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BTEB Polytechnic Admission study materials
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BTEB Polytechnic Admission practice questions

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Question 1Mathematics

What is the value of the expression 3 + 4 × 2?

  1. 11 Correct answer.
  2. 24
  3. 14
  4. 9

Explanation

Multiplication is performed before addition, so 4 × 2 = 8 and then 3 + 8 = 11. Evaluating strictly left to right would give a different, incorrect result.

Question 2Mathematics

What is the greatest common divisor of 36 and 60?

  1. 12 Correct answer.
  2. 6
  3. 4
  4. 18

Explanation

Factor both numbers: 36 = 2² × 3² and 60 = 2² × 3 × 5. The common prime factors with the smallest exponents give 2² × 3 = 12.

Question 3Mathematics

A triangle has interior angles measuring 50° and 60°. What is the third angle?

  1. 80°
  2. 110°
  3. 70° Correct answer.
  4. 60°

Explanation

The angles of a triangle always add up to 180°. Subtracting the two known angles gives 180° − 50° − 60° = 70°.

Question 4Mathematics

What is the slope of the line passing through the points (1, 2) and (4, 11)?

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

Explanation

Slope equals the change in y divided by the change in x. Here (11 − 2)/(4 − 1) = 9/3 = 3.

Question 5Mathematics

What is the value of 2⁵?

  1. 32 Correct answer.
  2. 25
  3. 64
  4. 10

Explanation

The exponent indicates repeated multiplication of the base: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.

Question 6Mathematics

What is the median of the data set 4, 7, 9, 12, 15?

  1. 9 Correct answer.
  2. 12
  3. 7
  4. 9.4

Explanation

The median is the middle value when the data are arranged in order. With five ordered values, the third one, 9, is the median.

Question 7Mathematics

If f(x) = 2x + 3, what is f(5)?

  1. 10
  2. 8
  3. 13 Correct answer.
  4. 16

Explanation

Substitute x = 5 into the rule: 2(5) + 3 = 10 + 3 = 13.

Question 8Mathematics

What is the probability of getting a head when a fair coin is tossed once?

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

Explanation

A fair coin has two equally likely outcomes, head and tail. The probability of a head is therefore one favourable outcome out of two, namely 1/2.

Question 9Mathematics

Solve for x: 3x − 7 = 11.

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

Explanation

Add 7 to both sides to get 3x = 18, then divide both sides by 3 to obtain x = 6.

Question 10Mathematics

The sum of two consecutive integers is 47. What is the smaller integer?

  1. 22
  2. 25
  3. 24
  4. 23 Correct answer.

Explanation

Let the integers be n and n + 1, so 2n + 1 = 47, giving 2n = 46 and n = 23. The pair is 23 and 24.

Question 11Mathematics

What is the area of a circle with radius 7 cm, using π = 22/7?

  1. 44 cm²
  2. 49 cm²
  3. 154 cm² Correct answer.
  4. 308 cm²

Explanation

The area of a circle is πr². With r = 7, this is (22/7) × 49 = 22 × 7 = 154 cm².

Question 12Mathematics

Simplify the expression (x³ · x⁴) / x².

  1. x⁶
  2. x⁹
  3. x²
  4. x⁵ Correct answer.

Explanation

When multiplying powers with the same base, add the exponents to get x⁷. Dividing by x² subtracts the exponents, giving x⁷⁻² = x⁵.

Question 13Mathematics

In a right triangle, the legs measure 6 cm and 8 cm. What is the length of the hypotenuse?

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

Explanation

By the Pythagorean theorem the hypotenuse satisfies c² = 6² + 8² = 36 + 64 = 100. Taking the positive square root gives c = 10 cm.

Question 14Mathematics

What is log₂ 32?

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

Explanation

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

Question 15Mathematics

A shop offers a 20% discount on an item priced at 250 taka. What is the selling price?

  1. 50 taka
  2. 300 taka
  3. 230 taka
  4. 200 taka Correct answer.

Explanation

The discount is 20% of 250, which equals 50 taka. Subtracting this from the marked price gives 250 − 50 = 200 taka.

