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Afghanistan Kankor study materials
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Afghanistan Kankor practice questions

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Question 1Mathematics

What is the value of 7 + 5 × 2?

  1. 24
  2. 14
  3. 17 Correct answer.
  4. 19

Explanation

By the order of operations, multiplication is performed before addition, so 5 × 2 = 10 is computed first. Adding 7 gives 7 + 10 = 17.

Question 2Mathematics

Which number is prime?

  1. 27
  2. 21
  3. 29 Correct answer.
  4. 33

Explanation

A prime number has exactly two positive divisors: 1 and itself. The number 29 is not divisible by 2, 3, or 5, and no factor below its square root divides it, so it is prime.

Question 3Mathematics

Solve for x: 3x − 7 = 11.

  1. x = 6 Correct answer.
  2. x = 18
  3. x = 3
  4. x = 4

Explanation

Add 7 to both sides to obtain 3x = 18, then divide both sides by 3 to get x = 6. Each step preserves equality, so the solution is unique.

Question 4Mathematics

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

  1. 1/4
  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. The formula m = (y₂ − y₁)/(x₂ − x₁) gives the constant rate of change of the line.

Question 5Mathematics

What is the value of sin 30°?

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

Explanation

In a 30-60-90 triangle the side opposite 30° is half the hypotenuse, so sin 30° = 1/2. This is a standard exact trigonometric value.

Question 6Mathematics

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

  1. 120 Correct answer.
  2. 20
  3. 60
  4. 25

Explanation

The factorial n! is the product of all positive integers up to n, so 5! = 5 × 4 × 3 × 2 × 1 = 120.

Question 7Mathematics

What is the next term in the arithmetic sequence 4, 9, 14, 19, ...?

  1. 23
  2. 24 Correct answer.
  3. 25
  4. 28

Explanation

An arithmetic sequence adds a fixed common difference each step; here the difference is 9 − 4 = 5. Adding 5 to 19 gives 24.

Question 8Mathematics

What is the value of |−9|?

  1. 0
  2. 9 Correct answer.
  3. −9
  4. 1/9

Explanation

The absolute value of a number is its distance from zero on the number line, which is always non-negative. Since −9 is 9 units from zero, |−9| = 9.

Question 9Mathematics

If f(x) = 2x² − 3x + 1, what is f(2)?

  1. 7
  2. 11
  3. 5
  4. 3 Correct answer.

Explanation

Substitute x = 2 into the expression: 2(2²) − 3(2) + 1 = 8 − 6 + 1 = 3. Evaluating carefully term by term avoids sign errors.

Question 10Mathematics

What is the sum of the roots of the quadratic equation x² − 7x + 10 = 0?

  1. −7
  2. 10
  3. 7 Correct answer.
  4. −10

Explanation

For ax² + bx + c = 0, the sum of the roots equals −b/a. Here a = 1 and b = −7, so the sum is 7.

Question 11Mathematics

Solve the inequality 2x + 5 > 13.

  1. x > 9
  2. x < 4
  3. x > 18
  4. x > 4 Correct answer.

Explanation

Subtract 5 from both sides to get 2x > 8, then divide by the positive 2 to obtain x > 4. Dividing by a positive number does not reverse the inequality.

Question 12Mathematics

In a right triangle, the two legs have lengths 6 and 8. What is the length of the hypotenuse?

  1. 48
  2. 12
  3. 14
  4. 10 Correct answer.

Explanation

By the Pythagorean theorem, the hypotenuse squared equals the sum of the squares of the legs: 6² + 8² = 36 + 64 = 100. Thus the hypotenuse is √100 = 10.

Question 13Mathematics

What is the area of a circle with radius 3?

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

Explanation

The area of a circle is A = πr². With r = 3, this gives A = π(3²) = 9π.

Question 14Mathematics

What is log₂ 32?

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

Explanation

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

Question 15Mathematics

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

Explanation

There are 4 red balls out of 10 total balls, so the probability is 4/10 = 2/5. Probability is favorable outcomes divided by total outcomes.

Question 16Mathematics

What is the 10th term of the arithmetic sequence with first term 3 and common difference 4?

