Q. Which of the following numbers is divisible by 11?
A.
121
B.
123
C.
124
D.
125
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Solution
121 is divisible by 11, as 121 = 11 x 11.
Correct Answer: A — 121
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Q. Which of the following numbers is divisible by 8?
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Solution
A number is divisible by 8 if the last three digits form a number that is divisible by 8. 64 is divisible by 8.
Correct Answer: A — 64
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Q. Which of the following numbers is NOT divisible by 12?
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Solution
55 is not divisible by 12, as it does not meet the criteria of being divisible by both 3 and 4.
Correct Answer: C — 55
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Q. Which of the following numbers is NOT divisible by 3?
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Solution
A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 22 (2 + 2 = 4) is not divisible by 3.
Correct Answer: C — 22
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Q. Which of the following options best completes the sentence: 'The research findings indicate that...'? (2023)
A.
the hypothesis was proven wrong.
B.
further studies are needed to confirm the results.
C.
the initial assumptions were correct.
D.
the data was inconclusive.
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Solution
The context suggests that research findings often lead to the conclusion that further studies are necessary, making option 2 the best completion.
Correct Answer: B — further studies are needed to confirm the results.
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Q. Which of the following options best fits in the blank: 'The rapid pace of technological change has led to a _______ in the workforce, requiring new skills and adaptability.'? (2023)
A.
stagnation
B.
transformation
C.
decrease
D.
uniformity
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Solution
The context indicates that the workforce is changing significantly, thus 'transformation' is the most appropriate choice.
Correct Answer: B — transformation
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Q. Which of the following options best summarizes the main argument of the passage?
A.
The benefits of technology outweigh its drawbacks.
B.
Technology is detrimental to human interaction.
C.
The relationship between technology and society is complex.
D.
Society must adapt to technological advancements.
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Solution
The passage discusses both the positive and negative impacts of technology, suggesting a nuanced view rather than a purely beneficial or detrimental stance.
Correct Answer: C — The relationship between technology and society is complex.
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Q. Which of the following pairs of angles are complementary?
A.
30 degrees and 60 degrees
B.
45 degrees and 45 degrees
C.
90 degrees and 0 degrees
D.
All of the above
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Solution
Complementary angles are two angles whose sum is 90 degrees. All the given pairs meet this criterion.
Correct Answer: D — All of the above
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Q. Which of the following pairs of angles are supplementary?
A.
Two acute angles
B.
Two obtuse angles
C.
An acute angle and an obtuse angle
D.
Two right angles
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Solution
Supplementary angles are two angles that add up to 180 degrees. An acute angle (less than 90 degrees) and an obtuse angle (more than 90 degrees) can add up to 180 degrees.
Correct Answer: C — An acute angle and an obtuse angle
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Q. Which of the following pairs of equations represents parallel lines?
A.
2x + 3y = 6 and 4x + 6y = 12
B.
x - y = 1 and x + y = 1
C.
3x + 2y = 5 and 3x - 2y = 5
D.
x + 2y = 3 and 2x + 4y = 6
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Solution
The first pair has the same slope (2/3) and thus represents parallel lines.
Correct Answer: A — 2x + 3y = 6 and 4x + 6y = 12
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Q. Which of the following pairs of linear equations has no solution?
A.
x + y = 2 and x + y = 4
B.
2x - y = 1 and 4x - 2y = 2
C.
3x + 2y = 6 and 6x + 4y = 12
D.
x - 2y = 3 and 2x - 4y = 6
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Solution
The first pair represents parallel lines, which means they will never intersect, hence no solution.
Correct Answer: A — x + y = 2 and x + y = 4
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Q. Which of the following pairs of numbers has an HCF of 1? (2023)
A.
8 and 12
B.
15 and 28
C.
9 and 27
D.
14 and 21
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Solution
The HCF of 15 and 28 is 1, making them coprime.
Correct Answer: B — 15 and 28
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Q. Which of the following phrases could replace 'the crux of the matter' in the sentence: 'The crux of the matter lies in understanding the data'? (2023)
A.
The main point
B.
The side issue
C.
The minor detail
D.
The irrelevant fact
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Solution
The phrase 'the main point' accurately captures the essence of 'the crux of the matter'.
Correct Answer: A — The main point
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Q. Which of the following points is closest to the origin (0, 0)?
A.
(1, 1)
B.
(2, 2)
C.
(3, 3)
D.
(0, 1)
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Solution
The distance from the origin to a point (x, y) is given by √(x² + y²). The point (0, 1) has a distance of 1, which is the smallest.
Correct Answer: D — (0, 1)
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Q. Which of the following points lies on the line represented by the equation y = 2x + 1?
A.
(0, 1)
B.
(1, 2)
C.
(2, 5)
D.
(3, 6)
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Solution
Substituting x = 2 into the equation y = 2(2) + 1 gives y = 5, so the point (2, 5) lies on the line.
Correct Answer: C — (2, 5)
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Q. Which of the following polygons cannot be classified as a convex polygon?
A.
A square
B.
A rectangle
C.
A concave hexagon
D.
An equilateral triangle
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Solution
A concave hexagon has at least one interior angle greater than 180 degrees, which makes it a non-convex polygon.