Question 16Mathematics

The roots of the quadratic equation x² − 5x + 6 = 0 are:

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

Explanation

We need two numbers whose product is 6 and whose sum is 5. These are 2 and 3, so the equation factors as (x − 2)(x − 3) = 0.

Question 17Mathematics

Two triangles are similar, and the ratio of their corresponding sides is 3:5. What is the ratio of their areas?

  1. 6:10
  2. 3:5
  3. 9:25 Correct answer.
  4. 27:125

Explanation

For similar figures, the ratio of areas equals the square of the ratio of corresponding lengths. Squaring 3:5 gives 9:25.

Question 18Mathematics

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

  1. 1 Correct answer.
  2. 0
  3. √3/2
  4. 1/2

Explanation

Both sin 30° and cos 60° equal 1/2. Adding them gives 1/2 + 1/2 = 1.

Question 19Mathematics

A bag contains 3 red and 5 blue balls. Two balls are drawn without replacement. What is the probability that both are red?

  1. 1/4
  2. 3/28 Correct answer.
  3. 3/8
  4. 9/64

Explanation

The probability of a red ball first is 3/8, and then 2/7 for the second since one red ball is removed. Multiplying gives (3/8)(2/7) = 6/56 = 3/28.

Question 20Mathematics

What is the sum of the first 20 terms of the arithmetic sequence 2, 5, 8, 11, ...?

  1. 610 Correct answer.
  2. 580
  3. 600
  4. 620

Explanation

Here a = 2 and d = 3, so the 20th term is 2 + 19 × 3 = 59. The sum is (20/2)(2 + 59) = 10 × 61 = 610.

Question 21Mathematics

For what value of k does the system kx + 2y = 4 and 4x + y = 3 have no unique solution?

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

Explanation

A square linear system fails to have a unique solution when the coefficient determinant vanishes. The determinant is k(1) − 2(4) = k − 8, which is zero when k = 8.

Question 22Mathematics

The polynomial x³ − 6x² + 11x − 6 has roots 1, 2, and 3. What is the value of the expression 1/1 + 1/2 + 1/3 formed from these roots?

  1. 5/6
  2. 1
  3. 11/6 Correct answer.
  4. 6/11

Explanation

Combine the fractions over the common denominator 6: 6/6 + 3/6 + 2/6 = 11/6. This also equals the sum of pairwise products divided by the product of roots, 11/6.

Question 23Mathematics

What is the value of the limit as x approaches 2 of (x² − 4)/(x − 2)?

  1. 0
  2. The limit does not exist
  3. 2
  4. 4 Correct answer.

Explanation

Factor the numerator as (x − 2)(x + 2), which cancels the denominator for x ≠ 2. The expression then equals x + 2, whose value at x = 2 is 4.

Question 24Mathematics

If tan θ = 3/4 and θ lies in the first quadrant, what is the value of sin θ + cos θ?

  1. 1
  2. 5/7
  3. 7/5 Correct answer.
  4. 12/25

Explanation

With tan θ = 3/4, take the opposite side as 3 and the adjacent as 4, so the hypotenuse is 5. Then sin θ = 3/5 and cos θ = 4/5, giving a sum of 7/5.

Question 25Mathematics

A matrix A is 2×2 with determinant 5. What is the determinant of 3A?

  1. 45 Correct answer.
  2. 5
  3. 9
  4. 15

Explanation

For an n×n matrix, det(kA) = kⁿ det(A). Here n = 2 and k = 3, so det(3A) = 3² × 5 = 9 × 5 = 45.

Question 26Mathematics

What is the value of the expression 5 + 3 × 2² − 4 ÷ 2?

  1. 15 Correct answer.
  2. 18
  3. 13
  4. 11

Explanation

Order of operations requires evaluating the exponent first: 2² = 4. Then multiply and divide left to right: 3 × 4 = 12 and 4 ÷ 2 = 2. Finally add and subtract: 5 + 12 − 2 = 15.

Question 27Mathematics

A number is increased by 25% and the result is 150. What was the original number?

