PAF Mathematics Past Questions of Initial Tests

Mathematics Past Questions and Answers of PAF

Mathematics Past Questions Part-4

• What is the determinant of the matrix [2 3; 2 2]?
• Answer: The determinant is “-2.”
• What is the reciprocal of cot(θ)?
• Answer: The reciprocal of cot(θ) is “1/Tan.”
• What is the reciprocal of 1/cosec(θ)?
• Answer: The reciprocal of 1/cosec(θ) is “Sin.”
• How many degrees is 2π radians equal to?
• Answer: 2π radians is equal to “360 degrees.”
• How many degrees is 3π/2 radians equal to?
• Answer: 3π/2 radians is equal to “270 degrees.”
• How many degrees is 3π/3 radians equal to?
• Answer: 3π/3 radians is equal to “180 degrees.”
• When are two matrices conformable for multiplication?
• Answer: Two matrices are conformable for multiplication when the number of columns in the first matrix is equal to the number of rows in the second matrix.
• In the ratio A:b, what is “A” called?
• Answer: “A” is called the “antecedent.”
• In the ratio A:b, what is “b” called?
• Answer: “b” is called the “consequent.”
• What do you call a relationship where increasing one quantity decreases the other?
• Answer: This relationship is called “Inverse.”
• If a team wins 5 matches and loses 7 matches, what is the ratio of matches won to lost?
• Answer: The ratio is “5:7.”
• What is a matrix called if its transpose is equal to the negative of the matrix?
• Answer: It is called a “Skew symmetric matrix.”
• What is the arrangement of columns and rows in square brackets commonly referred to as?
• Answer: This arrangement is called a “Matrix.”
• What is the determinant of the matrix [2 3; 2 2]?
• Answer: The determinant is “-2.”
• What is the value of cot(θ)?
• Answer: The value of cot(θ) is “1/Tan.”
• What is the reciprocal of 1/cosec(θ)?
• Answer: The reciprocal of 1/cosec(θ) is “Sin.”
• How many degrees is 2π radians equal to?
• Answer: 2π radians is equal to “360 degrees.”
• How many degrees is 3π/2 radians equal to?
• Answer: 3π/2 radians is equal to “270 degrees.”
• How many degrees is 3π/3 radians equal to?
• Answer: 3π/3 radians is equal to “180 degrees.”
• When are two matrices conformable for multiplication?
• Answer: Two matrices are conformable for multiplication when the number of columns and the number of rows are equal in both matrices.
• In the ratio A:b, what is “A” called?
• Answer: “A” is called the “antecedent.”
• In the ratio A:b, what is “b” called?
• Answer: “b” is called the “consequent.”
• What is the term for a relationship in which increasing one quantity causes another quantity to decrease?
• Answer: This relationship is called “Inverse.”
• If a team wins 5 matches and loses 7 matches, what is the ratio of matches won to matches lost?
• Answer: The ratio is “5:7.”
• What is the name for the equation X^2 – 16 = 0?
• Answer: It is called a “Pure quadratic equation.”
• What is the solution for the equation W^37 + W^37 – 5=?
• Answer: The solution is “-5.”
• What is the value of 2π?
• Answer: The value of 2π is “360 degrees.”
• What is the value of 3π/2?
• Answer: The value of 3π/2 is “270 degrees.”
• In the ratio A:B, what is “A” called?
• Answer: In A:B, “A” is called the “antecedent.”
• In the ratio A:B, what is “B” called?
• Answer: In A:B, “B” is called the “consequent.”
• What do you call an angle less than 90 degrees in terms of quadrants?
• Answer: An angle less than 90 degrees lies in the “1st quadrant.”
• What is the definition of cumulative frequency?
• Answer: The definition of cumulative frequency is not provided in the original text.
• Food is to eating as book is to?
• Answer: Food is to eating as “book is to reading.”
• What is the task when you are given an equation and asked to find its alpha and beta roots?
• Answer: The task is to find the “alpha and beta roots” of the equation.
