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Afghan Air Force University Kankor study materials
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Afghan Air Force University Kankor practice questions

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Question 1Mathematics

What is the value of 7 × 8 − 12 ÷ 4?

  1. 50
  2. 47
  3. 53 Correct answer.
  4. 11

Explanation

Order of operations requires division before subtraction: 12 ÷ 4 = 3, then 7 × 8 = 56, and 56 − 3 = 53. Multiplication and division are performed before addition and subtraction.

Question 2Mathematics

Which of the following numbers is prime?

  1. 21
  2. 33
  3. 29 Correct answer.
  4. 39

Explanation

A prime number has exactly two distinct positive divisors, 1 and itself. The number 29 is not divisible by 2, 3, or 5, so it is prime.

Question 3Mathematics

Solve for x: 3x + 5 = 20.

  1. 6
  2. 4
  3. 5 Correct answer.
  4. 3

Explanation

Subtract 5 from both sides to get 3x = 15, then divide both sides by 3 to obtain x = 5.

Question 4Mathematics

What is the slope of the line passing through the points (2, 3) and (6, 11)?

  1. 8
  2. 4
  3. 2 Correct answer.
  4. 1/2

Explanation

The slope equals the change in y divided by the change in x: (11 − 3)/(6 − 2) = 8/4 = 2.

Question 5Mathematics

Simplify: (x³)(x⁴).

  1. x^7 Correct answer.
  2. 2x^7
  3. x^12
  4. x

Explanation

When multiplying powers with the same base, add the exponents: x³ · x⁴ = x^(3+4) = x⁷.

Question 6Mathematics

What is the area of a triangle with base 10 cm and height 6 cm?

  1. 60 cm²
  2. 15 cm²
  3. 30 cm² Correct answer.
  4. 16 cm²

Explanation

The area of a triangle is one-half times base times height: (1/2)(10)(6) = 30 cm².

Question 7Mathematics

Which of the following is equal to 0.375 as a fraction in lowest terms?

  1. 3/5
  2. 3/8 Correct answer.
  3. 3/4
  4. 5/8

Explanation

The decimal 0.375 equals 375/1000, which reduces by dividing numerator and denominator by 125 to give 3/8.

Question 8Mathematics

If f(x) = 2x² − 3, what is f(−2)?

  1. −11
  2. 1
  3. 5 Correct answer.
  4. 11

Explanation

Substitute x = −2: 2(−2)² − 3 = 2(4) − 3 = 8 − 3 = 5. Squaring a negative number gives a positive result.

Question 9Mathematics

What is the value of log₂ 32?

  1. 6
  2. 5 Correct answer.
  3. 4
  4. 16

Explanation

The logarithm log₂ 32 asks for the exponent to which 2 must be raised to get 32. Since 2⁵ = 32, the answer is 5.

Question 10Mathematics

Find the sum of the first 20 positive integers.

  1. 210 Correct answer.
  2. 200
  3. 420
  4. 190

Explanation

The sum of the first n positive integers is n(n+1)/2. For n = 20 this gives 20 × 21 / 2 = 210.

Question 11Mathematics

The roots of x² − 5x + 6 = 0 are:

  1. −2 and −3
  2. −1 and −6
  3. 2 and 3 Correct answer.
  4. 1 and 6

Explanation

Factor the quadratic as (x − 2)(x − 3) = 0, since the numbers must multiply to 6 and add to 5. Setting each factor to zero gives x = 2 or x = 3.

Question 12Mathematics

A bag contains 4 red and 6 blue balls. If one ball is drawn at random, what is the probability that it is red?

  1. 2/5 Correct answer.
  2. 1/4
  3. 3/5
  4. 4/6

Explanation

There are 4 red balls out of 10 total, so the probability is 4/10, which simplifies to 2/5.

Question 13Mathematics

What is the value of sin 30° + cos 60°?

  1. 1 Correct answer.
  2. √3/2
  3. 1/2
  4. 2

Explanation

Both sin 30° and cos 60° equal 1/2. Their sum is 1/2 + 1/2 = 1.