  1. 112.5
  2. 125
  3. 120 Correct answer.
  4. 100

Explanation

An increase of 25% means the new value equals 1.25 times the original, so the original equals 150 ÷ 1.25 = 120. Checking: 120 + 0.25 × 120 = 120 + 30 = 150.

Question 28Mathematics

What is the value of (2/3) ÷ (4/9)?

  1. 27/8
  2. 8/27
  3. 2/3
  4. 3/2 Correct answer.

Explanation

Dividing by a fraction is the same as multiplying by its reciprocal, so (2/3) ÷ (4/9) = (2/3) × (9/4). Simplifying gives 18/12 = 3/2.

Question 29Mathematics

Which of the following numbers is irrational?

  1. 22/7
  2. √49
  3. 0.333... (repeating)
  4. √11 Correct answer.

Explanation

A number is irrational when it cannot be written as a ratio of two integers. The square root of 11 is not a perfect square, so it has a non-terminating, non-repeating decimal expansion. The other three values are all rational.

Question 30Mathematics

A train travels 180 km in 2.5 hours. What is its average speed in km/h?

  1. 90
  2. 80
  3. 72 Correct answer.
  4. 75

Explanation

Average speed equals total distance divided by total time. Dividing 180 by 2.5 gives 72 km/h. Checking: 72 × 2.5 = 180 km.

Question 31Mathematics

If x + y = 10 and x − y = 4, what is the value of xy?

  1. 25
  2. 40
  3. 21 Correct answer.
  4. 24

Explanation

Adding the two equations gives 2x = 14, so x = 7, and then y = 3. Their product is 7 × 3 = 21. Alternatively, xy = ((x+y)² − (x−y)²)/4 = (100 − 16)/4 = 21.

Question 32Mathematics

The 4th term of an arithmetic sequence is 11 and the 9th term is 26. What is the first term?

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

Explanation

The difference between the 9th and 4th terms spans 5 common differences: 26 − 11 = 15, so d = 3. Since the 4th term equals a + 3d = a + 9 = 11, the first term a = 2.

Question 33Mathematics

What is the sum of the interior angles of a regular hexagon?

  1. 540°
  2. 1080°
  3. 720° Correct answer.
  4. 900°

Explanation

The interior angles of an n-sided polygon sum to (n − 2) × 180°. For a hexagon, n = 6, so the sum is 4 × 180° = 720°. Each interior angle of a regular hexagon is therefore 120°.

Question 34Mathematics

A cylinder has radius 3 cm and height 10 cm. Using π = 3.14, what is its total surface area?

  1. 244.92 cm² Correct answer.
  2. 188.4 cm²
  3. 282.6 cm²
  4. 94.2 cm²

Explanation

The total surface area of a cylinder is 2πr² + 2πrh. Here 2πr² = 2 × 3.14 × 9 = 56.52 and 2πrh = 2 × 3.14 × 3 × 10 = 188.4, giving 244.92 cm².

Question 35Mathematics

If the roots of x² + bx + c = 0 are 4 and −2, what are the values of b and c?

  1. b = −2, c = 8
  2. b = 2, c = −8
  3. b = 2, c = 8
  4. b = −2, c = −8 Correct answer.

Explanation

For a quadratic with roots p and q, the sum of roots equals −b and the product equals c. The sum 4 + (−2) = 2, so b = −2, and the product 4 × (−2) = −8, so c = −8.

Question 36Mathematics

In how many ways can the letters of the word 'LEVEL' be arranged?

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

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 37Mathematics

What is the value of cos 0° + tan 45° − sin 90°?

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

Explanation

Using standard values, cos 0° = 1, tan 45° = 1, and sin 90° = 1. Substituting gives 1 + 1 − 1 = 1.

Question 38Mathematics

If the point (2, 5) lies on the line 3x − ky = 1, what is the value of k?

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

Explanation

Substituting x = 2 and y = 5 into the equation gives 6 − 5k = 1. Solving, −5k = −5, so k = 1. Checking: 3(2) − 1(5) = 6 − 5 = 1.

