How to Effectively Use PAF Maths Tests Online Preparation for High Scores?
If you want to achieve a high score in the initial mathematics tests for PAF Aeronautical Engineering, Engineering Branch, Account Branch, Education Branch, Education Instructor Jobs, Airman Jobs, and PAF Civilians Tests, then PAF Maths Tests Online Preparation is your ultimate solution. This platform offers carefully curated past test questions based on the experiences of successful candidates who have cleared these exams.
By practicing these free online tests, you can familiarize yourself with the exact pattern, difficulty level, and key topics that frequently appear in the assessments. Whether you’re aiming for a technical or non-technical position in the Pakistan Air Force, mastering these maths questions is essential for passing the initial screening. Start your PAF Maths Tests Online Preparation today and boost your chances of success!
Related: How to Join PAF Aeronautical Branch?
Why PAF Maths Tests Online Preparation is Crucial for Initial Test Success
Q. If R={(1,2),(3,4)}, then its range will be:
a) (1,2,3)
b) (1,2,3,4)
c) (1,3)
d) (2,4)
Correct Answer: d) (2,4)
Q. If A={1,3,5,7,9}, then in set builder notation:
a) {x∣x∈O∧1≤x≤9}
b) {x∣x∈P∧1≤x≤9}
c) {x∣x∈O∧9≤x≤1}
d) {x∣x∈P∧1≤x≤8}
Correct Answer: a) {x∣x∈O∧1≤x≤9}
Q. (5−√2)(5+√2)= ______
a) 27
b) 21
c) 23
d) 25
Correct Answer: c) 23
Q. The HCF of x²−1 and x³−1 is:
a) (x+1)(x−1)
b) (x−1)(x²−x+1)
c) (x+1)(x³−1)
d) (x−1)
Correct Answer: d) (x−1)
Q. The solution set of the equation x−3=4 is:
a) {7}
b) {15}
c) {19}
d) {34}
Correct Answer: a) {7}
Q. The matrix [5 0; 0 5] is a:
a) Singular matrix
b) Scalar matrix
c) Diagonal matrix
d) Null matrix
Correct Answer: b) Scalar matrix
Q. If two opposite angles of an isosceles triangle are equal, then the triangles are also:
a) Congruent
b) Similar
c) Equilateral
d) Right angle
Correct Answer: a) Congruent
Q. The conjugate of ax+by is:
a) ay−bx
b) ax−by
c) xa−yb
d) xa−yb
Correct Answer: b) ax−by
Q. How many lines can pass through two different points?
a) 2
b) Infinite
c) Only one line
d) More than one line
Correct Answer: c) Only one line
Q. sin²θ+cos²θ= ______
a) 1
b) 1−2cos²θ
c) cos²θsin²θ
d) 0
Correct Answer: a) 1
Q. Two vectors will be equal if their ______ are equal.
a) Length & direction
b) Norm
c) Direction
d) Unit
Correct Answer: a) Length & direction
Q. The angle inscribed in a semicircle is a ______ angle.
a) Acute
b) Obtuse
c) Supplementary
d) Right
Correct Answer: d) Right
Q. log(mⁿ)= ______
a) nlogm
b) mlogn
c) mlogm
d) nlogn
Correct Answer: a) nlogm
Q. The characteristic of log8463 is:
a) 4
b) 3
c) 5
d) -3
Correct Answer: b) 3
Q. If log₁₀x = 3, then x= ______
a) 10²
b) x¹⁰
c) 1000
d) x³
Correct Answer: c) 1000
Q. The base of common logarithms is:
a) e
b) 1
c) 10
d) a
Correct Answer: c) 10
Q. Scientific notation for 0.00054 Coulombs is:
a) 5.4×10⁴
b) 5.4×10⁵
c) 54×10⁻⁴
d) 5.4×10⁻⁴
Correct Answer: d) 5.4×10⁻⁴
Q. If R={(1,2),(3,4)}, its domain is:
a) (1,2,3)
b) (1,3)
c) (2,4)
d) (1,2,3,4)
Correct Answer: b) (1,3)
