College Entrance Exam Reviewer 3

College Entrance 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. Evaluate the limit: \( \lim_{x \to 0} \frac{\sin(3x)}{x} \)

A) 3
B) 1
C) 0
D) Undefined

2. In Shakespeare's "Hamlet", what is the significance of the phrase "To be, or not to be"?

A) Contemplation of existence
B) Reflection on love
C) Commentary on revenge
D) Expression of anger

3. Which of the following compounds is aromatic?

A) Benzene
B) Cyclohexane
C) Propane
D) Ethyne

4. Solve the system: 2x + 3y = 7 and 4x - y = 5

A) (2,1)
B) (2,1/3)
C) (1,1)
D) (3,1)

5. Which planet has the strongest magnetic field in the solar system?

A) Earth
B) Saturn
C) Jupiter
D) Neptune

6. In English grammar, which of the following is an example of a subjunctive mood?

A) If I were taller, I would play basketball.
B) I will play basketball tomorrow.
C) I am tall enough to play basketball.
D) I have played basketball yesterday.

7. What is the solution to the differential equation \( \frac{dy}{dx} = ky \)?

A) y = kx
B) y = Ce^{kx}
C) y = kx²
D) y = ln(kx)

8. What is the powerhouse of the cell?

A) Nucleus
B) Ribosome
C) Mitochondrion
D) Endoplasmic reticulum

9. Which philosopher is associated with the "Allegory of the Cave"?

A) Aristotle
B) Plato
C) Socrates
D) Descartes

10. What is the determinant of the matrix \[ \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \]?

A) 5
B) 10
C) 8
D) 2

11. Find the derivative of \( f(x) = \ln(x^2 + 1) \).

A) \( \frac{2x}{x^2} \)
B) \( \frac{2x}{x^2+1} \)
C) \( \frac{1}{2x+1} \)
D) \( \frac{x^2+1}{2x} \)

12. In English literature, what does the term "bildungsroman" refer to?

A) A tragedy
B) A coming-of-age story
C) A dystopian tale
D) A mystery novel

13. Which quantum number indicates the orientation of an orbital?

A) Principal quantum number (n)
B) Magnetic quantum number (m_l)
C) Spin quantum number (m_s)
D) Azimuthal quantum number (l)

14. Solve for x: \( 3^{2x+1} = 81 \).

A) 2
B) 1
C) 1.5
D) 3

15. Which scientist first proposed that electrons orbit the nucleus in fixed paths?

A) Schrödinger
B) Heisenberg
C) Rutherford
D) Bohr

16. Identify the grammatical error: "Each of the students have submitted their papers."

A) "have" should be "has"
B) "their" should be "his or her"
C) "submitted" should be "submitting"
D) No error

17. A projectile is fired with an initial velocity of 40 m/s at 30° above the horizontal. What is the maximum height?

A) 20.4 m
B) 25.5 m
C) 30.1 m
D) 18.9 m

18. Who painted the "School of Athens"?

A) Michelangelo
B) Da Vinci
C) Raphael
D) Botticelli

19. Which of the following series converges?

A) \( \sum \frac{n}{n+1} \)
B) \( \sum \frac{1}{n} \)
C) \( \sum \frac{1}{n^2} \)
D) \( \sum 1 \)

20. What is the main function of ribosomes in a cell?

A) Energy production
B) Protein synthesis
C) DNA replication
D) Lipid storage

21. If a 6-kg object is moving at 3 m/s, what is its kinetic energy?

A) 18 J
B) 27 J
C) 54 J
D) 9 J

22. What is the value of \( \int_0^1 3x^2 dx \)?

A) 1
B) 3
C) 0.5
D) 1.5

23. Which novel is considered the first modern novel?

A) Don Quixote
B) Paradise Lost
C) The Odyssey
D) Beowulf

24. What is the oxidation state of Cr in \( Cr_2O_7^{2-} \)?

A) +2
B) +6
C) +3
D) +4

25. Solve: \( \sqrt{2x+3} = 5 \)

A) x = 10
B) x = 6
C) x = 11
D) x = 8

26. What is the largest organ in the human body?

A) Liver
B) Heart
C) Skin
D) Brain

27. The binomial expansion of \( (x + 2)^3 \) is:

A) \( x^3 + 6x^2 + 4x + 8 \)
B) \( x^3 + 6x^2 + 12x + 8 \)
C) \( x^3 + 3x^2 + 6x + 8 \)
D) \( x^3 + 4x^2 + 6x + 8 \)

28. Who is considered the father of modern physics?

A) Albert Einstein
B) Isaac Newton
C) Galileo Galilei
D) Nikola Tesla

29. Which country has the most natural lakes?

A) Russia
B) USA
C) India
D) Canada

30. Simplify: \( \frac{4^3 \times 4^2}{4^4} \)

A) 4
B) 8
C) 2
D) 16

Result

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