  1. 36
  2. 43
  3. 39 Correct answer.
  4. 40

Explanation

The nth term of an arithmetic sequence is aₙ = a₁ + (n − 1)d. Substituting a₁ = 3, d = 4, and n = 10 gives 3 + 9(4) = 39.

Question 17Mathematics

What is the determinant of the matrix [[3, 4], [2, 5]]?

  1. 7 Correct answer.
  2. 23
  3. −7
  4. 15

Explanation

For a 2×2 matrix [[a, b], [c, d]], the determinant is ad − bc. Here that is (3)(5) − (4)(2) = 15 − 8 = 7.

Question 18Mathematics

Simplify (x³)(x⁴).

  1. 2x⁷
  2. x¹²
  3. x⁷ Correct answer.
  4. x

Explanation

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

Question 19Mathematics

The sum of two numbers is 20 and their difference is 4. What is the larger number?

  1. 10
  2. 12 Correct answer.
  3. 16
  4. 8

Explanation

Let the numbers be x and y with x + y = 20 and x − y = 4. Adding the equations gives 2x = 24, so x = 12.

Question 20Mathematics

If a fair coin is tossed three times, what is the probability of getting exactly two heads?

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

Explanation

There are 2³ = 8 equally likely outcomes, and exactly three of them (HHT, HTH, THH) have two heads. Thus the probability is 3/8.

Question 21Mathematics

What is the vertex of the parabola y = x² − 4x + 1?

  1. (2, −3) Correct answer.
  2. (4, 1)
  3. (−2, 13)
  4. (2, 1)

Explanation

The x-coordinate of the vertex is −b/(2a) = 4/2 = 2. Substituting x = 2 gives y = 4 − 8 + 1 = −3, so the vertex is (2, −3).

Question 22Mathematics

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

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

Explanation

An infinite geometric series with |r| < 1 sums to a/(1 − r). Here a = 1 and r = 1/2, so the sum is 1/(1 − 1/2) = 2.

Question 23Mathematics

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

  1. k = 6 Correct answer.
  2. k = 0
  3. k = 3
  4. k = 9

Explanation

A quadratic has exactly one real root when its discriminant b² − 4ac equals zero. Here that means k² − 36 = 0, so k = 6 (or −6).

Question 24Mathematics

If tan θ = 3/4 and θ is an acute angle, what is sin θ?

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

Explanation

With tan θ = opposite/adjacent = 3/4, the hypotenuse is √(3² + 4²) = 5. Thus sin θ = opposite/hypotenuse = 3/5.

Question 25Mathematics

How many distinct ways can the letters of the word LEVEL be arranged?

  1. 120
  2. 60
  3. 20
  4. 30 Correct answer.

Explanation

The word has 5 letters with L repeated twice and E repeated twice. The number of distinct arrangements is 5!/(2!·2!) = 120/4 = 30.

Question 26Mathematics

What is the value of 7P2, the number of ordered arrangements of 2 objects chosen from 7 distinct objects?

  1. 49
  2. 14
  3. 21
  4. 42 Correct answer.

Explanation

The permutation formula is nPr = n!/(n−r)!. Here 7P2 = 7!/5! = 7 × 6 = 42, since only the last two factors of 7! survive the division.

Question 27Mathematics

What is the slope of the line passing through the points (2, 5) and (6, 13)?

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

Explanation

Slope equals the change in y divided by the change in x. Here (13 − 5)/(6 − 2) = 8/4 = 2.

Question 28Mathematics

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

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

Explanation

The standard exact values are sin 30° = 1/2 and cos 60° = 1/2. Their sum is 1/2 + 1/2 = 1.

Question 29Mathematics

What is the modulus (absolute value) of the complex number 3 − 4i?

  1. 1
  2. 7
  3. 5 Correct answer.
  4. 25

Explanation

For z = a + bi the modulus is √(a² + b²). Here √(9 + 16) = √25 = 5.

Question 30Mathematics

What is the remainder when the polynomial x³ − 2x² + 4x − 7 is divided by x − 1?

