Q. Which of the following statements about triangles is true?
A.
All triangles are equilateral.
B.
The sum of the angles in a triangle is 180 degrees.
C.
A triangle can have two right angles.
D.
The area of a triangle is always greater than its perimeter.
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Solution
The sum of the angles in any triangle is always 180 degrees, which is a fundamental property of triangles.
Correct Answer: B — The sum of the angles in a triangle is 180 degrees.
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Q. Which of the following statements can be inferred from the passage about the future of digital sum? (2023)
A.
It will become obsolete with the rise of quantum computing.
B.
It will continue to evolve and integrate with new technologies.
C.
It is likely to be replaced by simpler methods.
D.
It will remain unchanged for the foreseeable future.
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Solution
The passage suggests that digital sum will evolve and integrate with emerging technologies, indicating a promising future.
Correct Answer: B — It will continue to evolve and integrate with new technologies.
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Q. Which of the following statements can be inferred from the passage about the importance of digital sum? (2023)
A.
Digital sum is obsolete in today's technology.
B.
Understanding digital sum is crucial for data analysis.
C.
Digital sum has no practical applications.
D.
Only mathematicians need to understand digital sum.
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Solution
The passage suggests that a solid understanding of digital sum is essential for effective data analysis in various fields.
Correct Answer: B — Understanding digital sum is crucial for data analysis.
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Q. Which of the following statements is logically consistent with the definition of a multiple?
A.
A multiple of a number is always greater than the number itself.
B.
A multiple of a number can be negative.
C.
A multiple of a number is always an integer.
D.
All of the above.
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Solution
All statements are true; multiples can be negative, can be equal to the number, and are always integers.
Correct Answer: D — All of the above.
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Q. Which of the following statements is true about the graph of a function that is periodic?
A.
It repeats its values at regular intervals.
B.
It is always increasing.
C.
It has no maximum or minimum values.
D.
It is a straight line.
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Solution
A periodic function is characterized by repeating values at regular intervals, such as sine and cosine functions.
Correct Answer: A — It repeats its values at regular intervals.
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Q. Which of the following statements is true about the inverse of a function?
A.
The inverse of a function is always a function.
B.
The inverse of a function is not necessarily a function.
C.
The inverse of a function is always linear.
D.
The inverse of a function cannot be graphed.
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Solution
The inverse of a function is a function only if the original function is one-to-one.
Correct Answer: B — The inverse of a function is not necessarily a function.
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Q. Which of the following statements is true regarding an arithmetic progression?
A.
The sum of any two terms is constant.
B.
The difference between consecutive terms is constant.
C.
The product of any two terms is constant.
D.
The ratio of any two terms is constant.
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Solution
In an arithmetic progression, the difference between consecutive terms is constant, which is the defining property of an AP.
Correct Answer: B — The difference between consecutive terms is constant.
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Q. Which of the following statements is true regarding divisibility by 5?
A.
A number must end in 0 or 5
B.
A number must be even
C.
A number must be a multiple of 10
D.
A number must be a prime number
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Solution
A number is divisible by 5 if it ends in either 0 or 5.
Correct Answer: A — A number must end in 0 or 5
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Q. Which of the following statements is true regarding harmonic progressions?
A.
The sum of the terms is always constant.
B.
The product of the terms is always constant.
C.
The reciprocals of the terms form an arithmetic progression.
D.
The terms are always integers.
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Solution
In a harmonic progression, the reciprocals of the terms indeed form an arithmetic progression.
Correct Answer: C — The reciprocals of the terms form an arithmetic progression.
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Q. Which of the following statements is true regarding modular arithmetic?
A.
It is only applicable to integers.
B.
It can be used for real numbers.
C.
It is not useful in computer science.
D.
It is only used in cryptography.
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Solution
Modular arithmetic is primarily applicable to integers, making the first statement true.
Correct Answer: A — It is only applicable to integers.
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Q. Which of the following statements is true regarding the angles formed when two lines intersect?
A.
Vertical angles are always supplementary
B.
Adjacent angles are always equal
C.
