Q. A ray of light passes from air into water. If the angle of incidence is 30 degrees, what is the angle of refraction in water? (Refractive index of water = 1.33)
A.22.1 degrees
B.30 degrees
C.36.9 degrees
D.45 degrees
Solution
Using Snell's law, n1*sin(θ1) = n2*sin(θ2), we find θ2 = 22.1 degrees.
Q. A ray of light strikes a glass surface at an angle of incidence of 30 degrees. If the refractive index of glass is 1.5, what is the angle of refraction? (2022)
A.20 degrees
B.30 degrees
C.40 degrees
D.50 degrees
Solution
Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), i = 30 degrees, n2 = 1.5 (glass). Therefore, sin(r) = (1 * sin(30))/1.5 = 0.333. Thus, r = sin^(-1)(0.333) ≈ 19.5 degrees, which is approximately 20 degrees.
Q. A recent analysis shows that cities with better public transportation systems have lower traffic congestion. What can be inferred from this analysis?
A.Traffic congestion is solely caused by poor public transportation.
B.Better public transportation may help reduce traffic congestion.
C.All cities with low congestion have excellent public transportation.
D.Public transportation has no effect on traffic patterns.
Solution
The analysis indicates a potential benefit of improved public transportation in reducing traffic congestion.
Correct Answer: B — Better public transportation may help reduce traffic congestion.
Q. A recent report claims that students who participate in extracurricular activities have better time management skills. What can be inferred from this report?
A.All students with good time management participate in extracurricular activities.
B.Extracurricular activities improve time management skills.
C.Students without extracurricular activities have poor time management skills.
D.There is a relationship between extracurricular participation and time management skills.
Solution
The report suggests a relationship between participation in extracurricular activities and time management skills, but does not imply causation or that all students fit this pattern.
Correct Answer: D — There is a relationship between extracurricular participation and time management skills.
Q. A recent report states that students who engage in extracurricular activities tend to perform better academically. What can be concluded from this report?
A.Extracurricular activities are the only factor influencing academic performance.
B.Students who perform well academically do not participate in extracurricular activities.
C.Engaging in extracurricular activities may contribute to better academic performance.
D.All students should participate in extracurricular activities to succeed.
Solution
The report indicates a positive relationship between extracurricular activities and academic performance, suggesting that participation may enhance performance.
Correct Answer: C — Engaging in extracurricular activities may contribute to better academic performance.
Q. A recent survey found that 70% of people who exercise regularly report feeling happier. What can be inferred from this survey?
A.Exercise causes happiness.
B.People who are happier tend to exercise more.
C.70% of all people are happy.
D.Regular exercise is the only factor affecting happiness.
Solution
While the survey shows a correlation between exercise and happiness, it does not establish causation, suggesting that happier people may be more inclined to exercise.
Correct Answer: B — People who are happier tend to exercise more.
Q. A recent survey found that students who study in groups tend to perform better than those who study alone. What can be inferred from this survey?
A.Studying alone is ineffective for all students.
B.Group study is the only way to succeed academically.
C.Collaboration may enhance understanding and retention of material.
D.All students prefer studying in groups.
Solution
The survey indicates a trend that suggests collaboration may improve academic performance, but it does not claim it is the only method or that all students prefer it.
Correct Answer: C — Collaboration may enhance understanding and retention of material.
Q. A rectangle has a length that is twice its width. If the area of the rectangle is 200 square units, what is the width of the rectangle?
A.10 units
B.20 units
C.15 units
D.25 units
Solution
Let the width be x units. Then the length is 2x units. Area = length × width = 2x * x = 2x^2. Setting this equal to 200 gives 2x^2 = 200, so x^2 = 100, and x = 10 units.