Correct Answer: C — A concave hexagon
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Q. Which of the following polygons is classified as a concave polygon?
A.
Square
B.
Regular pentagon
C.
Star-shaped polygon
D.
Equilateral triangle
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Solution
A star-shaped polygon has at least one interior angle greater than 180 degrees, making it concave.
Correct Answer: C — Star-shaped polygon
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Q. Which of the following polynomials is a perfect square?
A.
x^2 + 4x + 4
B.
x^2 - 4
C.
x^2 + 2x + 3
D.
x^2 - 2x + 1
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Solution
The polynomial x^2 + 4x + 4 can be factored as (x + 2)^2, making it a perfect square.
Correct Answer: A — x^2 + 4x + 4
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Q. Which of the following polynomials is a quadratic polynomial?
A.
x^3 - 2x + 1
B.
2x^2 + 3x - 5
C.
4x + 7
D.
x^4 - x^2 + 1
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Solution
A quadratic polynomial is defined as a polynomial of degree 2, which is 2x^2 + 3x - 5.
Correct Answer: B — 2x^2 + 3x - 5
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Q. Which of the following quadrilaterals has all sides equal and opposite angles equal?
A.
Square
B.
Rectangle
C.
Trapezium
D.
Rhombus
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Solution
A rhombus has all sides equal and opposite angles equal.
Correct Answer: D — Rhombus
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Q. Which of the following quadrilaterals has the property that its diagonals are equal in length? (2023)
A.
Square
B.
Rhombus
C.
Trapezium
D.
Kite
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Solution
A square has equal diagonals, which is a property of squares and rectangles.
Correct Answer: A — Square
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Q. Which of the following represents the slope of the line represented by the equation y = mx + b?
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Solution
In the equation y = mx + b, 'm' represents the slope of the line.
Correct Answer: A — m
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Q. Which of the following sentences best summarizes the author's argument? (2023)
A.
Education should remain traditional and resist technological changes.
B.
Technology should be integrated into education to improve learning outcomes.
C.
All students should have equal access to technology.
D.
Teachers should be trained to use technology effectively.
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Solution
The author's argument emphasizes the importance of integrating technology into education to enhance learning outcomes.
Correct Answer: B — Technology should be integrated into education to improve learning outcomes.
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Q. Which of the following sentences best summarizes the main idea of the passage?
A.
Urbanization leads to economic growth but also environmental challenges.
B.
Pollution is a minor issue compared to other urban problems.
C.
Youth are primarily responsible for environmental degradation.
D.
Social media is the main cause of urban pollution.
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Solution
The passage discusses the dual nature of urbanization, emphasizing both its economic benefits and environmental challenges.
Correct Answer: A — Urbanization leads to economic growth but also environmental challenges.
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Q. Which of the following sentences contains a logical fallacy?
A.
If it rains, the ground will be wet.
B.
All birds can fly, so penguins are not birds.
C.
Some fruits are sweet, like apples.
D.
If you study hard, you will pass the exam.
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Solution
The statement about birds incorrectly generalizes that all birds can fly, which is false.
Correct Answer: B — All birds can fly, so penguins are not birds.
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Q. Which of the following sentences is least relevant to the topic of climate change?
A.
Rising sea levels threaten coastal cities.
B.
Deforestation contributes to global warming.
C.
The stock market fluctuates daily.
D.
Renewable energy sources can reduce carbon emissions.
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Solution
The stock market fluctuating daily is unrelated to climate change, while the other options directly address environmental issues.
Correct Answer: C — The stock market fluctuates daily.
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Q. Which of the following sentences would best fit in the blank in the passage to enhance its argument?
A.
This is a complex issue that requires a nuanced approach.
B.
Many people are unaware of the severity of the situation.
C.
The solutions are often more political than scientific.
D.
Public awareness is crucial for effective policy-making.
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Solution
The sentence emphasizes the complexity of the issue, aligning with the author's argument for a nuanced approach to climate change.
Correct Answer: A — This is a complex issue that requires a nuanced approach.
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Q. Which of the following sentences would best fit in the blank in the passage? (2023)
A.
This shift has been largely beneficial.
B.
Many people oppose this change.
C.
The consequences are still being evaluated.
D.
It has sparked a significant debate.
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Solution
The context of the passage suggests that the shift mentioned has led to considerable discussion, making this option the most fitting.
Correct Answer: D — It has sparked a significant debate.
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Q. Which of the following sentences would best fit in the blank space in the passage?
A.
The CAT exam is known for its unpredictability.
B.
Many students underestimate the verbal section.
C.
Preparation strategies vary among candidates.
D.
Success in CAT requires a balanced approach.
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Solution
The context suggests that unpredictability is a significant aspect of the CAT exam, making this option the best fit.
Correct Answer: B — Many students underestimate the verbal section.
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Q. Which of the following sentences would best serve as a conclusion to the paragraph? (2023)
A.
Thus, the implications of these findings are profound.
B.
In conclusion, the study was inconclusive.
C.
Therefore, further research is unnecessary.
D.
As a result, the data was flawed.
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Solution
The first option summarizes the significance of the findings, making it a suitable conclusion.
Correct Answer: A — Thus, the implications of these findings are profound.
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