Q. Which of the following represents the slope of the line in the equation y = 3x + 2?
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Solution
In the slope-intercept form y = mx + b, m represents the slope. Here, m = 3.
Correct Answer:
B
— 3
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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 sequences cannot be a harmonic progression?
A.
1, 1/2, 1/3
B.
2, 4, 8
C.
3, 1, 1/3
D.
5, 10, 15
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Solution
The sequence 2, 4, 8 does not have reciprocals that form an arithmetic progression, hence it cannot be a harmonic progression.
Correct Answer:
B
— 2, 4, 8
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Q. Which of the following sequences is a geometric progression?
A.
1, 2, 4, 8
B.
1, 3, 6, 10
C.
2, 4, 8, 16
D.
1, 1, 1, 1
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Solution
The sequence 2, 4, 8, 16 has a constant ratio of 2, making it a geometric progression.
Correct Answer:
C
— 2, 4, 8, 16
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Q. Which of the following sequences is a harmonic progression?
A.
1, 2, 3
B.
1, 1/2, 1/3
C.
2, 4, 6
D.
3, 6, 9
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Solution
The sequence 1, 1/2, 1/3 has reciprocals 1, 2, 3 which are in arithmetic progression, thus it is a harmonic progression.
Correct Answer:
B
— 1, 1/2, 1/3
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Q. Which of the following sequences is an arithmetic progression?
A.
2, 4, 8, 16
B.
1, 3, 5, 7
C.
5, 10, 15, 25
D.
3, 6, 9, 12
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Solution
An arithmetic progression has a constant difference between consecutive terms. The sequence 1, 3, 5, 7 has a common difference of 2.
Correct Answer:
B
— 1, 3, 5, 7
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Q. Which of the following shapes is a polygon? (2023)
A.
Circle
B.
Triangle
C.
Ellipse
D.
Curve
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Solution
A triangle is a polygon as it is a closed figure with straight sides.
Correct Answer:
B
— Triangle
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Q. Which of the following statements about 'matrices' is correct?
A.
Matrices can only represent linear equations.
B.
Matrices are used exclusively in computer graphics.
C.
Matrices can represent data in multiple dimensions and are used in various applications.
D.
Matrices are irrelevant in modern mathematics.
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Solution
Matrices are versatile mathematical structures that can represent data in multiple dimensions and are widely used in various fields, including computer science, engineering, and statistics.
Correct Answer:
C
— Matrices can represent data in multiple dimensions and are used in various applications.
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Q. Which of the following statements about 'probability' is true?
A.
Probability can only be calculated for discrete events.
B.
The sum of probabilities of all possible outcomes is always 1.
C.
Probability is independent of the sample space.
D.
Probability can never exceed 1.
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Solution
The sum of probabilities of all possible outcomes must equal 1, which is a fundamental principle in probability theory.
Correct Answer:
B
— The sum of probabilities of all possible outcomes is always 1.
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Q. Which of the following statements about a geometric progression is true?
A.
The ratio of consecutive terms is constant.
B.
The difference between consecutive terms is constant.
C.
The sum of the terms is always positive.
D.
The first term is always the largest.
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Solution
In a geometric progression, the ratio of consecutive terms is indeed constant, which defines the progression.
Correct Answer:
A
— The ratio of consecutive terms is constant.
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Q. Which of the following statements about a kite is true?
A.
All sides are equal.
B.
Diagonals are equal.
C.
One pair of opposite angles are equal.
D.
It is a type of parallelogram.
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Solution
In a kite, one pair of opposite angles are equal, while the other properties do not hold true.
Correct Answer:
C
— One pair of opposite angles are equal.
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Q. Which of the following statements about a parallelogram is true? (2023)
A.
All sides are equal.
B.
Diagonals bisect each other.
C.
All angles are right angles.
D.
It has exactly one pair of parallel sides.
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Solution
In a parallelogram, the diagonals bisect each other, which is a defining property of parallelograms.
Correct Answer:
B
— Diagonals bisect each other.
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Q. Which of the following statements about a rectangle is false?
A.
All angles are right angles.
B.
Opposite sides are equal.
C.
Diagonals are equal and bisect each other.
D.
All sides are equal.
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Solution
In a rectangle, all angles are right angles and opposite sides are equal, but not all sides are equal.
Correct Answer:
D
— All sides are equal.
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Q. Which of the following statements about a rectangle is true?
A.
All sides are equal
B.
Opposite sides are equal and all angles are 90 degrees
C.
Diagonals are perpendicular
D.
Only one pair of opposite sides is equal
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Solution
In a rectangle, opposite sides are equal and all angles are indeed 90 degrees.
Correct Answer:
B
— Opposite sides are equal and all angles are 90 degrees
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Q. Which of the following statements about a rhombus is false?
A.
All sides are equal.
B.
Opposite angles are equal.
C.
Diagonals bisect each other at right angles.
D.
All angles are right angles.
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Solution
In a rhombus, while all sides are equal and diagonals bisect at right angles, not all angles are right angles.
Correct Answer:
D
— All angles are right angles.
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Q. Which of the following statements about a rhombus is incorrect?
A.
All sides are equal.
B.
Diagonals bisect each other at right angles.
C.
Diagonals are equal in length.
D.
Opposite angles are equal.
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Solution
In a rhombus, while all sides are equal and diagonals bisect each other at right angles, the diagonals are not equal in length.
Correct Answer:
C
— Diagonals are equal in length.
