specimen
G. On the slide cover
H. Under the stage
I. Eyepiece
J. Objective lens
Answer: A
What is the first structure formed by ferns after undergoing meiosis?

Options:
A. Sporophyte
B. Frond
C. Sperm
D. Zygote
E. Spore
F. Rhizome
G. Chloroplast
H. Embryo
I. Gametophyte
J. Seed
Answer: E
The horticulturist wants to collect seeds from a newly transplanted pine tree. He discovered that this pine tree had female cones in April 2009. When can the horticulturist expect to collect mature seeds from these female cones?

Options:
A. October 2010
B. September 2010
C. December 2009
D. July 2010
E. September 2009
F. November 2009
G. February 2010
H. August 2009
I. January 2010
J. March 2010
Answer: B
The pectoralis major and pectoralis minor muscles are responsible for the lifting and lowering of a bird's wings. Which of the following descriptions about the attachment points on both sides of the pectoralis major and pectoralis minor is correct?

Options:
A. The pectoralis major and the pectoralis minor, like each other, are both attached at one end to the sternum and at the other end to the clavicle.
B. The two ends of the pectoralis major are attached to the sternum keel protrusion and the humerus, while the two ends of the pectoralis minor are attached to the sternum keel protrusion and the coracoid bone.
C. The pectoralis major and the pectoralis minor, like each other, are both attached at one end to the sternum and at the other end to the ribs.
D. The pectoralis major and the pectoralis minor, like each other, are both attached at one end to the vertebrae and at the other end to the coracoid.
E. The pectoralis major attaches at one end to the sternum's keel and at the other end to the coracoid, while the pectoralis minor attaches at one end to the sternum's keel and at the other end to the humerus.
F. The pectoralis major muscle, like the pectoralis minor, is attached at both ends to the sternum's keel process and the coracoid.
G. The pectoralis major and the pectoralis minor, like each other, are both attached at one end to the scapula and at the other end to the humerus.
H. The pectoralis major and the pectoralis minor, like each other, are both attached at one end to the keel and at the other end to the scapula.
I. The pectoralis major and the pectoralis minor, like each other, are both attached at one end to the clavicle and at the other end to the humerus.
J. The pectoralis major and the pectoralis minor, like each other, are both attached at one end to the sternum and at the other end to the humerus.
Answer: J
The Clark's Nutcracker (*Nucifraga columbiana*), the Pinyon Jay (*Gymnorhinus cyanocephalus*), and the Steller's Jay (*Cyanocitta stelleri*) are closely related species within the same family. The Clark's Nutcracker inhabits high-altitude regions and relies almost entirely on seeds stored during the autumn for its food supply in winter and spring, with each bird storing approximately 33,000 seeds annually. The Pinyon Jay is distributed in slightly lower-altitude areas and lives in social groups year-round. Each bird stores about 20,000 seeds annually, which constitute 70-90% of its winter diet. The Steller's Jay, residing in low-altitude regions, is the smallest in size and stores around 6,000 seeds per bird each year, accounting for 60% of its winter diet. If the three species are placed together in a small experimental area to store and retrieve seeds, what would the ranking of their memory abilities be from strongest to weakest?

Options:
A. Pinyon Jay > Steller's Nutcracker > Blue Bird
B. Nutcracker Nutbird > Pine Jay > Steller Bird
C. Steller's jay > Pine jay > Nutcracker
D. Steller's Nutbird > Spotted Jay > Pinyon Bird
E. Nutcracker Jay > Blue Nutbird > Spotted Jay
F. Starling jay > Pine nut jay > Blue jay
G. Steller's Jay > Pinyon Nutbird > Nutcracker
H. Nutcracker Jay > Spotted Nutcracker > Blue Jay
I. Spotted Nutcracker > Pinyon Jay > Steller's Jay
J. Three Types are similar
Answer: H
There is a type of animal that possesses a true coelom and develops anterior, middle, and posterior coelomic cavities during its developmental process. It has a developed metanephros that also functions as a reproductive duct. Marine species of this group exhibit a larval stage similar to the trochophore larva, and their fertilized eggs undergo radial cleavage. What type of animal does this group belong to?

Options:
A. Vertebrates Exhibiting Radial Cleavage
B. Early Echinoderm Larvae
C. Transitional Types Between Protostomes and Deuterostomes
D. Marine Mollusks with Radial Cleavage
E. True Coelomates with Spiral Cleavage
F. Deuterostomes
G. Original Mouth Animals
H. Protostome Animals with Trochophore Larvae
I. Chordates with Unsegmented Coelom
J. Protostomes
Answer: C
Which class of animals listed below has all its members go through at least one parasitic stage in their life cycle?

Options:
A. Phylum Rotifera
B. Class Amoebida
C. Phylum Nematoda
D. Class Ciliophora
E. Sporozoa
F. Class Monogenea
G. Class Oligochaeta
H. Class Trematoda
I. Class Hirudinea
J. Class Mastigophora
Answer: E
Which group of animals all have an anus?