Question 14Mathematics

The distance between the points (1, 2) and (4, 6) is:

  1. 5 Correct answer.
  2. 3
  3. 7
  4. 4

Explanation

Using the distance formula, d = √((4−1)² + (6−2)²) = √(9 + 16) = √25 = 5.

Question 15Mathematics

If the arithmetic mean of the numbers 4, 7, 9, x, and 12 is 8, what is x?

  1. 8 Correct answer.
  2. 6
  3. 10
  4. 7

Explanation

The mean equals the sum divided by 5, so the sum must be 5 × 8 = 40. The known numbers sum to 32, so x = 40 − 32 = 8.

Question 16Mathematics

Solve the inequality 2x − 3 > 7.

  1. x > 5 Correct answer.
  2. x < 5
  3. x > 10
  4. x > 2

Explanation

Add 3 to both sides to get 2x > 10, then divide both sides by 2 to obtain x > 5. Dividing by a positive number does not reverse the inequality.

Question 17Mathematics

A rectangle has a perimeter of 40 cm and a length of 12 cm. What is its width?

  1. 16 cm
  2. 14 cm
  3. 10 cm
  4. 8 cm Correct answer.

Explanation

The perimeter of a rectangle is 2(length + width). So 40 = 2(12 + w), giving 20 = 12 + w and w = 8 cm.

Question 18Mathematics

What is the value of 5! (5 factorial)?

  1. 720
  2. 25
  3. 120 Correct answer.
  4. 60

Explanation

The factorial 5! equals 5 × 4 × 3 × 2 × 1 = 120.

Question 19Mathematics

Simplify the expression (2x + 3)(x − 4).

  1. 2x² − 5x + 12
  2. 2x² + 5x − 12
  3. 2x² − 11x − 12
  4. 2x² − 5x − 12 Correct answer.

Explanation

Expand using the distributive property: 2x·x = 2x², 2x·(−4) = −8x, 3·x = 3x, and 3·(−4) = −12. Combining like terms gives 2x² − 5x − 12.

Question 20Mathematics

The sum of two numbers is 15 and their product is 56. What is the larger number?

  1. 14
  2. 8 Correct answer.
  3. 9
  4. 7

Explanation

The numbers must satisfy x + y = 15 and xy = 56, so they are roots of t² − 15t + 56 = 0, which factors as (t − 7)(t − 8) = 0. The larger of the two numbers is 8.

Question 21Mathematics

For what value of k does the equation x² + kx + 9 = 0 have exactly one real solution?

  1. 12
  2. 6 Correct answer.
  3. 3
  4. 9

Explanation

A quadratic has exactly one real root when its discriminant b² − 4ac equals zero. Here k² − 4(1)(9) = 0, so k² = 36 and k = 6 (taking the positive value).

Question 22Mathematics

If log₁₀ 2 ≈ 0.3010, then log₁₀ 8 is closest to:

  1. 0.6020
  2. 1.2040
  3. 0.4515
  4. 0.9030 Correct answer.

Explanation

Since 8 = 2³, we have log₁₀ 8 = 3 log₁₀ 2 ≈ 3 × 0.3010 = 0.9030. This uses the power rule for logarithms.

Question 23Mathematics

In an arithmetic sequence, the 5th term is 17 and the 9th term is 33. What is the 1st term?

  1. 5
  2. 3
  3. 1 Correct answer.
  4. 9

Explanation

The common difference d satisfies 4d = 33 − 17 = 16, so d = 4. Then a₁ = a₅ − 4d = 17 − 16 = 1.

Question 24Mathematics

What is the minimum value of the function f(x) = x² − 6x + 11?

  1. 3
  2. 11
  3. 1
  4. 2 Correct answer.

Explanation

Complete the square: f(x) = (x − 3)² + 2. Since a square is never negative, the minimum value is 2, occurring at x = 3.

Question 25Mathematics

How many distinct four-letter arrangements can be made from the letters of the word BOOK?

  1. 48
  2. 4
  3. 24
  4. 12 Correct answer.

Explanation

There are 4 letters in total with the letter O repeated twice. The number of distinct arrangements is 4!/2! = 24/2 = 12.

