Q. The scalar product of vectors A = (a, b, c) and B = (1, 2, 3) is 14. If a = 2, what is the value of b + c?
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Solution
A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12. Solving gives b + c = 6.
Correct Answer:
C
— 6
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Q. The scientific study of classification is known as: (2022)
A.
Taxonomy
B.
Morphology
C.
Anatomy
D.
Ecology
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Solution
Taxonomy is the scientific study of classification of organisms.
Correct Answer:
A
— Taxonomy
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Q. The scientist made a significant ___ in the field of genetics.
A.
mistake
B.
discovery
C.
failure
D.
theory
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Solution
The word 'discovery' indicates a positive contribution to genetics.
Correct Answer:
B
— discovery
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Q. The scientist's findings were met with ______ from the academic community, leading to further research in the field.
A.
apathy
B.
enthusiasm
C.
skepticism
D.
indifference
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Solution
The word 'enthusiasm' indicates a positive reception of the findings, which is likely to encourage further research.
Correct Answer:
B
— enthusiasm
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Q. The scientist's findings were met with __________ from the academic community, as they challenged long-held beliefs. (2023)
A.
applause
B.
skepticism
C.
indifference
D.
enthusiasm
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Solution
Challenging long-held beliefs typically leads to skepticism rather than applause or enthusiasm.
Correct Answer:
B
— skepticism
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Q. The scientist's findings were met with __________ from the academic community, leading to further investigation into the results.
A.
applause
B.
skepticism
C.
indifference
D.
enthusiasm
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Solution
The word 'skepticism' indicates doubt or disbelief, which is a common reaction to new scientific findings.
Correct Answer:
B
— skepticism
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Q. The scientist's groundbreaking research has opened new avenues for understanding the complexities of human behavior, suggesting that our actions are not merely the result of instinct but are also _____ by social and environmental factors.
A.
influenced
B.
ignored
C.
restricted
D.
simplified
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Solution
The word 'influenced' fits well, indicating that behavior is shaped by various factors beyond instinct.
Correct Answer:
A
— influenced
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Q. The scientist's groundbreaking research was met with skepticism, but over time, it became ______ in the field.
A.
obsolete
B.
irrelevant
C.
pioneering
D.
controversial
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Solution
The term 'pioneering' suggests that the research was innovative and influential, which aligns with the context of it becoming accepted in the field.
Correct Answer:
C
— pioneering
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Q. The scientist's groundbreaking research was met with skepticism, yet it ultimately __________.
A.
reinforced existing theories.
B.
was dismissed by the academic community.
C.
opened new avenues for exploration.
D.
failed to gain any recognition.
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Solution
The phrase 'groundbreaking research' implies that it led to new opportunities, making option 2 the most appropriate completion.
Correct Answer:
C
— opened new avenues for exploration.
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Q. The scientist's groundbreaking research was met with skepticism, yet it ultimately ________ the long-held beliefs in the field.
A.
reinforced
B.
challenged
C.
ignored
D.
validated
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Solution
The phrase 'met with skepticism' implies that the research questioned existing beliefs, making 'challenged' the right answer.
Correct Answer:
B
— challenged
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Q. The scientist's theory was initially met with skepticism, but over time it gained __________ as more evidence emerged. (2021)
A.
credibility
B.
doubt
C.
rejection
D.
confusion
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Solution
The context indicates that the theory gained acceptance, which aligns with credibility rather than doubt or rejection.
Correct Answer:
A
— credibility
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Q. The scores of a class in a test are: 10, 12, 14, 16, 18. What is the variance? (2022)
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Solution
Mean = 14. Variance = [(10-14)² + (12-14)² + (14-14)² + (16-14)² + (18-14)²] / 5 = 8.
Correct Answer:
A
— 4
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Q. The scores of a test are: 20, 30, 40, 50. Calculate the variance. (2020)
A.
100
B.
200
C.
300
D.
400
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Solution
Mean = (20 + 30 + 40 + 50) / 4 = 35. Variance = [(20-35)² + (30-35)² + (40-35)² + (50-35)²] / 4 = 250.
Correct Answer:
B
— 200
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Q. The scores of a test are: 20, 30, 40, 50. What is the standard deviation? (2020)
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Solution
Mean = (20 + 30 + 40 + 50) / 4 = 35. Variance = [(20-35)² + (30-35)² + (40-35)² + (50-35)²] / 4 = 125. SD = √125 = 11.18 (approx 10).
Correct Answer:
B
— 15
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Q. The scores of five students are: 20, 22, 24, 26, 28. Calculate the variance. (2020)
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Solution
Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8.