Q. If set A has 4 members, then A×A has ______ members.
a) 16
b) 17
c) 35
d) None
Correct Answer: a) 16
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Key Topics Covered in PAF Maths Tests Online Preparation
Q. A∪(B∩C) = ______
a) (A∪B)∪(A∪C)
b) (A∪B)∩(A∪C)
c) (A∩B)∪(A∩C)
d) (A∪B)∪(A∩B)
Correct Answer: b) (A∪B)∩(A∪C)
Q. If A={1,2,3} and B={1,2}, then:
a) A⊆B
b) B⊆A
c) B⊈A
d) A⊈B
Correct Answer: b) B⊆A
Q. The power set of a set with n elements has ______ subsets.
a) 2²ⁿ
b) 2³ⁿ
c) 2ⁿ
d) n²
Correct Answer: c) 2ⁿ
Q. The factors of x²−5x+6 are:
a) (x+1)(x−6)
b) (x−2)(x−3)
c) (x+6)(x−1)
d) (x+2)(x+3)
Correct Answer: b) (x−2)(x−3)
Q. The solution set of x²−5x=0 is:
a) {0,5}
b) {5,1}
c) {0,5}
d) {6,0}
Correct Answer: a) {0,5}
Q. The HCF of a²−5a+6 and a²−4a+3 is:
a) a²−4a+3
b) a−3
c) a+3
d) a²+4a+3
Correct Answer: b) a−3
Q. The solution set of |x|−2=0 is:
a) {−2,2}
b) {2,2}
c) {−2,−2}
d) {2,0}
Correct Answer: a) {−2,2}
Q. The solution set of √x=6 is:
a) {6}
b) {36}
c) {}
d) {−6}
Correct Answer: b) {36}
Q. If R={(1,2),(3,4)}, then its range will be:
a) (1,2,3)
b) (1,2,3,4)
c) (1,3)
d) (2,4)
Correct Answer: d) (2,4)
Q. If A={1,3,5,7,9}, then in set builder notation:
a) {x∣x∈O∧1≤x≤9}
b) {x∣x∈P∧1≤x≤9}
c) {x∣x∈O∧9≤x≤1}
d) {x∣x∈P∧1≤x≤8}
Correct Answer: a) {x∣x∈O∧1≤x≤9}
Q. (5−√2)(5+√2) = ______
a) 27
b) 21
c) 23
d) 25
Correct Answer: c) 23
Q. The HCF of x²−1 and x³−1 is:
a) (x+1)(x−1)
b) (x−1)(x²−x+1)
c) (x+1)(x³−1)
d) (x−1)
Correct Answer: d) (x−1)
Q. The solution set of the equation x−3=4 is:
a) {7}
b) {15}
c) {19}
d) {34}
Correct Answer: a) {7}
Q. If two opposite angles of an isosceles triangle are equal, then the triangles are also:
a) Congruent
b) Similar
c) Equilateral
d) Right angle
Correct Answer: a) Congruent
Q. The conjugate of ax+by is:
a) ay−bx
b) ax−by
c) xa−yb
d) xa−yb
Correct Answer: b) ax−by
Q. How many lines can pass through two different points?
a) 2
b) Infinite
c) Only one line
d) More than one line
Correct Answer: c) Only one line
Q. sin²θ+cos²θ = ______
a) 1
b) 1−2cos²θ
c) cos²θsin²θ
d) 0
Correct Answer: a) 1
Q. tanθ = ______
a) 1/cosθ
b) 1/secθ
c) 1/sinθ
d) 1/cotθ
Correct Answer: d) 1/cotθ
Q. Two vectors will be equal if their ______ are equal.
a) Length & direction
b) Norm
c) Direction
d) Unit
Correct Answer: a) Length & direction
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PAF Maths Tests Online Preparation
Q. The angle inscribed in a semicircle is a ______ angle.
a) Acute
b) Obtuse
c) Supplementary
d) Right
Correct Answer: d) Right
Q. log(mⁿ) = ______
a) nlogm
b) mlogn
c) logm
d) nlogn
Correct Answer: a) nlogm
Q. If x = 3log10, then x = ______
a) 10²
b) x¹⁰
c) 1000
d) x³
Correct Answer: c) 1000
Q. The base of common logarithms is:
a) e
b) 1
c) 10
d) a
Correct Answer: c) 10
Q. Scientific notation for 0.00054 Coulombs is:
a) 5.4×10⁴
b) 5.4×10⁵
c) 54×10⁻⁴
d) 5.4×10⁻⁴
Correct Answer: d) 5.4×10⁻⁴
Q. If R={(1,2),(3,4)}, its domain is:
a) (1,2,3)
b) (1,3)
c) (2,4)
d) (1,2,3,4)
Correct Answer: b) (1,3)
Q. A∪(B∩C) = ______
a) (A∪B)∪(A∪C)
b) (A∪B)∩(A∪C)
c) (A∩B)∪(A∩C)
d) (A∪B)∪(A∩B)
Correct Answer: b) (A∪B)∩(A∪C)