  1. −7
  2. −4 Correct answer.
  3. 4
  4. 0

Explanation

By the remainder theorem, the remainder on division by x − 1 equals the polynomial evaluated at x = 1. Substituting gives 1 − 2 + 4 − 7 = −4.

Question 31Mathematics

A geometric sequence has first term 3 and common ratio 2. What is the sum of its first 5 terms?

  1. 96
  2. 93 Correct answer.
  3. 45
  4. 48

Explanation

The sum of n terms is a(rⁿ − 1)/(r − 1). With a = 3, r = 2, n = 5: 3(32 − 1)/(2 − 1) = 3 × 31 = 93.

Question 32Mathematics

What is the value of the expression cos² 40° + cos² 50°?

  1. 0
  2. sin 40°
  3. 1 Correct answer.
  4. 2

Explanation

Since 50° = 90° − 40°, we have cos 50° = sin 40°. Then cos²40° + sin²40° = 1 by the Pythagorean identity.

Question 33Mathematics

A cone has base radius 3 and height 4. What is its slant height?

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

Explanation

The slant height, radius, and height form a right triangle, so l = √(r² + h²) = √(9 + 16) = 5.

Question 34Mathematics

What is the inverse of the function f(x) = 3x − 6?

  1. f⁻¹(x) = 3x + 6
  2. f⁻¹(x) = (x + 6)/3 Correct answer.
  3. f⁻¹(x) = 1/(3x − 6)
  4. f⁻¹(x) = (x − 6)/3

Explanation

Set y = 3x − 6 and solve for x: x = (y + 6)/3. Swapping the variable names gives f⁻¹(x) = (x + 6)/3.

Question 35Mathematics

What is the value of the binomial coefficient C(6, 2)?

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

Explanation

C(n, r) = n!/(r!(n−r)!). Thus C(6,2) = 6!/(2!·4!) = (6 × 5)/2 = 15, dividing out the order of the chosen pair.

Question 36Mathematics

What is the equation of the line perpendicular to y = 2x + 1 that passes through the point (4, 3)?

  1. y = −x/2 + 5 Correct answer.
  2. y = x/2 + 1
  3. y = 2x − 5
  4. y = −2x + 11

Explanation

A perpendicular line has slope equal to the negative reciprocal, here −1/2. Using point-slope form: y − 3 = −(1/2)(x − 4), which simplifies to y = −x/2 + 5.

Question 37Mathematics

In how many ways can a committee of 3 people be chosen from 8 people?

  1. 24
  2. 512
  3. 336
  4. 56 Correct answer.

Explanation

Order does not matter for a committee, so this is a combination: C(8,3) = 8!/(3!·5!) = (8 × 7 × 6)/6 = 56.

Question 38Mathematics

What is the sum of the first 20 positive odd integers 1 + 3 + 5 + ... + 39?

  1. 420
  2. 400 Correct answer.
  3. 800
  4. 380

Explanation

The sum of the first n odd integers equals n². With n = 20 the sum is 20² = 400.

Question 39Mathematics

The roots of a quadratic equation are 3 and −5. Which equation has exactly these roots?

  1. x² + 2x + 15 = 0
  2. x² − 2x − 15 = 0
  3. x² − 8x + 15 = 0
  4. x² + 2x − 15 = 0 Correct answer.

Explanation

A quadratic with roots r and s is x² − (r + s)x + rs = 0. Here the sum is 3 + (−5) = −2 and the product is −15, giving x² + 2x − 15 = 0.

Question 40Mathematics

If a fair six-sided die is rolled twice, what is the probability that the sum of the two results is 8?

  1. 1/9
  2. 5/36 Correct answer.
  3. 7/36
  4. 1/6

Explanation

There are 36 equally likely ordered outcomes. The pairs summing to 8 are (2,6), (3,5), (4,4), (5,3), (6,2), giving 5 outcomes and a probability of 5/36.

Question 41Physics

A body moves with constant velocity in a straight line. What is the net force acting on it?

  1. Constant and non-zero along the motion
  2. Zero Correct answer.
  3. Directed opposite to the motion
  4. Directed perpendicular to the motion

Explanation

Newton's first law states that a body keeps constant velocity only when the net force on it is zero. Constant velocity means both speed and direction are unchanged, so there is no acceleration. By Newton's second law, zero acceleration requires zero net force.