Options:
A. Sea lamprey, bony fish, dog
B. Amphibians, sea lamprey, reptiles
C. Birds, cartilaginous fish, monotremes
D. Cartilaginous fish, birds, monotremes
E. Cartilaginous fish, reptiles, amphibians
F. Reptiles, birds, amphibians
G. Amphibians, reptiles, birds
H. Amphibians, bony fish, monotremes
I. Monotremes, bony fish, reptiles
J. Cartilaginous fish, bony fish, reptiles
Answer: A
It is estimated that the number of HIV-infected individuals in mainland China has already reached how many people?

Options:
A. A few dozen
B. 10 million
C. Several million
D. Thousands
E. Over ten billion
F. Billions
G. More than a billion
H. Hundreds of thousands
I. Millions
J. Tens of thousands
Answer: H
What is produced when one molecule of pyruvate undergoes oxidation through the TCA cycle and the respiratory chain?

Options:
A. There are four instances of dehydrogenation, all of which enter the respiratory chain through NAD-.
B. Produces 2 molecules of $\mathrm{CO_2}$
C. There are six instances of dehydrogenation, all of which enter the respiratory chain through NAD-.
D. Generate 15 molecules of ATP.
E. Generate 10 molecules of ATP.
F. There are five instances of dehydrogenation, all of which enter the respiratory chain through NAD-.
G. Produces 4 molecules of $\mathrm{CO_2}$
H. Generate 5 molecules of $\mathrm{H_2O}$.
I. Generate 12 molecules of ATP.
J. Generate 3 molecules of $\mathrm{CO_2}$.
Answer: J
What are the germination characteristics of rice seeds under conditions of insufficient oxygen supply?

Options:
A. The radicle elongates faster, and the epicotyl halts growth.
B. The epicotyl is long, and the radicle is short.
C. The epicotyl remains undeveloped, while the radicle elongates.
D. Embryonic shoot short, embryonic root short
E. The embryonic shoot is short, and the embryonic root is long.
F. The embryo grows, the radicle grows.
G. The epicotyl is short, and the radicle is long.
H. The coleoptile is short, and the radicle is undeveloped.
I. The embryonic shoot is long, and the radicle stops growing.
J. The radicle does not grow, but the coleoptile grows.
Answer: B
What is the approximate ratio of the intracellular potassium ion (K⁺) concentration to the extracellular potassium ion (K⁺) concentration in normal cells?

Options:
A. 12 times
B. 7 times
C. 50 times
D. 90 times
E. 10 times
F. 5 times
G. 120 times
H. 30 times
I. 25 times
J. 15 times
Answer: G
What type of bacteria produces soil elements?

Options:
A. Mold
B. Bacteria
C. Halobacteria
D. Methanococci
E. Spirochaetes
F. Toxoid
G. Rhizobiales
H. Enterobacter
I. Actinomycetes
J. Thermoplasma
Answer: I
What feature is common to algae, mosses, and ferns?

Options:
A. The presence of seeds and pollen in reproduction.
B. All possess vascular tissues for nutrient transport.
C. Dependence exclusively on animal pollination for reproduction.
D. Light and pigments containing both chlorophyll a and b
E. All require symbiotic fungi for nutrient absorption.
F. They all reproduce asexually through spores.
G. Both the sporophyte and gametophyte are capable of independent living.
H. Growth influenced by circadian light rhythms alone.
I. Oviparous reproduction
J. Habitat restricted strictly to freshwater environments.
Answer: F
What causes the normal termination of a peptide chain?

Options:
A. The lack of a start codon halts translation prematurely.
B. Does not possess an anticodon tRNA corresponding to the chain-terminating triplet.
C. A tRNA carries an amino acid to the stop codon.
D. A releasing factor triggers peptide elongation to continue.
E. Due to the termination codon appearing on the tRNA.
F. A tRNA corresponding to a chain-terminating triplet cannot carry an amino acid.
G. A ribosome binds an incorrect tRNA at the stop codon.
H. The peptide chain dissociates at an internal codon.
I. mRNA synthesis stops at the termination triplet.
J. A promoter sequence prevents the termination codon translation.
Answer: B
Sometimes, a considerable number of white flowers display many red spots. Which of the following statements is correct?

Options:
A. It results from a prolonged environmental stress.
B. It is the result of a reverse mutation.
C. It is possible that somatic cell recombination has occurred.
D. It happens because of random epigenetic silencing.
E. It occurs due to chromosomal non-disjunction.
F. It is the result of genetic complementation.
G. It may be the result of transposon activity.
H. It is evidence of hybrid sterility in the plants.
I. The white-flowered plants are heterozygous, with one allele controlling the red phenotype.
J. It arises because of incomplete mitotic segregation.
Answer: G
A large number of red blood cells in human blood transport oxygen and carbon dioxide. How do oxygen and carbon dioxide enter cells?

Options:
A. Diffusive Transfer
B. Osmotic Balance
C. Endocytosis
D. Active Transport
E. Protein Export
F. Phagocytosis
G. Passive Transport
H. Facilitated Diffusion
I. Lobule
J. Active Uptake
Answer: G
In bacterial conjugation experiments, what is it that very rarely causes the recipient cell to change sex after conjugating with strains of different sexes?

Options:
A. Hfr×Hfr
B. F'×F-
C. F'×Hfr
D. F+×F'
E. F'×F+
F. F-×F+
G. F+×F-
H. F-×F-
I. F+×Hfr
J. Hfr×F-
Answer: J