Q. What is the primary argument made by the author regarding economic inequalities?
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A.
They are the most significant type of inequality.
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B.
They can be addressed through education.
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C.
They are often ignored in policy discussions.
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D.
They are a result of individual choices.
Solution
The author emphasizes that economic inequalities are a critical issue that deserves attention in policy discussions.
Correct Answer: A — They are the most significant type of inequality.
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Q. What is the primary disadvantage of a general partnership?
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A.
Limited access to capital
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B.
Unlimited personal liability for partners
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C.
Difficulty in decision-making
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D.
Lack of business continuity
Solution
The primary disadvantage of a general partnership is that partners have unlimited personal liability for business debts.
Correct Answer: B — Unlimited personal liability for partners
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Q. What is the primary focus of the passage regarding digital sum? (2023)
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A.
The historical development of digital sum techniques.
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B.
The application of digital sum in modern technology.
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C.
The mathematical principles behind digital sum.
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D.
The comparison between digital sum and traditional arithmetic.
Solution
The passage emphasizes how digital sum is utilized in various modern technological applications, highlighting its relevance today.
Correct Answer: B — The application of digital sum in modern technology.
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Q. What is the primary purpose of using matrices in modern mathematics?
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A.
To simplify polynomial equations
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B.
To represent and solve systems of linear equations
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C.
To calculate derivatives
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D.
To analyze geometric transformations
Solution
Matrices are primarily used to represent and solve systems of linear equations, making them a fundamental tool in modern mathematics.
Correct Answer: B — To represent and solve systems of linear equations
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Q. What is the product of the roots of the polynomial P(x) = x^2 - 7x + 10?
Solution
The product of the roots of a quadratic polynomial ax^2 + bx + c is given by c/a, which is 10/1 = 10.
Correct Answer: A — 10
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Q. What is the relationship between a function and its inverse?
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A.
They are always identical.
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B.
The inverse function undoes the action of the original function.
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C.
They can never intersect on a graph.
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D.
The inverse function is always a polynomial.
Solution
The inverse function undoes the action of the original function, meaning that applying a function and then its inverse returns the original input.
Correct Answer: B — The inverse function undoes the action of the original function.
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Q. What is the relationship between digital sum and error detection as mentioned in the passage? (2023)
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A.
Digital sum is irrelevant to error detection.
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B.
Digital sum can enhance error detection methods.
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C.
Error detection methods are based solely on digital sum.
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D.
Digital sum complicates error detection processes.
Solution
The passage indicates that digital sum plays a significant role in improving error detection techniques.
Correct Answer: B — Digital sum can enhance error detection methods.
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Q. What is the relationship between the radius and the chord length in a circle?
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A.
Chords are always longer than the radius.
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B.
Chords can be equal to the radius.
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C.
Chords can be shorter than the radius.
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D.
All of the above.
Solution
Chords can vary in length and can be longer, equal to, or shorter than the radius.
Correct Answer: D — All of the above.
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Q. What is the relationship between the radius and the diameter of a circle?
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A.
The radius is half of the diameter.
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B.
The diameter is half of the radius.
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C.
The radius and diameter are equal.
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D.
The diameter is the sum of two radii.
Solution
The radius is defined as half of the diameter.
Correct Answer: A — The radius is half of the diameter.
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Q. What is the remainder when 1000 is divided by 6?
Solution
1000 divided by 6 gives a quotient of 166 and a remainder of 4.
Correct Answer: A — 4
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Q. What is the remainder when 145 is divided by 12?
Solution
145 divided by 12 gives a remainder of 1.
Correct Answer: B — 2
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Q. What is the remainder when 250 is divided by 7?
Solution
250 divided by 7 gives a quotient of 35 and a remainder of 5.
Correct Answer: A — 1
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Q. What is the remainder when 256 is divided by 7?
Solution
256 divided by 7 gives a quotient of 36 and a remainder of 4.
Correct Answer: B — 4
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Q. What is the remainder when 987654 is divided by 9?
Solution
The sum of the digits of 987654 is 39, which is divisible by 9, hence the remainder is 0.
Correct Answer: A — 0
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Q. What is the result of adding the binary numbers 1011 and 1101?
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A.
11000
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B.
10100
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C.
10010
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D.
11110
Solution
Adding 1011 and 1101 in binary results in 11110.
Correct Answer: D — 11110
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Q. What is the result of adding the polynomials P(x) = 3x^2 + 2x + 1 and Q(x) = x^2 - x + 4?
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A.
4x^2 + x + 5
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B.
4x^2 + 3x + 5
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C.
2x^2 + x + 5
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D.