Q. If A={1,2,3} and B={1,2}, then:
a) A⊆B
b) B⊆A
c) B⊈A
d) A⊈B
Correct Answer: b) B⊆A
Q. The power set of a set with n elements has ______ subsets.
a) 2²ⁿ
b) 2³ⁿ
c) 2ⁿ
d) n²
Correct Answer: c) 2ⁿ
Q. The factors of x²−5x+6 are:
a) (x+1)(x−6)
b) (x−2)(x−3)
c) (x+6)(x−1)
d) (x+2)(x+3)
Correct Answer: b) (x−2)(x−3)
Q. The solution set of x²−5x=0 is:
a) {0,5}
b) {5,1}
c) {0,5}
d) {6,0}
Correct Answer: a) {0,5}
Q. The HCF of a²−5a+6 and a²−4a+3 is:
a) a²−4a+3
b) a−3
c) a+3
d) a²+4a+3
Correct Answer: b) a−3
Q. The solution set of |x|−2=0 is:
a) {−2,2}
b) {2,2}
c) {−2,−2}
d) {2,0}
Correct Answer: a) {−2,2}
Q. The solution set of √x=6 is:
a) {6}
b) {36}
c) {}
d) {−6}
Correct Answer: b) {36}
Q. The LCM of (A−B)³ and (A−B)² is:
a) A−B
b) (A−B)²
c) (A−B)³
d) (A−B)⁵
Correct Answer: c) (A−B)³
Q. The solution set of 5−4x=−7 is ______ (where x∈N):
a) {12}
b) {3}
c) {1,2,3}
d) {1,2}
Correct Answer: b) {3}
Q. If x−y=4, which statement is true?
a) x³−y³−12xy=64
b) x³−y³−3xy=64
c) x³−y³−12xy=12
d) None
Correct Answer: a) x³−y³−12xy=64
Q. If x+y=5 and xy=6, then x³+y³= ______
a) 35
b) 95
c) 107
d) 125
Correct Answer: a) 35
Q. The solution set of 3x²−1=0 is ______
a) {10}
b) {10/3}
c) {√3/3}
d) {0}
Correct Answer: c) {√3/3}
Q. The matrix [3 x; 6 8] is regular if x= ______
a) −4
b) 4
c) 16
d) −24
Correct Answer: b) 4
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PAF Maths Online Tests Practice
Q. cotθ = ______
a) secθ
b) 1/tanθ
c) sinθ
d) cosθ
Correct Answer: b) 1/tanθ
Q. Simplified form of ³√27 is ______
a) 3
b) 2
c) 9
d) 5
Correct Answer: a) 3
Q. The middle point of a line joining midpoints of two sides of a triangle is 10 cm. The third side’s length is ______
a) 10 cm
b) 5 cm
c) 20 cm
d) 15 cm
Correct Answer: c) 20 cm
Q. A line intersecting a triangle perpendicularly is called ______
a) Altitude
b) Bisector
c) Right bisector
d) None
Correct Answer: a) Altitude
Q. In an equilateral triangle, opposite angles are ______
a) Congruent
b) Supplementary
c) Perpendicular
d) None
Correct Answer: a) Congruent
Q. 3 x 4 + 1 – 5 = ______
a) 9
b) 17
c) 25
d) 8
Correct Answer: d). 8
Q. The characteristic of log765.3 is ______
a) +2
b) -2
c) 3
d) -3
Correct Answer: a) +2
Q. 0.00416 in scientific notation is ______
a) 0.0416×10⁻¹
b) 0.416×10⁻²
c) 4.16×10⁻³
d) 41.6×10⁻⁴
Correct Answer: c) 4.16×10⁻³
Q. If x + 1/x = a and x² + 1/x² = b, then ______
a) a² = b²
b) a² = b² + 2
c) a² + 2 = b²
d) a² + b² = 2
Correct Answer: b) a² = b² + 2
Q. The additive inverse of [-3, -2] is ______
a) [3, 2]
b) [-3, 2]
c) [-3]
d) [3]
Correct Answer: a) [3, 2]
Q. The set {0,1,2,…,100} in set-builder notation is ______
a) {x | x∈W ∧ 0≤x≤100}
b) {x | x∈P ∧ 0≥x≥100}
c) {x | x∈W ∧ 0≤x≥100}
d) {x | x∈W ∧ 0≤x≤99}
Correct Answer: a) {x | x∈W ∧ 0≤x≤100}
Q. If A={1,2,3} and B={2,4,6}, then A∪B = ______
a) {1,2,2,3,4,6}
b) {1,2,3,4,6}
c) {2,3,4,6}
d) {1,2,3,4,6}
Correct Answer: b) {1,2,3,4,6}
Q. If U={1,2,…,20} and A={1,3,5,…,19}, then A’ = ______
a) {2,4,6,…,19}
b) {1,3,5,…,19}
c) {2,4,6,…,20}
d) {2,3,…,19}
Correct Answer: c) {2,4,6,…,20}
