[ DOST 25 ] DOST SCHOLARSHIP EXAM REVIEWER XXV

DOST SCHOLARSHIP EXAM REVIEWER

Instructions:

Please answer each question to the best of your ability. Each question is multiple choice, and only one answer per question is correct. Select the most appropriate answer from the options provided.

When you have completed all questions, click the "Submit" button at the bottom of the page to see your score. Good luck!

1. What is the limit of (sin x)/x as x approaches 0?

A) 1
B) 0
C) Undefined
D) Infinity

2. A particle moves along a line with position given by s(t) = t³ - 6t² + 9t. At what time is the particle at rest?

A) t = 1 and t = 3
B) t = 0 and t = 2
C) t = 2 only
D) t = 0 only

3. Which of the following is NOT a vector quantity?

A) Energy
B) Displacement
C) Force
D) Momentum

4. Simplify: (3√2)(2√3)

A) 5√6
B) 6√2
C) 6√6
D) 5√3

5. The half-life of a certain isotope is 3 years. How much of a 100g sample remains after 9 years?

A) 12.5g
B) 25g
C) 50g
D) 6.25g

6. Solve: ∫ (2x)/(x²+1) dx

A) ln|x² + 1| + C
B) arctan(x) + C
C) x² + 1 + C
D) ln|x| + C

7. Which law states that the total entropy of an isolated system always increases over time?

A) First Law of Thermodynamics
B) Second Law of Thermodynamics
C) Third Law of Thermodynamics
D) Zeroth Law of Thermodynamics

8. Find the sum of the infinite geometric series: 4 + 2 + 1 + 0.5 + ...

A) 8
B) 6
C) 10
D) 7

9. A box is pushed with a force of 20 N causing an acceleration of 2 m/s². What is the mass of the box?

A) 10 kg
B) 5 kg
C) 40 kg
D) 2 kg

10. If f(x) = 2x² - 3x + 5, find f'(x).

A) 4x - 3
B) 2x - 3
C) 4x + 3
D) x² - 3

11. Which trigonometric identity is equivalent to 1 + tan²θ?

A) sec θ
B) sec²θ
C) csc²θ
D) cos²θ

12. What is the molar volume of an ideal gas at STP?

A) 11.2 L
B) 22.4 L
C) 44.8 L
D) 33.6 L

13. Solve: If log₂(x) = 5, what is x?

A) 10
B) 32
C) 2⁵
D) 25

14. An object is thrown upward at 20 m/s. How long will it take to reach its maximum height? (g = 9.8 m/s²)

A) 3.0 s
B) 2.04 s
C) 1.5 s
D) 2.5 s

15. What is the derivative of sin(x)cos(x)?

A) cos²(x)
B) cos(2x)
C) sin²(x)
D) 2sin(x)cos(x)

16. In an arithmetic sequence, the 3rd term is 10 and the 7th term is 22. What is the common difference?

A) 2
B) 3
C) 4
D) 5

17. Which of the following compounds has the highest boiling point?

A) CH₄
B) CO₂
C) H₂O
D) O₂

18. If the vectors a = (2,3) and b = (4,1), what is a · b?

A) 11
B) 10
C) 12
D) 8

19. What is the oxidation number of sulfur in H₂SO₄?

A) +4
B) +6
C) +2
D) +8

20. The probability of getting a head when tossing two coins is:

A) 1/2
B) 1/4
C) 1/3
D) 1/6

21. Solve for x: 2^x = 32

A) 5
B) 4
C) 6
D) 3

22. Which of the following is a prime number?

A) 21
B) 23
C) 25
D) 27

23. Which branch of physics deals with the behavior of objects at very high velocities close to the speed of light?

A) Classical Mechanics
B) Relativity
C) Thermodynamics
D) Electromagnetism

24. What is the solution to the differential equation dy/dx = y?

A) y = x²
B) y = ln(x)
C) y = Ce^x
D) y = x

25. Find the domain of f(x) = 1/√(x-2).

A) x ≥ 0
B) x > 2
C) x ≥ 2
D) All real numbers

26. Which of the following is a Lewis acid?

A) NH₃
B) H₂O
C) BF₃
D) CH₄

27. If a = 2 and b = -3, what is the value of (a-b)²?

A) 1
B) 10
C) 25
D) 5

28. What is the energy of a photon with a frequency of 3 × 10¹⁵ Hz? (Planck's constant h = 6.63×10⁻³⁴ J·s)

A) 2.21×10⁻¹⁹ J
B) 1.99×10⁻¹⁸ J
C) 5.00×10⁻²⁰ J
D) 3.00×10⁻¹⁹ J

29. In probability, the event that includes all outcomes is called:

A) Impossible event
B) Certain event
C) Mutually exclusive event
D) Random event

30. Solve: If the radius of a circle is doubled, the area becomes:

A) Twice
B) Three times
C) Four times
D) Five times

Result

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