Question 26Mathematics

What is the value of 7² − 4²?

  1. 11
  2. 33 Correct answer.
  3. 45
  4. 65

Explanation

Compute each square first: 7² = 49 and 4² = 16. Subtracting gives 49 − 16 = 33.

Question 27Mathematics

A circle has radius 7 cm. What is its circumference, taking π = 22/7?

  1. 44 cm Correct answer.
  2. 22 cm
  3. 154 cm
  4. 49 cm

Explanation

Circumference equals 2πr, so 2 × (22/7) × 7 = 44 cm. The factor of 7 cancels the denominator.

Question 28Mathematics

What is the slope of the line passing through (2, 3) and (6, 11)?

  1. 1/2
  2. 2 Correct answer.
  3. 8
  4. 4

Explanation

Slope equals the change in y divided by the change in x: (11 − 3)/(6 − 2) = 8/4 = 2.

Question 29Mathematics

Which of the following numbers is irrational?

  1. √2 Correct answer.
  2. −9
  3. 22/7
  4. 0.75

Explanation

An irrational number cannot be written as a ratio of integers; √2 has a non-terminating, non-repeating decimal expansion. The other three are all rational.

Question 30Mathematics

A fair six-sided die is rolled once. What is the probability of getting a number greater than 4?

  1. 2/3
  2. 1/3 Correct answer.
  3. 1/6
  4. 1/2

Explanation

The outcomes greater than 4 are 5 and 6, giving 2 favourable outcomes out of 6. So the probability is 2/6 = 1/3.

Question 31Mathematics

What is the median of the data set 3, 8, 5, 12, 7?

  1. 5
  2. 8
  3. 7 Correct answer.
  4. 12

Explanation

Ordering the values gives 3, 5, 7, 8, 12. With five values the median is the middle one, which is 7.

Question 32Mathematics

What is the next term in the geometric sequence 3, 6, 12, 24, ...?

  1. 27
  2. 48 Correct answer.
  3. 30
  4. 36

Explanation

Each term is obtained by multiplying the previous term by the common ratio 2. Thus 24 × 2 = 48.

Question 33Mathematics

Simplify (x³ · x⁴) / x².

  1. x²⁴
  2. x⁵ Correct answer.
  3. x⁹
  4. x⁶

Explanation

When multiplying powers with the same base, add the exponents: x³ · x⁴ = x⁷. Then subtract the exponent in the denominator: x⁷ / x² = x⁵.

Question 34Mathematics

If 2x + 3y = 12 and x = 3, what is the value of y?

  1. 1
  2. 3
  3. 2 Correct answer.
  4. 6

Explanation

Substituting x = 3 gives 6 + 3y = 12. Subtracting 6 from both sides gives 3y = 6, so y = 2.

Question 35Mathematics

The sum of the interior angles of a regular polygon is 1080°. How many sides does the polygon have?

  1. 6
  2. 10
  3. 8 Correct answer.
  4. 12

Explanation

The interior angle sum of an n-sided polygon is (n − 2) × 180°. Setting (n − 2) × 180 = 1080 gives n − 2 = 6, so n = 8.

Question 36Mathematics

What is the value of tan 45° · sin 30°?

  1. 1
  2. 2
  3. 1/2 Correct answer.
  4. √3/2

Explanation

tan 45° = 1 and sin 30° = 1/2, so their product is 1 × 1/2 = 1/2.

Question 37Mathematics

If logₐ 4 = 2, what is the value of a?

  1. 4
  2. 8
  3. 2 Correct answer.
  4. 16

Explanation

The statement logₐ 4 = 2 means a² = 4. Since a must be positive and not equal to 1, a = 2.

Question 38Mathematics

For what value of x is the expression 1/(x − 5) undefined?

  1. −5
  2. 5 Correct answer.
  3. 1
  4. 0

Explanation

A fraction is undefined when its denominator equals zero. Solving x − 5 = 0 gives x = 5.

Question 39Mathematics

Two events A and B are independent with P(A) = 0.5 and P(B) = 0.4. What is P(A and B)?