Question 39Mathematics

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

  1. 16 Correct answer.
  2. 15
  3. 12
  4. 24

Explanation

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

Question 40Mathematics

A function is defined by f(x) = x² − 4x + 7 for all real x. What is the minimum value of f(x)?

  1. 7
  2. 3 Correct answer.
  3. −9
  4. 4

Explanation

Completing the square gives f(x) = (x − 2)² + 3. Since a square is never negative, the smallest value occurs at x = 2 and equals 3.

Question 41Physics

Which SI unit is used to express the amount of electric current flowing through a conductor?

  1. Coulomb
  2. Volt
  3. Ampere Correct answer.
  4. Ohm

Explanation

Electric current is the rate at which charge passes a point, and its SI unit is the ampere, defined as one coulomb per second. Coulomb measures charge, volt measures potential difference, and ohm measures resistance.

Question 42Physics

A body moves along a straight line with constant acceleration. Its velocity-time graph is a straight line that crosses the time axis. What does the point where it crosses the axis represent?

  1. The body has maximum acceleration
  2. The body has reversed its direction of acceleration
  3. The body has travelled maximum distance
  4. The body is at rest instantaneously Correct answer.

Explanation

Velocity is plotted on the vertical axis, so a crossing of the time axis means velocity equals zero at that instant. The body is momentarily at rest there and then reverses its direction of motion.

Question 43Physics

A block of mass 5 kg rests on a horizontal surface. What is the normal force exerted by the surface on the block when the block is at rest? (Take g = 9.8 m/s²)

  1. 98 N
  2. 49 N Correct answer.
  3. 5 N
  4. 0 N

Explanation

With no vertical acceleration, the normal force balances the weight of the block. Weight equals mass times gravitational acceleration, so 5 kg × 9.8 m/s² = 49 N.

Question 44Physics

Two forces of 3 N and 4 N act at right angles to each other on a particle. What is the magnitude of the resultant force?

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

Explanation

Perpendicular forces combine by the Pythagorean rule, since the resultant is the vector sum. The magnitude is the square root of (3² + 4²) = 25, which gives 5 N.

Question 45Physics

Which quantity remains constant for a body moving in a circle at uniform speed?

  1. Speed Correct answer.
  2. Acceleration
  3. Momentum
  4. Velocity

Explanation

In uniform circular motion the direction of motion changes continuously, so velocity, acceleration, and momentum all change direction. Speed, the magnitude of velocity, stays constant.

Question 46Physics

A force of 20 N acts on a body and displaces it 3 m in the direction of the force. How much work is done by the force?

  1. 60 J Correct answer.
  2. 180 J
  3. 6.7 J
  4. 23 J

Explanation

Work equals the product of force and displacement when both point in the same direction. Multiplying 20 N by 3 m gives 60 J.

Question 47Physics

The period of a simple pendulum is independent of which of the following?

  1. Mass of the bob Correct answer.
  2. Amplitude for small oscillations
  3. Acceleration due to gravity
  4. Length of the pendulum

Explanation

For small swings the period is 2π times the square root of length divided by g. The mass of the bob does not appear in this expression, so it has no effect on the period.

Question 48Physics

Which of the following is a scalar quantity?

  1. Torque
  2. Force
  3. Displacement
  4. Temperature Correct answer.

Explanation

A scalar is fully described by magnitude alone, and temperature is such a quantity. Displacement, torque, and force all require a direction as well as a magnitude.

Question 49Physics

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

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

Explanation

Using s = ut + ½at² with initial velocity zero gives s = ½ × 2 × 25 = 25 m. The final velocity would be 10 m/s, but distance depends on the average velocity of 5 m/s.

Question 50Physics

A ball is thrown vertically upward with a speed of 20 m/s. Taking g = 10 m/s², what is the maximum height reached?

  1. 10 m
  2. 20 m Correct answer.
  3. 40 m
  4. 80 m

Explanation

At the highest point the velocity is zero, so v² = u² − 2gh gives h = u²/(2g). Substituting 400/(2 × 10) yields 20 m.