Q. The family of curves represented by the equation y = e^(kx) is characterized by:
A.
Linear growth
B.
Exponential growth
C.
Quadratic growth
D.
Logarithmic growth
Show solution
Solution
The equation y = e^(kx) represents exponential growth for different values of k.
Correct Answer:
B
— Exponential growth
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Q. The family of curves represented by the equation y = e^(kx) is classified as:
A.
Linear
B.
Polynomial
C.
Exponential
D.
Logarithmic
Show solution
Solution
The equation y = e^(kx) represents an exponential function.
Correct Answer:
C
— Exponential
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Q. The family of curves represented by the equation y = kx^2, where k is a constant, is known as:
A.
Linear curves
B.
Parabolic curves
C.
Circular curves
D.
Exponential curves
Show solution
Solution
The equation y = kx^2 represents a parabola for different values of k.
Correct Answer:
B
— Parabolic curves
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Q. The family of curves represented by the equation y = kx^n, where n is a constant, is known as:
A.
Polynomial curves
B.
Rational curves
C.
Trigonometric curves
D.
Exponential curves
Show solution
Solution
The equation y = kx^n represents a family of polynomial curves.
Correct Answer:
A
— Polynomial curves
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Q. The family of curves represented by the equation y = mx + c, where m and c are constants, is known as:
A.
Linear functions
B.
Quadratic functions
C.
Cubic functions
D.
Exponential functions
Show solution
Solution
The equation y = mx + c represents a straight line, which is a linear function.
Correct Answer:
A
— Linear functions
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Q. The family of curves represented by y = a sin(bx + c) is known as:
A.
Linear functions
B.
Trigonometric functions
C.
Polynomial functions
D.
Exponential functions
Show solution
Solution
The equation y = a sin(bx + c) represents a family of trigonometric functions.
Correct Answer:
B
— Trigonometric functions
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Q. The family of curves represented by y = kx^n, where n is a constant, is known as:
A.
Polynomial curves
B.
Rational curves
C.
Trigonometric curves
D.
Logarithmic curves
Show solution
Solution
The equation y = kx^n represents a family of polynomial curves.
Correct Answer:
A
— Polynomial curves
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Q. The family of curves represented by y = mx + c can be described as:
A.
Quadratic functions
B.
Linear functions
C.
Cubic functions
D.
Exponential functions
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Solution
The equation y = mx + c describes linear functions for varying m and c.
Correct Answer:
B
— Linear functions
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Q. The family of curves represented by y^2 = 4ax is known as:
A.
Parabolas
B.
Ellipses
C.
Hyperbolas
D.
Circles
Show solution
Solution
The equation y^2 = 4ax represents a family of parabolas.
Correct Answer:
A
— Parabolas
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Q. The family of curves y = ax^3 + bx^2 + cx + d is classified as:
A.
Linear
B.
Quadratic
C.
Cubic
D.
Quartic
Show solution
Solution
The equation y = ax^3 + bx^2 + cx + d represents a family of cubic curves.
Correct Answer:
C
— Cubic
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Q. The family of curves y = kx^3 is known for having:
A.
One turning point
B.
Two turning points
C.
No turning points
D.
Three turning points
Show solution
Solution
The cubic function y = kx^3 has one turning point at x = 0.
Correct Answer:
A
— One turning point
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Q. The family of curves y = kx^n, where n is a constant, represents:
A.
Linear functions
B.
Polynomial functions
C.
Rational functions
D.
Trigonometric functions
Show solution
Solution
The equation y = kx^n represents a family of polynomial functions.
Correct Answer:
B
— Polynomial functions
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Q. The famous rock edicts were issued by which Mauryan emperor?
A.
Ashoka
B.
Bindusara
C.
Chandragupta
D.
Samudragupta
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Solution
The rock edicts were issued by Emperor Ashoka, promoting Buddhism and moral governance.
Correct Answer:
A
— Ashoka
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Q. The Faraday's first law of electrolysis states that: (2018)
A.
The mass of substance deposited is directly proportional to the current
B.
The voltage is directly proportional to the current
C.
The energy is conserved
D.
The temperature remains constant
Show solution
Solution
Faraday's first law states that the mass of a substance deposited at an electrode is directly proportional to the quantity of electricity passed through the electrolyte.
Correct Answer:
A
— The mass of substance deposited is directly proportional to the current
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Q. The female reproductive part of a flower is called the: (2022)
A.
Stamen
B.
Pistil
C.
Petal
D.
Sepal
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Solution
The pistil is the female reproductive part of the flower, consisting of the ovary, style, and stigma.
Correct Answer:
B
— Pistil
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Q. The Fields Medal is awarded in which discipline? (2023)
A.
Physics
B.