Q. The relation R={(0,1),(1,2),(3,4)} has range ______
a) {0,1,3}
b) {1,2,3}
c) {2,3,4}
d) {1,2,4}
Correct Answer: d) {1,2,4}
Q. A point (0,b) lies on the ______
a) 2nd quadrant
b) 3rd quadrant
c) Y-axis
d) X-axis
Correct Answer: c) Y-axis
Q. The numbers whose sum is -13 and product is -30 are ______
a) 2,15
b) 2,-15
c) -3,10
d) 3,-10
Correct Answer: b) 2,-15
Q. The solution set of x²-x-2=0 is ______
a) {1}
b) {2}
c) {2,-1}
d) {1,-2}
Correct Answer: c) {2,-1}
Q. The solution set of 5x²=3x is ______
a) {0, 3/5}
b) {0, 5/3}
c) {0, 3/5}
d) {0, 5/3}
Correct Answer: a) {0, 3/5}
Q. If x=√2-1, then x²= ______
a) 1/2-1
b) 2+1
c) 1
d) 3-2√2
Correct Answer: d) 3-2√2
Q. The solution set of |2x|<8 is ______
a) {4}
b) {-4}
c) {-4<x<4}
d) {4,-4}
Correct Answer: c) {-4<x<4}
Q. The expression x²+6x+9 is a perfect square of:
a) (x+3)
b) (x-3)
c) (x+3)(x-3)
d) (x+3)²
Correct Answer: d) (x+3)²
Q. If xy=15 and x+y=8, then x²+y²=:
a) 36
b) 34
c) 48
d) 41
Correct Answer: b) 34
Q. The LCM of (a-b)³ and (a-b)² is:
a) a-b
b) (a-b)²
c) (a-b)³
d) (a-b)⁵
Correct Answer: c) (a-b)³
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PAF Maths Past Papers with Solutions
Q. The dot product of vectors [a b] and [c d] is:
a) ab + cd
b) ab – cd
c) ac + bd
d) ac – bd
Solution: The dot product is calculated as (a×c) + (b×d)
Correct Answer: c) ac + bd
Q. A first degree equation is called:
a) Quadratic
b) Linear
c) Cubic
d) Exponential
Solution: First degree equations have degree 1 and are called linear equations
Correct Answer: b) Linear
Q. cos(90°−θ) = ______
a) cosθ
b) tanθ
c) sinθ
d) cotθ
Solution: This is the co-function identity: cos(90°-θ) = sinθ
Correct Answer: c) sinθ
Q. The value of cot60° is:
a) √3/2
b) 2/√3
c) 1/√3
d) √3
Solution: cot60° = cos60°/sin60° = (1/2)/(√3/2) = 1/√3
Correct Answer: c) 1/√3
Q. A circle passing through all three vertices of a triangle is called:
a) Incircle
b) Circumcircle
c) Excircle
d) Tangent circle
Solution: The circumcircle is the circle passing through all vertices
Correct Answer: b) Circumcircle
Q. The matrix [1 0; 0 1] is called:
a) Scalar matrix
b) Identity matrix
c) Zero matrix
d) Diagonal matrix
Solution: This is the 2×2 identity matrix with 1s on diagonal and 0s elsewhere
Correct Answer: b) Identity matrix
Q. A line that touches a circle at exactly one point is called:
a) Chord
b) Radius
c) Tangent
d) Secant
Solution: By definition, a tangent touches at exactly one point
Correct Answer: c) Tangent
Q. The exponential form of y=logₐx is:
a) yᵃ = x
b) xᵃ = y
c) aʸ = x
d) aˣ = y
Solution: Logarithmic form y=logₐx converts to exponential form aʸ=x
Correct Answer: c) aʸ = x
Q. If log₁₀x = 3, then x = ______
a) 500
b) 1000
c) 700
d) 100
Solution: x = 10³ = 1000
Correct Answer: b) 1000
Q. (a+b)² + (a−b)² = ______
a) 4ab
b) a² + b²
c) 2a² + 2b²
d) 2ab
Solution: Expanding both terms gives a²+2ab+b² + a²-2ab+b² = 2a²+2b²
Correct Answer: c) 2a² + 2b²
Q. The characteristic of log3.216 is:
a) 0
b) 1
c) 2
d) 3
Solution: Characteristic is the integer part (3 is between 10⁰ and 10¹)
Correct Answer: a) 0