• How do you determine whether the roots of an equation are imaginary or real?
• Answer: You determine whether the roots of an equation are “imaginary or real.”
• What is the term “Antecedent” related to?
• Answer: “Antecedent” is related to ratios or proportions.
• How can you represent the proportion of a, b, c, and d in ratio form?
• Answer: You can represent the proportion of a, b, c, and d in the form of “a:b:c:d.”
• What are the “extreme” and “mean” in a mathematical context?
• Answer: In a mathematical context, the “extreme” refers to the first and last terms in a sequence, while the “mean” refers to the average or middle value.
• Can you provide an example of a matrix equation?
• Answer: An example of a matrix equation would be helpful for better understanding.
• What is an “Identity matrix”?
• Answer: An “Identity matrix” is a square matrix with ones on the main diagonal and zeros elsewhere.
• What kind of line passes through the center of a circle?
• Answer: A “diameter” is a line that passes through the center of a circle.
• What is the “angle of elevation”?
• Answer: The “angle of elevation” is the angle formed between the horizontal and the line of sight to an object above the horizontal level.
• What is the definition of a “Pure quadratic equation”?
• Answer: A “Pure quadratic equation” is a quadratic equation with no linear or constant terms.
• Can you provide a description of a “quadratic equation”?
• Answer: A “quadratic equation” is a second-degree polynomial equation that can be written in the form ax² + bx + c = 0.
• What is the significance of a circle passing through the vertices of a quadrilateral?
• Answer: When a circle passes through the vertices of a quadrilateral, it is of interest for some specific geometric properties.
• What is the term for the expression b² – 4ac in a quadratic equation?
• Answer: The term is known as the “discriminant.”
• How much is 1 Mega equal to?
• Answer: 1 Mega is equal to “10^9.”
• What is a set with only one element called?
• Answer: A set with only one element is called a “singleton set.”
• What happens to the sum of angles when they add up to 90 degrees?
• Answer: When the sum of angles adds up to 90 degrees, they are called “complementary.”
• What term is used for angles that sum up to 180 degrees?
• Answer: Angles that sum up to 180 degrees are termed “supplementary.”
• What is the condition for a matrix B to be considered “symmetric”?
• Answer: A matrix B is considered “symmetric” if B^t = B.
• What is the result when you take the inverse of the product of matrices AB?
• Answer: The result is (AB)^-¹ = (B^-1)(A^-1).
• What is the definition of “Diameter” in geometry?
• Answer: In geometry, a “diameter” is a line that passes through the center of a circle, touching two points on the circle.
• What does it mean when an angle is clockwise in orientation (positive or negative)?
• Answer: When an angle is measured in the clockwise direction, it is considered “positive.”
• Which law is not followed by matrices when it comes to multiplication?
• Answer: Matrices do not follow the “inverse law” of multiplication.
• Can you provide the definition of a “Power set”?
• Answer: A “power set” is the set of all subsets of a given set, including the empty set and the set itself.
• What is the set of positive integers starting from 1 and continuing indefinitely known as?
• Answer: The set of positive integers starting from 1 and continuing indefinitely is called “natural numbers.”
• What is the definition of “Diameter” in a geometric context?
• Answer: In geometry, a “diameter” is a line segment that passes through the center of a circle, touching two points on the circle.
• How is the equation “a=n^x” defined, with “x” as “Logan”?
• Answer: In the equation “a=n^x,” “x” is defined as “Logan.”
• What is the definition of a “Quadratic equation”?
• Answer: A “Quadratic equation” is a second-degree polynomial equation that can be written in the form ax² + bx + c = 0.
• How is “Cosec” related to “Sin”?
• Answer: “Cosec” is the reciprocal of “Sin,” where Cosec(θ) = 1/Sin(θ).
• What is the reciprocal of “Cosec”?
• Answer: The reciprocal of “Cosec” is “Sin,” where Sin(θ) = 1/Cosec(θ).
• What is the reciprocal of “Tan”?
