Q. What is 25 × 4? (2014)
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Q. What is a trophic level? (2020)
A.
A level of energy in an ecosystem
B.
A level of biodiversity
C.
A level of pollution
D.
A level of soil fertility
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Solution
A trophic level refers to the position an organism occupies in a food chain, indicating its energy level.
Correct Answer:
A
— A level of energy in an ecosystem
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Q. What is adaptive radiation? (1960)
A.
Rapid evolution of many species from a common ancestor
B.
Evolution of similar traits in unrelated species
C.
The extinction of a species
D.
The migration of species to new habitats
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Solution
Adaptive radiation is the rapid evolution of many species from a common ancestor, often occurring when species colonize new environments with diverse ecological niches.
Correct Answer:
A
— Rapid evolution of many species from a common ancestor
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Q. What is binomial nomenclature? (2021)
A.
A method of classifying organisms
B.
A two-part naming system
C.
A type of genetic mutation
D.
A method of reproduction
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Solution
Binomial nomenclature is a two-part naming system for organisms, consisting of the genus and species names.
Correct Answer:
B
— A two-part naming system
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Q. What is carrying capacity? (2021)
A.
The maximum number of individuals an environment can support
B.
The minimum number of individuals needed for a population to survive
C.
The average number of individuals in a population
D.
The number of species in a community
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Solution
Carrying capacity is the maximum number of individuals of a species that an environment can sustainably support.
Correct Answer:
A
— The maximum number of individuals an environment can support
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Q. What is genetic drift? (2015)
A.
Change in allele frequencies due to chance
B.
Natural selection acting on a population
C.
Migration of individuals into a population
D.
Mutation of genes
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Solution
Genetic drift refers to changes in allele frequencies in a population due to random sampling of organisms, which can lead to significant changes over time, especially in small populations.
Correct Answer:
A
— Change in allele frequencies due to chance
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Q. What is ovulation? (2023)
A.
Release of an egg from the ovary
B.
Fertilization of the egg
C.
Implantation of the embryo
D.
Menstruation
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Solution
Ovulation is the process of releasing an egg from the ovary, which is a key event in the female reproductive cycle.
Correct Answer:
A
— Release of an egg from the ovary
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Q. What is parthenogenesis? (2020)
A.
Development of an embryo from an unfertilized egg
B.
A form of asexual reproduction
C.
A type of sexual reproduction
D.
Both a and b
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Solution
Parthenogenesis is a form of asexual reproduction where an embryo develops from an unfertilized egg, and it is considered a type of asexual reproduction.
Correct Answer:
D
— Both a and b
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Q. What is the 10th term of the arithmetic sequence where the first term is 5 and the common difference is 3?
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Solution
The nth term of an arithmetic sequence is given by a_n = a + (n-1)d. Here, a = 5, d = 3, n = 10. So, a_10 = 5 + (10-1) * 3 = 5 + 27 = 32.
Correct Answer:
B
— 35
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Q. What is the 12th term of the arithmetic sequence where the first term is 7 and the common difference is 5?
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Solution
Using the formula a_n = a + (n-1)d, we have a_12 = 7 + (12-1) * 5 = 7 + 55 = 62.
Correct Answer:
A
— 62
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Q. What is the 3rd term in the expansion of (2x + 3)^4?
A.
108x^2
B.
216x^2
C.
324x^2
D.
432x^2
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Solution
The 3rd term is given by C(4,2) * (2x)^2 * (3)^2 = 6 * 4x^2 * 9 = 216x^2.
Correct Answer:
B
— 216x^2
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Q. What is the 3rd term in the expansion of (2x + 5)^6? (2000)
A.
600x^4
B.
1500x^4
C.
1800x^4
D.
2000x^4
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Solution
The 3rd term is given by C(6,2) * (2x)^2 * (5)^4 = 15 * 4 * 625 = 37500.
Correct Answer:
B
— 1500x^4
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Q. What is the 3rd term in the expansion of (2x - 3)^5? (2022)
A.
-90x^3
B.
90x^3
C.
-60x^3
D.
60x^3
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Solution
The 3rd term is C(5,2) * (2x)^3 * (-3)^2 = 10 * 8x^3 * 9 = -720x^3.
Correct Answer:
A
— -90x^3
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Q. What is the 3rd term in the expansion of (x + 2)^5? (2021)
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Solution
The 3rd term is given by C(5,2) * (x)^3 * (2)^2 = 10 * x^3 * 4 = 40.
Correct Answer:
C
— 60
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Q. What is the 3rd term in the expansion of (x + 2)^8? (2022)
A.
112
B.
128
C.
256
D.
64
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Solution
The 3rd term is given by 8C2 * (2)^2 * (x)^6 = 28 * 4 * x^6 = 112x^6.