Q. Scientific notation for 0.00416 is:
a) 4.16×10⁻³
b) 41.6×10⁻⁴
c) 0.416×10⁻²
d) 0.0416×10⁻¹
Solution: Proper form has one non-zero digit before decimal: 4.16×10⁻³
Correct Answer: a) 4.16×10⁻³
Q. If A={1,2,3} and B={2,4,6}, then A∪B = ______
a) {1,2,3,4,6}
b) {2}
c) {1,2,2,3,4,6}
d) {1,3,4,6}
Solution: Union includes all distinct elements from both sets
Correct Answer: a) {1,2,3,4,6}
Q. The relation R={(0,1),(1,2),(3,4)} has range:
a) {0,1,3}
b) {1,2,4}
c) {1,2,3}
d) {2,3,4}
Solution: Range is the set of second elements {1,2,4}
Correct Answer: b) {1,2,4}
Q. The point (0,b) lies on:
a) X-axis
b) Y-axis
c) 1st quadrant
d) 3rd quadrant
Solution: Points with x=0 lie on the Y-axis
Correct Answer: b) Y-axis
Q. For real numbers x, y, z:
a) x(yz) = (xy)z
b) x = y = z
c) x = y
d) y = z
Solution: This demonstrates the associative property of multiplication
Correct Answer: a) x(yz) = (xy)z
Q. The power set of a set with n elements has:
a) 2ⁿ elements
b) n² elements
c) nⁿ elements
d) 2²ⁿ elements
Solution: Power set contains all subsets, and has cardinality 2ⁿ
Correct Answer: a) 2ⁿ elements
Q. The factors of x²−5x+6 are:
a) (x+1)(x−6)
b) (x−2)(x−3)
c) (x+6)(x−1)
d) (x+2)(x+3)
Solution: x²−5x+6 = (x−2)(x−3)
Correct Answer: b) (x−2)(x−3)
Q. The solution set of x²−x−2=0 is:
a) {1}
b) {2}
c) {2,−1}
d) {1,−2}
Solution: Factors to (x−2)(x+1)=0 → x=2 or x=−1
Correct Answer: c) {2,−1}
Q. The numbers with sum -13 and product -30 are:
a) 2, -15
b) -3, 10
c) 3, -10
d) 5, -18
Solution: 2+(-15)=-13 and 2×(-15)=-30
Correct Answer: a) 2, -15
Q. The factorization of 8x³+27y³ is:
a) (2x+3y)(4x²+9y²)
b) (2x−3y)(4x²−9y²)
c) (2x+3y)(4x²−6xy+9y²)
d) (2x−3y)(4x²+6xy+9y²)
Solution: Sum of cubes formula: a³+b³=(a+b)(a²−ab+b²)
Correct Answer: c) (2x+3y)(4x²−6xy+9y²)
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How to Pass PAF Initial Maths Test?
Those who want to prepare initial tests of Maths for Airman and Civilian jobs they must do practice of Maths tests Matric Level, and those who want to prepare initial tests of commissioned officer exam then they must do practice of matric and intermediate level questions, and those who are applying in Education branch for maths subjects, they must prepare Master Level preparation. Moreover, they must also do practice from matric to master all levels because they have to prepare from basic to Master level.
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Maths Practice Tests For Matriculate Students
PAF Maths Online Tests Practice is given here for getting high score in maths tests of PAF.
Free Online Practice Tests of Maths for Intermediate Students
PAF Maths Tests Online Preparation is given here to prepare PAF initial tests with full confidence.
Free Online Tests of Mathematics for Master Students
It is best for those who are apply at master level like in PAF Education branch in the subject of Mathematics.
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Useful Links for Mathematics Tests Preparation
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