Correct Answer:
A
— 8
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Q. The scores of five students are: 20, 22, 24, 26, 28. What is the standard deviation? (2020)
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Solution
Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8. SD = √8 = 2.83 (approximately 3).
Correct Answer:
A
— 2
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Q. The scores of five students are: 20, 22, 24, 26, 28. What is the variance? (2020)
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Solution
Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8.
Correct Answer:
A
— 4
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Q. The self-inductance of a coil depends on which of the following factors? (2021)
A.
Number of turns
B.
Area of cross-section
C.
Length of the coil
D.
All of the above
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Solution
The self-inductance of a coil depends on the number of turns, area of cross-section, and length of the coil.
Correct Answer:
D
— All of the above
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Q. The Sendai Framework for Disaster Risk Reduction was adopted in which year, emphasizing the need for a proactive approach to disaster management? (2015)
A.
2005
B.
2010
C.
2015
D.
2020
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Solution
The Sendai Framework was adopted in 2015, focusing on reducing disaster risk and enhancing resilience.
Correct Answer:
C
— 2015
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Q. The shape of a soap bubble is spherical because:
A.
It minimizes volume
B.
It maximizes surface area
C.
It minimizes surface area for a given volume
D.
It is the only stable shape
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Solution
A soap bubble adopts a spherical shape because it minimizes the surface area for a given volume, which is energetically favorable due to surface tension.
Correct Answer:
C
— It minimizes surface area for a given volume
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Q. The slope of the line represented by the equation 2x - 3y + 6 = 0 is:
A.
2/3
B.
-2/3
C.
3/2
D.
-3/2
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Solution
Rearranging gives y = (2/3)x + 2, so slope = 2/3.
Correct Answer:
B
— -2/3
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Q. The slope of the line represented by the equation 3x - 4y + 12 = 0 is:
A.
3/4
B.
4/3
C.
-3/4
D.
-4/3
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Solution
Rearranging gives y = (3/4)x + 3. Slope = 3/4.
Correct Answer:
C
— -3/4
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Q. The slope of the tangent line to the curve y = x^2 at the point (2, 4) is: (2022)
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Solution
The derivative y' = 2x. At x = 2, y' = 2(2) = 4.
Correct Answer:
A
— 2
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Q. The slope of the tangent to the curve y = sin(x) at x = π/4 is:
A.
1
B.
√2/2
C.
√3/3
D.
√2
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Solution
The derivative f'(x) = cos(x). At x = π/4, f'(π/4) = cos(π/4) = √2/2.
Correct Answer:
B
— √2/2
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Q. The slope of the tangent to the curve y = x^3 - 3x at x = 1 is:
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Solution
The derivative f'(x) = 3x^2 - 3. At x = 1, f'(1) = 3(1)^2 - 3 = 0, so the slope is 0.
Correct Answer:
B
— 1
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Q. The slopes of the lines represented by the equation 2x^2 + 3xy + y^2 = 0 are:
A.
-1, -2
B.
1, 2
C.
-1, 1
D.
2, -2
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Solution
The slopes can be found by solving the quadratic equation derived from the given equation.
Correct Answer:
A
— -1, -2
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Q. The slopes of the lines represented by the equation 5x^2 + 6xy + 2y^2 = 0 are given by:
A.
-3/5 and -2/5
B.
2/5 and -5/2
C.
1/2 and -2
D.
None of the above
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Solution
Using the quadratic formula, the slopes are found to be -3/5 and -2/5.
Correct Answer:
A
— -3/5 and -2/5
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Q. The slopes of the lines represented by the equation 5x^2 + 6xy + 2y^2 = 0 are:
A.
-3/5, -2/5
B.
2/5, 3/5
C.
1, -1
D.
0, ∞
Show solution
Solution
The slopes can be calculated using the quadratic formula, yielding -3/5 and -2/5.
Correct Answer:
A
— -3/5, -2/5
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Q. The social contract theory, as proposed by Rousseau, emphasized which of the following?
A.
The divine right of kings.
B.
The importance of individual freedom and collective governance.
C.
The necessity of a strong authoritarian government.
D.
The preservation of traditional social hierarchies.
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Solution
Rousseau's social contract theory argued for the importance of individual freedom and the idea that legitimate political authority comes from the collective will of the people.
Correct Answer:
B
— The importance of individual freedom and collective governance.
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Q. The soil of a riverbank is composed of 40% sand, 30% silt, and 30% clay. What is the percentage of silt in the soil? (2019)
A.
30%
B.
40%
C.
50%
D.
60%
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Solution
The percentage of silt is given as 30%.
Correct Answer:
A
— 30%
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