Correct Answer:
A
— 112
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Q. What is the 3rd term in the expansion of (x + 3)^4? (2023)
A.
36x^2
B.
54x^2
C.
72x^2
D.
108x^2
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Solution
The 3rd term is C(4,2) * (3)^2 * (x)^2 = 6 * 9 * x^2 = 54x^2.
Correct Answer:
B
— 54x^2
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Q. What is the 3rd term in the expansion of (x + 3)^5? (2023)
A.
45
B.
90
C.
135
D.
180
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Solution
The 3rd term is C(5,2) * (3)^2 * (x)^3 = 10 * 9 * x^3 = 90.
Correct Answer:
B
— 90
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Q. What is the 3rd term in the expansion of (x + 3)^7? (2023)
A.
189
B.
441
C.
729
D.
1024
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Solution
The 3rd term is C(7,2) * (3)^2 * (x)^5 = 21 * 9 * x^5 = 189.
Correct Answer:
B
— 441
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Q. What is the 3rd term in the expansion of (x + 4)^5? (2023)
A.
80x^3
B.
160x^3
C.
240x^3
D.
320x^3
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Solution
The 3rd term is given by C(5,2) * (4)^2 * (x)^3 = 10 * 16 * x^3 = 160x^3.
Correct Answer:
C
— 240x^3
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Q. What is the 3rd term in the expansion of (x + 4)^6? (2020)
A.
240x^4
B.
360x^4
C.
480x^4
D.
600x^4
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Solution
The 3rd term is C(6,2) * (4)^2 * (x)^4 = 15 * 16 * x^4 = 240x^4.
Correct Answer:
B
— 360x^4
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Q. What is the 4th term in the expansion of (2x - 3)^6? (2020)
A.
-540
B.
540
C.
-720
D.
720
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Solution
The 4th term is C(6,3) * (2x)^3 * (-3)^3 = 20 * 8x^3 * -27 = -540.
Correct Answer:
A
— -540
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Q. What is the 5th term in the expansion of (2 + 3x)^6? (2023)
A.
486
B.
540
C.
729
D.
810
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Solution
The 5th term is given by 6C4 * (2)^(6-4) * (3x)^4 = 15 * 4 * 81x^4 = 4860x^4.
Correct Answer:
B
— 540
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Q. What is the 5th term in the expansion of (3x - 2)^7? (2023)
A.
-1680x^3
B.
1680x^3
C.
-2520x^3
D.
2520x^3
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Solution
The 5th term is given by C(7,4) * (3x)^4 * (-2)^3 = 35 * 81 * (-8) = -1680x^3.
Correct Answer:
A
— -1680x^3
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Q. What is the 5th term in the expansion of (x - 1)^8? (2022)
A.
-56x^4
B.
56x^4
C.
-70x^4
D.
70x^4
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Solution
The 5th term corresponds to k=4. Using the binomial theorem, it is given by 8C4 * (x)^4 * (-1)^4 = 70x^4.
Correct Answer:
A
— -56x^4
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Q. What is the 5th term of the sequence defined by a_n = 2n^2 + 3n - 1?
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Solution
To find the 5th term, substitute n = 5 into the formula: a_5 = 2(5^2) + 3(5) - 1 = 2(25) + 15 - 1 = 50 + 15 - 1 = 64.
Correct Answer:
B
— 47
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Q. What is the 8th term of the sequence defined by a_n = 3n - 2?
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Solution
Substituting n = 8 into the formula: a_8 = 3(8) - 2 = 24 - 2 = 22.
Correct Answer:
A
— 22
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Q. What is the absolute error if the true value is 50 and the measured value is 48? (2022)
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Solution
Absolute error is calculated as the absolute difference between the true value and the measured value, which is |50 - 48| = 2.
Correct Answer:
A
— 2
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Q. What is the absolute error in a measurement of 50.0 cm if the true value is 48.0 cm? (2022)
A.
2.0 cm
B.
1.0 cm
C.
3.0 cm
D.
4.0 cm
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Solution
Absolute error = |Measured value - True value| = |50.0 cm - 48.0 cm| = 2.0 cm.
Correct Answer:
A
— 2.0 cm
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Q. What is the absolute error in a measurement of 50.0 cm if the true value is 52.0 cm? (2022)
A.
2.0 cm
B.
1.0 cm
C.
0.5 cm
D.
3.0 cm
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Solution
Absolute error = |Measured value - True value| = |50.0 cm - 52.0 cm| = 2.0 cm.
Correct Answer:
A
— 2.0 cm
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Q. What is the absolute error in a measurement? (2021)
A.
The difference between the measured value and the true value
B.
The average of all measurements
C.
The maximum value in a set of measurements
D.
The minimum value in a set of measurements
Show solution
Solution
Absolute error is defined as the difference between the measured value and the true value.
Correct Answer:
A
— The difference between the measured value and the true value
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