• Answer: The reciprocal of “Tan” is “Cot,” where Cot(θ) = 1/Tan(θ).
• What is the reciprocal of “Cot”?
• Answer: The reciprocal of “Cot” is “Tan,” where Tan(θ) = 1/Cot(θ).
• What defines an “Equilateral triangle”?
• Answer: An “Equilateral triangle” is a triangle with three equal sides and three equal angles.
• What is the term for matrices with the same elements in corresponding positions?
• Answer: Matrices with the same elements in corresponding positions are called “Equal Matrices.”
• What is the solution to the equation “x³+8=(x+8)(x²-x+2)”?
• Answer: The solution is not provided in the original text.
• How can you rewrite the equation “a^x=y” in terms of logarithms?
• Answer: The equation “a^x=y” can be rewritten as “logₐ(y) = x.”
• What do the ratios “a:b=4:8” represent, where “a,” “b,” “4,” and “8” are coefficients?
• Answer: The ratios represent the relationship between the coefficients “a” and “b,” and they are written as “a:b=4:8.”
• What is the significance of the condition “b²+4ac<0” in the equation “4x²+2x+6”?
• Answer: The condition “b²+4ac<0” indicates that the solutions to the equation “4x²+2x+6” are imaginary.
• In which quadrant do angles between 90 and 180 degrees lie?
• Answer: Angles between 90 and 180 degrees lie in the “2nd quadrant.”
• What is the relationship between “2π” and “360°”?
• Answer: “2π” is equivalent to “360°.”
• What is the definition of a “Triangle” in geometry?
• Answer: A “Triangle” is a geometric figure composed of three sides and three angles.
• How is the ratio of quantities A and B typically written?
• Answer: The ratio of quantities A and B is typically written as “(A: B).”
• What are the values of 2π and 3π/2 in radians?
• Answer: 2π is equal to 360 radians, and 3π/2 is equal to 270 radians.
• In a ratio A:B, what is A commonly referred to as?
• Answer: In a ratio A:B, A is commonly referred to as the “antecedent.”
• What term is assigned to B in the ratio A:B?
• Answer: In the ratio A:B, the term assigned to B is the “consequent.”
• In which quadrant does an angle greater than 0 and less than 90 degrees lie?
• Answer: An angle greater than 0 and less than 90 degrees lies in the “1st quadrant.”
• What do you call a matrix where the transpose is equal to the negative of that matrix?
• Answer: A matrix where the transpose is equal to the negative of that matrix is called a “Skew symmetric matrix.”
• What is the term for the arrangement of columns and rows in square brackets?
• Answer: The arrangement of columns and rows in square brackets is called a “Matrix.”
• What is the determinant of a matrix with elements 2, 3, 2, and 2?
• Answer: The determinant of the matrix with elements 2, 3, 2, and 2 is “-2.”
• What is the value of cot(θ)?
• Answer: The value of cot(θ) is “1/tan(θ).”
• What is the reciprocal of cosec(θ)?
• Answer: The reciprocal of cosec(θ) is “sin(θ).”
• Under what condition are two matrices considered conformable for multiplication?
• Answer: Two matrices are considered conformable for multiplication when the number of columns in the first matrix is equal to the number of rows in the second matrix.
• In a ratio expressed as A:B, what is A typically called?
• Answer: In a ratio expressed as A:B, A is typically called the “antecedent.”
• What is the term assigned to B in a ratio expressed as A:B?
• Answer: In a ratio expressed as A:B, the term assigned to B is the “consequent.”
• What is the definition of “cumulative frequency”?
• Answer: “Cumulative frequency” is a statistical property that represents the cumulative total of frequencies up to a certain point in a dataset.
• What is the term for a relationship in which an increase in one quantity leads to a decrease in another?
• Answer: A relationship where an increase in one quantity leads to a decrease in another is called “inverse variation.”
• In a scenario where a team wins 5 matches and loses 7 matches, what is the ratio of matches won to matches lost?
• Answer: The ratio of matches won to matches lost in this scenario is “5:7.”