  1. 0.45
  2. 0.2 Correct answer.
  3. 0.9
  4. 0.1

Explanation

For independent events, P(A and B) = P(A) × P(B). Multiplying gives 0.5 × 0.4 = 0.2.

Question 40Mathematics

What is the sum of the roots of the equation 2x² − 8x + 6 = 0?

  1. −4
  2. 4 Correct answer.
  3. 8
  4. 3

Explanation

For ax² + bx + c = 0, the sum of the roots is −b/a. Here that is −(−8)/2 = 4.

Question 41Mathematics

A train travels 240 km in 3 hours and then 180 km in 2 hours. What is its average speed for the whole journey?

  1. 80 km/h
  2. 90 km/h
  3. 84 km/h Correct answer.
  4. 70 km/h

Explanation

Total distance is 240 + 180 = 420 km and total time is 3 + 2 = 5 hours. Average speed is 420/5 = 84 km/h.

Question 42Mathematics

If sin θ = 3/5 and θ is acute, what is cos θ?

  1. 3/4
  2. 4/5 Correct answer.
  3. 5/4
  4. 5/3

Explanation

Using sin²θ + cos²θ = 1 gives cos²θ = 1 − 9/25 = 16/25. Since θ is acute, cos θ = 4/5.

Question 43Mathematics

In how many ways can a committee of 2 be chosen from 6 people?

  1. 12
  2. 36
  3. 30
  4. 15 Correct answer.

Explanation

Choosing a committee is a combination because order does not matter. C(6,2) = (6 × 5)/2 = 15.

Question 44Mathematics

The line 3x + 4y = 12 intersects the x-axis at which point?

  1. (0, 4)
  2. (4, 0) Correct answer.
  3. (3, 0)
  4. (0, 3)

Explanation

On the x-axis, y = 0. Substituting gives 3x = 12, so x = 4, and the point is (4, 0).

Question 45Mathematics

What is the remainder when x³ − 2x² + x − 5 is divided by (x − 2)?

  1. 5
  2. 3
  3. −1
  4. −3 Correct answer.

Explanation

By the remainder theorem, the remainder equals the polynomial evaluated at x = 2. That gives 8 − 8 + 2 − 5 = −3.

Question 46Mathematics

If the roots of x² + bx + c = 0 are 3 and −5, what is the value of b + c?

  1. −13 Correct answer.
  2. 2
  3. −2
  4. 13

Explanation

The sum of the roots is −b, so −b = 3 + (−5) = −2, giving b = 2. The product is c, so c = 3 × (−5) = −15. Thus b + c = 2 − 15 = −13.

Question 47Mathematics

What is the sum of the infinite geometric series 8 + 4 + 2 + 1 + ...?

  1. 16 Correct answer.
  2. 32
  3. 15
  4. 14

Explanation

The first term is a = 8 and the ratio is r = 1/2, with |r| < 1 so the series converges. The sum is a/(1 − r) = 8/(1/2) = 16.

Question 48Mathematics

A bag holds 5 white and 3 black balls. Two balls are drawn without replacement. What is the probability that both are white?

  1. 5/14 Correct answer.
  2. 5/8
  3. 10/56
  4. 25/64

Explanation

The probability the first ball is white is 5/8. Given that, 4 white balls remain among 7, so the second is white with probability 4/7. Multiplying gives 20/56 = 5/14.

Question 49Mathematics

For what values of x is the function f(x) = x² − 4x + 3 negative?

  1. x < 1 or x > 3
  2. x < −3 or x > −1
  3. 1 < x < 3 Correct answer.
  4. −3 < x < −1

Explanation

Factor as (x − 1)(x − 3). The parabola opens upward, so it lies below the x-axis between its roots, that is, for 1 < x < 3.

Question 50Mathematics

The arithmetic mean of five numbers is 12. If four of the numbers are 8, 10, 14, and 15, what is the fifth number?

  1. 12
  2. 16
  3. 11
  4. 13 Correct answer.

Explanation

The mean of five numbers is 12, so their total is 5 × 12 = 60. The four given numbers add to 8 + 10 + 14 + 15 = 47, so the fifth number is 60 − 47 = 13.