3x^2 + x + 5
Solution
Adding the polynomials gives (3x^2 + x^2) + (2x - x) + (1 + 4) = 4x^2 + x + 5.
Correct Answer: A — 4x^2 + x + 5
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Q. What is the role of a 'silent partner' in a partnership?
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A.
To manage the business actively
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B.
To provide capital without participating in management
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C.
To take on all liabilities
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D.
To make all strategic decisions
Solution
A silent partner provides capital to the partnership but does not take part in the day-to-day management of the business.
Correct Answer: B — To provide capital without participating in management
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Q. What is the significance of digital sum in data analysis as mentioned in the passage? (2023)
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A.
It reduces the complexity of data sets.
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B.
It enhances the accuracy of data interpretation.
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C.
It simplifies the process of data storage.
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D.
It increases the speed of data processing.
Solution
The passage highlights that digital sum plays a crucial role in enhancing the accuracy of data interpretation.
Correct Answer: B — It enhances the accuracy of data interpretation.
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Q. What is the significance of historical context in understanding inequalities, according to the passage?
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A.
It is irrelevant to current discussions.
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B.
It provides insight into the roots of inequalities.
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C.
It complicates the issue unnecessarily.
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D.
It is only important for economic inequalities.
Solution
The passage highlights that understanding historical context is essential for grasping the roots and persistence of inequalities.
Correct Answer: B — It provides insight into the roots of inequalities.
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Q. What is the significance of the examples provided in the passage regarding inequalities?
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A.
They illustrate the author's personal experiences.
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B.
They serve to highlight the complexity of the issue.
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C.
They are irrelevant to the main argument.
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D.
They simplify the concept of inequalities.
Solution
The examples are used to illustrate the complexity of inequalities, reinforcing the author's argument.
Correct Answer: B — They serve to highlight the complexity of the issue.
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Q. What is the simplified form of (2^3)^2? (2023)
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A.
2^5
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B.
2^6
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C.
2^7
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D.
2^8
Solution
Using the property of exponents (a^m)^n = a^(m*n), we have (2^3)^2 = 2^(3*2) = 2^6.
Correct Answer: B — 2^6
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Q. What is the simplified form of (x^2 * y^3)^(2)? (2023)
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A.
x^4 * y^6
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B.
x^2 * y^3
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C.
x^6 * y^4
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D.
x^5 * y^3
Solution
Using the power of a product property, we have (x^2 * y^3)^(2) = x^(2*2) * y^(3*2) = x^4 * y^6.
Correct Answer: A — x^4 * y^6
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Q. What is the solution set of the inequality 2x - 4 < 0?
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A.
x < 2
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B.
x > 2
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C.
x = 2
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D.
x ≤ 2
Solution
Solving the inequality gives 2x < 4, thus x < 2.
Correct Answer: A — x < 2
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Q. What is the sum of the first 15 terms of an arithmetic progression where the first term is 2 and the common difference is 4?
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A.
120
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B.
130
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C.
140
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D.
150
Solution
The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_15 = 15/2 * (2*2 + 14*4) = 15/2 * (4 + 56) = 15/2 * 60 = 450.
Correct Answer: A — 120
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Q. What is the sum of the interior angles of a quadrilateral? (2023)
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A.
180 degrees
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B.
360 degrees
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C.
540 degrees
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D.
720 degrees
Solution
The sum of the interior angles of any quadrilateral is 360 degrees.
Correct Answer: B — 360 degrees
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Q. What is the sum of the numbers '101' and '110' in binary?
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A.
1011
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B.
111
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C.
1001
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D.
1100
Solution
In binary, '101' + '110' = '1011'.
Correct Answer: A — 1011
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Q. What is the sum of the roots of the quadratic equation 2x^2 - 8x + 6 = 0?
Solution
The sum of the roots is given by -b/a = 8/2 = 4.
Correct Answer: B — 4
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Q. What is the surface area of a cube with a side length of 5 cm? (2021)
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A.
50 cm²
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B.
75 cm²
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C.
100 cm²
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D.
125 cm²
Solution
Surface area = 6 * (side)² = 6 * (5)² = 6 * 25 = 150 cm².
Correct Answer: C — 100 cm²
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Q. What is the tone of the passage regarding the issue of inequalities?
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A.
Optimistic
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B.
Pessimistic
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C.
Neutral
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D.
Indifferent
Solution
The author maintains an optimistic tone, suggesting that change is possible and necessary.
Correct Answer: A — Optimistic
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Q. What is the value of (5^0 + 5^1 + 5^2)? (2023)
Solution
Calculating each term, we have 5^0 = 1, 5^1 = 5, and 5^2 = 25. Therefore, 1 + 5 + 25 = 31.
Correct Answer: C — 15
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