Mathematics
C.
Chemistry
D.
Biology
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Solution
The Fields Medal is awarded to mathematicians for outstanding achievements in mathematics.
Correct Answer:
B
— Mathematics
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Q. The Fields Medal is awarded in which field? (1936)
A.
Mathematics
B.
Physics
C.
Chemistry
D.
Economics
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Solution
The Fields Medal is awarded to mathematicians under 40 years of age for outstanding achievements in mathematics.
Correct Answer:
A
— Mathematics
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Q. The findings of a new study indicate that regular exercise is associated with improved mental health. What can be inferred from these findings?
A.
Exercise is the only way to improve mental health.
B.
All individuals who exercise regularly have good mental health.
C.
There is a relationship between exercise and mental health improvement.
D.
Mental health does not depend on physical activity.
Show solution
Solution
The findings suggest a relationship between exercise and mental health, but do not claim that exercise is the sole factor.
Correct Answer:
C
— There is a relationship between exercise and mental health improvement.
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Q. The findings of the research were ________ by the subsequent experiments, which confirmed the initial hypotheses.
A.
contradicted
B.
supported
C.
ignored
D.
questioned
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Solution
The phrase 'confirmed the initial hypotheses' indicates that the findings were backed up, making 'supported' the correct choice.
Correct Answer:
B
— supported
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Q. The findings of the study were ______, leading to a reevaluation of previously held beliefs about the effectiveness of the treatment.
A.
uncontroversial
B.
inconclusive
C.
groundbreaking
D.
predictable
Show solution
Solution
The phrase 'reevaluation of previously held beliefs' suggests that the findings were significant or 'groundbreaking'.
Correct Answer:
C
— groundbreaking
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Q. The first successful personal computer was introduced by which company? (1977)
A.
IBM
B.
Apple
C.
Microsoft
D.
Commodore
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Solution
Apple introduced the Apple II in 1977, which is considered one of the first successful personal computers.
Correct Answer:
B
— Apple
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Q. The five-kingdom classification system was proposed by: (2019)
A.
Linnaeus
B.
Whittaker
C.
Haeckel
D.
Darwin
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Solution
The five-kingdom classification system was proposed by Robert Whittaker.
Correct Answer:
B
— Whittaker
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Q. The flowers were watered by the gardener. What is the active voice of this sentence? (2023)
A.
The gardener waters the flowers.
B.
The gardener is watering the flowers.
C.
The gardener watered the flowers.
D.
The flowers are watered by the gardener.
Show solution
Solution
To convert to active voice, we say 'The gardener watered the flowers.' highlighting the gardener's action.
Correct Answer:
C
— The gardener watered the flowers.
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Q. The foci of the ellipse x^2/16 + y^2/9 = 1 are located at?
A.
(±4, 0)
B.
(0, ±3)
C.
(±3, 0)
D.
(0, ±4)
Show solution
Solution
For the ellipse x^2/16 + y^2/9 = 1, the foci are located at (±4, 0) where c = √(16 - 9) = 4.
Correct Answer:
A
— (±4, 0)
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Q. The foci of the ellipse x^2/25 + y^2/16 = 1 are located at which points?
A.
(±3, 0)
B.
(±4, 0)
C.
(±5, 0)
D.
(±6, 0)
Show solution
Solution
For the ellipse, c = √(a^2 - b^2) = √(25 - 16) = √9 = 3. The foci are at (±3, 0).
Correct Answer:
B
— (±4, 0)
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Q. The following data represents the number of books read by students in a month: 1, 2, 2, 3, 3, 3, 4, 4, 5. What is the mode?
Show solution
Solution
The mode is 3, as it appears most frequently (3 times) in the data set.
Correct Answer:
C
— 3
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Q. The following data represents the number of books read by students in a month: 4, 5, 6, 5, 4, 5, 7, 8, 5. What is the mode?
Show solution
Solution
The mode is 5, as it appears 4 times, more than any other number.
Correct Answer:
B
— 5
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Q. The following data set has the numbers: 2, 3, 4, 4, 5, 5, 5, 6, 7. What is the mode of this data set? (2020)
Show solution
Solution
The number 5 appears most frequently (3 times), so the mode is 5.
Correct Answer:
B
— 5
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Q. The following data set represents the ages of participants in a survey: 22, 25, 22, 30, 25, 22, 28. What is the mode?
Show solution
Solution
The mode is 22, as it appears most frequently (three times) in the data set.
Correct Answer:
A
— 22
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Q. The following data set shows the number of pets owned by families: 2, 3, 2, 4, 3, 2, 5. What is the mode?
Show solution
Solution
The mode is 2, as it appears 3 times, which is more than any other number.
Correct Answer:
A
— 2
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