Linear pairs are always complementary
D.
Vertical angles are always equal
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Solution
When two lines intersect, the angles opposite each other (vertical angles) are always equal. Therefore, the correct statement is that vertical angles are always equal.
Correct Answer: D — Vertical angles are always equal
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Q. Which of the following statements is true regarding the graph of a linear equation?
A.
It can be a curve.
B.
It is always a straight line.
C.
It can have multiple slopes.
D.
It can intersect the x-axis at multiple points.
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Solution
The graph of a linear equation is always a straight line.
Correct Answer: B — It is always a straight line.
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Q. Which of the following statements is true regarding the graph of the equation y = mx + b?
A.
The graph is always a circle.
B.
The slope m indicates the steepness of the line.
C.
The y-intercept b is always negative.
D.
The graph can never be horizontal.
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Solution
In the equation y = mx + b, m represents the slope, which indicates how steep the line is.
Correct Answer: B — The slope m indicates the steepness of the line.
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Q. Which of the following statements is true regarding the points (2, 3), (4, 5), and (6, 7)?
A.
They are collinear
B.
They form a triangle
C.
They are equidistant
D.
They lie on different lines
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Solution
The slope between any two pairs of these points is the same (1), indicating they are collinear.
Correct Answer: A — They are collinear
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Q. Which of the following terms best describes a polygon with all sides and angles equal?
A.
Irregular polygon
B.
Convex polygon
C.
Regular polygon
D.
Concave polygon
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Solution
A polygon with all sides and angles equal is known as a regular polygon.
Correct Answer: C — Regular polygon
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Q. Which of the following terms is used to describe a line that touches a circle at exactly one point?
A.
Chord
B.
Diameter
C.
Tangent
D.
Secant
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Solution
A tangent is defined as a line that touches a circle at exactly one point.
Correct Answer: C — Tangent
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Q. Which of the following terms refers to the middle value in a data set when arranged in ascending order?
A.
Mean
B.
Mode
C.
Median
D.
Range
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Solution
The median is defined as the middle value in a sorted data set, distinguishing it from mean and mode.
Correct Answer: C — Median
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Q. Which of the following triangles has the largest area?
A.
Triangle with sides 3, 4, 5
B.
Triangle with sides 5, 12, 13
C.
Triangle with sides 6, 8, 10
D.
Triangle with sides 7, 24, 25
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Solution
Using the formula for the area of a triangle, the triangle with sides 7, 24, 25 has the largest area due to its larger base and height.
Correct Answer: D — Triangle with sides 7, 24, 25
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Q. Which of the following words best captures the author's attitude towards the current state of inequality?
A.
Pessimistic.
B.
Indifferent.
C.
Concerned.
D.
Skeptical.
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Solution
The author expresses concern about the persistence and impact of inequality in society.
Correct Answer: C — Concerned.
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Q. Which of the following words best captures the author's view on the urgency of addressing inequalities?
A.
Critical.
B.
Optional.
C.
Negligible.
D.
Controversial.
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Solution
The author emphasizes the critical nature of addressing inequalities, suggesting it is an urgent issue.
Correct Answer: A — Critical.
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Q. Which of the following words best captures the essence of digital sum as described in the passage? (2023)
A.
Obsolete.
B.
Innovative.
C.
Complicated.
D.
Irrelevant.
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Solution
The passage describes digital sum as innovative, reflecting its role in advancing technology.
Correct Answer: B — Innovative.
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Q. Which of the following words from the passage is closest in meaning to 'perpetuate'?
A.
End
B.
Continue
C.
Diminish
D.
Challenge
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Solution
In the context of the passage, 'perpetuate' means to continue, as it refers to the ongoing nature of inequalities.
Correct Answer: B — Continue
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Q. Which quadrilateral has all sides equal but angles not necessarily equal? (2023)
A.
Square
B.
Rectangle
C.
Rhombus
D.
Trapezium
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Solution
A rhombus has all sides equal, but the angles are not necessarily equal.
Correct Answer: C — Rhombus
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