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Q. Which of the following statements about a square is false?
A.
All sides are equal.
B.
All angles are right angles.
C.
Diagonals are equal and bisect each other.
D.
Diagonals are perpendicular to each other.
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Solution
While the diagonals of a square are equal and bisect each other, they are not necessarily perpendicular to each other in all quadrilaterals.
Correct Answer:
D
— Diagonals are perpendicular to each other.
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Q. Which of the following statements about an arithmetic progression is true?
A.
The sum of any two terms is always even.
B.
The difference between any two consecutive terms is constant.
C.
The product of any two terms is constant.
D.
The terms are always positive.
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Solution
In an arithmetic progression, the difference between any two consecutive terms is indeed constant, which defines the sequence.
Correct Answer:
B
— The difference between any two consecutive terms is constant.
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Q. Which of the following statements about an equilateral triangle is true?
A.
All sides are equal
B.
All angles are 60 degrees
C.
It has one obtuse angle
D.
It can be isosceles
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Solution
In an equilateral triangle, all sides are equal and all angles measure 60 degrees.
Correct Answer:
A
— All sides are equal
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Q. Which of the following statements about angles formed by intersecting lines is false? (2023)
A.
Vertical angles are equal
B.
Adjacent angles are supplementary
C.
Linear pairs are equal
D.
Opposite angles are equal
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Solution
Linear pairs are not equal; they are supplementary, meaning they add up to 180 degrees.
Correct Answer:
C
— Linear pairs are equal
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Q. Which of the following statements about angles formed by intersecting lines is true?
A.
Vertical angles are always supplementary.
B.
Adjacent angles are always equal.
C.
Linear pairs of angles are supplementary.
D.
All angles formed are acute.
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Solution
Linear pairs of angles formed by intersecting lines are always supplementary, meaning they add up to 180 degrees.
Correct Answer:
C
— Linear pairs of angles are supplementary.
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Q. Which of the following statements about angles in a circle is true?
A.
The angle subtended by a diameter is always acute.
B.
Angles subtended by the same arc are equal.
C.
The sum of angles in a circle is 360 degrees.
D.
All angles in a circle are equal.
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Solution
Angles subtended by the same arc at the circumference of a circle are equal.
Correct Answer:
B
— Angles subtended by the same arc are equal.
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Q. Which of the following statements about base systems is incorrect? (2023)
A.
Base 2 is used in digital electronics.
B.
Base 10 is the most widely used numeral system.
C.
Base 16 can represent more values than base 10.
D.
Base 8 is more efficient than base 2.
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Solution
Base 8 (octal) is not more efficient than base 2 (binary); it simply represents values in a different way.
Correct Answer:
D
— Base 8 is more efficient than base 2.
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Q. Which of the following statements about exponents is false?
A.
a^m * a^n = a^(m+n)
B.
a^m / a^n = a^(m-n)
C.
a^0 = 0
D.
a^(-n) = 1/a^n
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Solution
The statement a^0 = 0 is false; in fact, a^0 = 1 for any non-zero a.
Correct Answer:
C
— a^0 = 0
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Q. Which of the following statements about exponents is incorrect?
A.
a^(m+n) = a^m * a^n
B.
a^(m-n) = a^m / a^n
C.
a^m * b^m = (ab)^m
D.
a^m + a^n = a^(m+n)
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Solution
The statement a^m + a^n = a^(m+n) is incorrect; addition of exponents does not apply in this manner.
Correct Answer:
D
— a^m + a^n = a^(m+n)
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Q. Which of the following statements about factors and multiples is correct? (2023)
A.
Every multiple of a number is also a factor of that number.
B.
Factors of a number are always greater than the number itself.
C.
A number can have an infinite number of multiples.
D.
The smallest multiple of any number is always the number itself.
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Solution
A number can have an infinite number of multiples, as you can keep adding the number to itself indefinitely.
Correct Answer:
C
— A number can have an infinite number of multiples.
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Q. Which of the following statements about factors and multiples is incorrect? (2023)
A.
Every multiple of a number is greater than or equal to that number.
B.
A number can have an infinite number of factors.
C.
The product of two numbers is always a multiple of both.
D.
A factor of a number is always greater than the number.
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Solution
A factor of a number is always less than or equal to that number, making the last statement incorrect.
Correct Answer:
D
— A factor of a number is always greater than the number.
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Q. Which of the following statements about factors is incorrect?
A.
Every number has at least two factors.
B.
Factors can be negative.
C.
The number itself is always a factor.
D.
Factors of a prime number are only 1 and the number itself.
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Solution
Every number has at least two factors: 1 and the number itself, but some numbers can have more than two factors.
Correct Answer:
A
— Every number has at least two factors.
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Q. Which of the following statements about geometric progressions is true?
A.
The ratio of consecutive terms is constant.
B.
The sum of terms is always positive.
C.
The first term must be greater than the second.
D.
The common ratio can only be an integer.
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Solution
In a geometric progression, the ratio of consecutive terms is indeed constant, which defines the progression.
Correct Answer:
A
— The ratio of consecutive terms is constant.
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Q. Which of the following statements about harmonic progression is false?
A.
The sum of the terms is finite
B.
The terms can be negative
C.
The terms can be zero
D.
The terms can be fractions
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Solution
In a harmonic progression, terms cannot be zero as it would make the reciprocal undefined.
Correct Answer:
C
— The terms can be zero
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