Question 42Physics

Which SI unit is used to express the work done by a force?

  1. Pascal
  2. Joule Correct answer.
  3. Watt
  4. Newton

Explanation

Work is the product of force and displacement along the force, so its unit is the newton metre, which is named the joule. The joule is the SI unit of energy and work. Newton measures force, watt measures power, and pascal measures pressure.

Question 43Physics

A car starts from rest and accelerates uniformly at 2 m/s² for 5 s. What distance does it cover in this time?

  1. 50 m
  2. 20 m
  3. 25 m Correct answer.
  4. 10 m

Explanation

For uniform acceleration starting from rest, distance is s = ½at². Substituting a = 2 m/s² and t = 5 s gives s = ½ × 2 × 25 = 25 m.

Question 44Physics

Two resistors of 3 Ω and 6 Ω are connected in parallel. What is the equivalent resistance of the combination?

  1. 0.5 Ω
  2. 4.5 Ω
  3. 2 Ω Correct answer.
  4. 9 Ω

Explanation

For two resistors in parallel, 1/R = 1/R₁ + 1/R₂. Here 1/R = 1/3 + 1/6 = 3/6 = 1/2, so R = 2 Ω. The equivalent resistance of a parallel combination is always smaller than the smallest branch resistance.

Question 45Physics

Which of the following is a vector quantity?

  1. Mass
  2. Time
  3. Temperature
  4. Displacement Correct answer.

Explanation

A vector quantity has both magnitude and direction, and displacement specifies how far and in which direction an object has moved. Mass, temperature, and time are scalars because they are fully described by magnitude alone.

Question 46Physics

What is the approximate value of the acceleration due to gravity near the Earth's surface?

  1. 9.8 m/s² Correct answer.
  2. 1.6 m/s²
  3. 6.7 × 10⁻¹¹ N·m²/kg²
  4. 3.0 × 10⁸ m/s

Explanation

Near the Earth's surface, freely falling bodies accelerate at about 9.8 m/s² downward. This value follows from the Earth's mass and radius through Newton's law of gravitation. It is often rounded to 10 m/s² in rough calculations.

Question 47Physics

A wave has a frequency of 50 Hz and a wavelength of 4 m. What is its speed?

  1. 54 m/s
  2. 12.5 m/s
  3. 200 m/s Correct answer.
  4. 0.08 m/s

Explanation

The wave speed equals frequency multiplied by wavelength, v = fλ. With f = 50 Hz and λ = 4 m, v = 200 m/s. Frequency and wavelength are inversely related for a fixed speed.

Question 48Physics

Which colour of visible light has the longest wavelength?

  1. Red Correct answer.
  2. Violet
  3. Green
  4. Yellow

Explanation

Within the visible spectrum, wavelength increases from violet at about 400 nm to red at about 700 nm. Red therefore has the longest wavelength and the lowest frequency of visible light. Violet lies at the opposite, short-wavelength end.

Question 49Physics

A block of mass 4 kg rests on a horizontal surface. If the coefficient of static friction is 0.5 and g = 10 m/s², what is the maximum static friction force?

  1. 8 N
  2. 40 N
  3. 2 N
  4. 20 N Correct answer.

Explanation

The normal force on a horizontal surface equals the weight, N = mg = 4 × 10 = 40 N. The maximum static friction is f = μN = 0.5 × 40 = 20 N. Static friction can take any value up to this maximum.

Question 50Physics

An object is placed 30 cm in front of a converging lens of focal length 10 cm. Where is the image formed?

  1. 10 cm on the same side as the object
  2. 30 cm on the opposite side of the lens
  3. 15 cm on the opposite side of the lens Correct answer.
  4. 20 cm on the same side as the object

Explanation

The thin-lens equation gives 1/f = 1/v + 1/u, with u = 30 cm and f = 10 cm. Thus 1/v = 1/10 − 1/30 = 2/30, so v = 15 cm. A positive image distance means a real image on the opposite side of the lens.