Q. What is the relationship between the angles formed by a transversal intersecting two parallel lines?
A.
All angles are equal
B.
Alternate angles are equal
C.
Consecutive angles are equal
D.
None of the above
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Solution
When a transversal intersects two parallel lines, alternate angles are equal.
Correct Answer:
B
— Alternate angles are equal
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Q. What is the relationship between the angles formed by two intersecting chords in a circle?
A.
They are always equal.
B.
They are supplementary.
C.
They are complementary.
D.
They are proportional to the lengths of the chords.
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Solution
The angles formed by two intersecting chords are supplementary.
Correct Answer:
B
— They are supplementary.
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Q. What is the relationship between the angles in a linear pair?
A.
They are equal.
B.
They are complementary.
C.
They are supplementary.
D.
They are adjacent.
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Solution
Angles in a linear pair are supplementary, meaning they add up to 180 degrees.
Correct Answer:
C
— They are supplementary.
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Q. What is the relationship between the angles in a triangle?
A.
They can be any combination of acute, right, or obtuse.
B.
They must all be acute.
C.
They must sum to 180 degrees.
D.
One angle must be obtuse.
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Solution
The sum of the angles in any triangle is always 180 degrees.
Correct Answer:
C
— They must sum to 180 degrees.
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Q. What is the relationship between the angles subtended by the same arc at the center and at the circumference of a circle?
A.
They are equal.
B.
The angle at the center is twice that at the circumference.
C.
The angle at the circumference is twice that at the center.
D.
They are complementary.
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Solution
The angle subtended at the center is always twice that subtended at the circumference.
Correct Answer:
B
— The angle at the center is twice that at the circumference.
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Q. What is the relationship between the first term and the common ratio if the sum of an infinite GP converges?
A.
The first term must be zero.
B.
The common ratio must be less than one in absolute value.
C.
The first term must be greater than the common ratio.
D.
The common ratio must be greater than one.
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Solution
For the sum of an infinite GP to converge, the common ratio must be less than one in absolute value.
Correct Answer:
B
— The common ratio must be less than one in absolute value.
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Q. What is the relationship between the harmonic mean and the terms of a harmonic progression?
A.
It is the average of the terms.
B.
It is the reciprocal of the arithmetic mean of the reciprocals.
C.
It is the sum of the terms.
D.
It is the product of the terms.
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Solution
The harmonic mean of a set of numbers is the reciprocal of the arithmetic mean of their reciprocals.
Correct Answer:
B
— It is the reciprocal of the arithmetic mean of the reciprocals.
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Q. What is the relationship between the radius and the area of a circle? (2022)
A.
Area is directly proportional to the radius.
B.
Area is inversely proportional to the radius.
C.
Area is proportional to the square of the radius.
D.
Area is independent of the radius.
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Solution
The area of a circle is given by A = πr², indicating that area is proportional to the square of the radius.
Correct Answer:
C
— Area is proportional to the square of the radius.
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Q. What is the relationship between the radius and the chord length in a circle?
A.
Chords are always longer than the radius.
B.
Chords can be equal to the radius.
C.
Chords can be shorter than the radius.
D.
All of the above.
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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?
A.
The radius is half of the diameter.
B.
The diameter is half of the radius.
C.
The radius and diameter are equal.
D.
The diameter is the sum of two radii.
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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 relationship between the sides of a rhombus?
A.
All sides are equal.
B.
Opposite sides are equal.
C.
Adjacent sides are equal.
D.
No sides are equal.
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Solution
In a rhombus, all sides are equal in length.
Correct Answer:
A
— All sides are equal.
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Q. What is the relationship between the terms of a harmonic progression and their reciprocals?
A.
They are in geometric progression.
B.
They are in arithmetic progression.
C.
They are in quadratic progression.
D.
They are in exponential progression.
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Solution
The terms of a harmonic progression are the reciprocals of the terms of an arithmetic progression.
Correct Answer:
B
— They are in arithmetic progression.
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Q. What is the remainder when 1000 is divided by 6?
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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 1000 is divided by 9? (2023)
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Solution
1000 divided by 9 gives a remainder of 1 (1000 = 9*111 + 1).
Correct Answer:
B
— 2
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Q. What is the remainder when 123456 is divided by 10? (2023)
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Solution
The remainder when a number is divided by 10 is the last digit of the number, which is 6.
Correct Answer:
D
— 6
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Q. What is the remainder when 123456 is divided by 11? (2023)
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Solution
123456 mod 11 = 0, as 123456 is divisible by 11.
Correct Answer:
A
— 0
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Q. What is the remainder when 144 is divided by 11?
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Solution
144 divided by 11 gives a remainder of 1.
Correct Answer:
A
— 0
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Q. What is the remainder when 145 is divided by 12?
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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?
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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 11?
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Solution
256 divided by 11 gives a quotient of 23 and a remainder of 3.
Correct Answer:
A
— 2
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Q. What is the remainder when 256 is divided by 7?
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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 256 is divided by 9?
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Solution
256 divided by 9 gives a quotient of 28 and a remainder of 4.
Correct Answer:
B
— 2
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Q. What is the remainder when 987654 is divided by 9?
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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 remainder when 987654321 is divided by 9? (2023)
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Solution
The remainder when a number is divided by 9 can be found by summing its digits. The sum of the digits of 987654321 is 45, which is divisible by 9, hence the remainder is 0.
Correct Answer:
A
— 0
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Q. What is the result of (10 + 15) mod 7?
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Solution
(10 + 15) = 25; 25 mod 7 = 4.
Correct Answer:
B
— 2
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Q. What is the result of (15 + 10) mod 12?
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Solution
(15 + 10) = 25; 25 mod 12 = 1.
Correct Answer:
A
— 5
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Q. What is the result of (2^3)^2?
A.
2^5
B.
2^6
C.
2^7
D.
2^8
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Solution
Using the power of a power property, (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 result of (3 * 4) mod 5?
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Solution
Calculating (3 * 4) = 12, and then 12 mod 5 = 2.
Correct Answer:
C
— 4
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Q. What is the result of 10 mod 3?
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Solution
10 divided by 3 gives a remainder of 1, so 10 mod 3 = 1.
Correct Answer:
B
— 2
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Q. What is the result of 5^2 * 5^(-3)? (2023)
A.
5^1
B.
5^(-1)
C.
5^0
D.
5^(-5)
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Solution
Using the property of exponents, we combine the exponents: 5^(2 + (-3)) = 5^(-1).
Correct Answer:
B
— 5^(-1)
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