Undergraduate
Q. What happens to the pressure of a gas if the volume is decreased while the temperature remains constant?
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A.
Increases
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B.
Decreases
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C.
Remains the same
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D.
Doubles
Solution
According to Boyle's Law, if the volume decreases and temperature is constant, the pressure increases.
Correct Answer: A — Increases
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Q. What happens to the temperature of a gas during an isothermal expansion? (2021)
-
A.
Increases
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B.
Decreases
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C.
Remains constant
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D.
Varies with pressure
Solution
During an isothermal expansion, the temperature of the gas remains constant as the system absorbs heat to do work.
Correct Answer: C — Remains constant
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Q. What happens to the volume of a gas when its temperature increases at constant pressure? (2020)
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A.
Volume decreases
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B.
Volume remains constant
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C.
Volume increases
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D.
Volume fluctuates
Solution
According to Charles's Law, the volume of a gas increases with an increase in temperature at constant pressure.
Correct Answer: C — Volume increases
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Q. What hormone is primarily responsible for regulating blood sugar levels? (2020)
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A.
Insulin
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B.
Glucagon
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C.
Adrenaline
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D.
Cortisol
Solution
Insulin is the hormone produced by the pancreas that lowers blood sugar levels by facilitating the uptake of glucose into cells.
Correct Answer: A — Insulin
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Q. What is 100 ÷ 4 + 25? (2018)
Solution
100 ÷ 4 = 25, then 25 + 25 = 50.
Correct Answer: B — 75
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Q. What is the 3rd term in the expansion of (2x + 3)^4?
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A.
108x^2
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B.
216x^2
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C.
324x^2
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D.
432x^2
Solution
The 3rd term is given by C(4,2) * (2x)^2 * (3)^2 = 6 * 4x^2 * 9 = 216x^2.
Correct Answer: B — 216x^2
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Q. What is the 3rd term in the expansion of (x + 3)^5? (2023)
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A.
45
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B.
90
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C.
135
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D.
180
Solution
The 3rd term is C(5,2) * (3)^2 * (x)^3 = 10 * 9 * x^3 = 90.
Correct Answer: B — 90
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Q. What is the 3rd term in the expansion of (x + 4)^5? (2023)
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A.
80x^3
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B.
160x^3
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C.
240x^3
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D.
320x^3
Solution
The 3rd term is given by C(5,2) * (4)^2 * (x)^3 = 10 * 16 * x^3 = 160x^3.
Correct Answer: C — 240x^3
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Q. What is the 3rd term in the expansion of (x + 4)^6? (2020)
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A.
240x^4
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B.
360x^4
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C.
480x^4
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D.
600x^4
Solution
The 3rd term is C(6,2) * (4)^2 * (x)^4 = 15 * 16 * x^4 = 240x^4.
Correct Answer: B — 360x^4
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Q. What is the 5th term in the expansion of (3x - 2)^7? (2023)
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A.
-1680x^3
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B.
1680x^3
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C.
-2520x^3
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D.
2520x^3
Solution
The 5th term is given by C(7,4) * (3x)^4 * (-2)^3 = 35 * 81 * (-8) = -1680x^3.
Correct Answer: A — -1680x^3
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Q. What is the absolute error in a measurement? (2021)
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A.
The difference between the measured value and the true value
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B.
The average of all measurements
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C.
The maximum value in a set of measurements
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D.
The minimum value in a set of measurements
Solution
Absolute error is defined as the difference between the measured value and the true value.
Correct Answer: A — The difference between the measured value and the true value
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Q. What is the acceleration due to gravity on the surface of the Earth? (2018)
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A.
9.8 m/s²
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B.
10 m/s²
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C.
9.81 m/s²
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D.
8.9 m/s²
Solution
The standard acceleration due to gravity on the surface of the Earth is approximately 9.81 m/s².
Correct Answer: C — 9.81 m/s²
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Q. What is the angle between the lines y = 2x + 1 and y = -1/2x + 3?
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A.
90 degrees
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B.
60 degrees
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C.
45 degrees
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D.
30 degrees
Solution
The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan^(-1) |(m1 - m2) / (1 + m1*m2)| = tan^(-1)(5/4) which is approximately 60 degrees.
Correct Answer: B — 60 degrees
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Q. What is the area of a circle with a diameter of 16 cm? (2023) 2023
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A.
64π cm²
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B.
32π cm²
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C.
16π cm²
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D.
8π cm²
Solution
Radius = diameter/2 = 16/2 = 8 cm. Area = πr² = π(8)² = 64π cm².
Correct Answer: A — 64π cm²
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Q. What is the area of a circle with a diameter of 16 cm? (Use π = 3.14) (2022)
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A.
201.06 cm²
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B.
100.48 cm²
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C.
50.24 cm²
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D.
25.12 cm²
Solution
Radius = diameter/2 = 16 cm / 2 = 8 cm. Area = πr² = 3.14 * 8² = 201.06 cm².
Correct Answer: A — 201.06 cm²
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Q. What is the area of a circle with a radius of 10 m? (2023)
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A.
314 m²
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B.
100 m²
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C.
200 m²
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D.
150 m²
Solution
Area = πr² = π * 10² = 314 m².
Correct Answer: A — 314 m²
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Q. What is the area of a circle with a radius of 3 cm? (2021)
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A.
28.26 cm²
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B.
9.42 cm²
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C.
12.56 cm²
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D.
18.84 cm²
Solution
Area = πr² = π * 3² = 28.26 cm².
Correct Answer: C — 12.56 cm²
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Q. What is the area of a circle with a radius of 3 m? (2020)
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A.
28.26 m²
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B.
9.42 m²
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C.
18.84 m²
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D.
12.56 m²
Solution
Area = πr²; = π * 3² = 28.26 m².
Correct Answer: A — 28.26 m²
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Q. What is the area of a circle with radius 7? (2022)
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A.
154
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B.
144
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C.
160
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D.
150
Solution
Area = πr^2 = π(7^2) = 49π ≈ 154.
Correct Answer: A — 154
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Q. What is the area of a sector of a circle with a radius of 4 cm and a central angle of 90 degrees? (2014)
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A.
6.28 cm²
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B.
12.56 cm²
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C.
3.14 cm²
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D.
9.42 cm²
Solution
Area of sector = (θ/360) * πr²; = (90/360) * π * 4² = 12.56 cm².
Correct Answer: B — 12.56 cm²
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Q. What is the area of a sector of a circle with a radius of 7 cm and an angle of 90 degrees? (2022)
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A.
38.5 cm²
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B.
12.25 cm²
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C.
15.4 cm²
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D.
25.5 cm²
Solution
Area of sector = (θ/360) * πr² = (90/360) * π * 7² = 38.5 cm².
Correct Answer: A — 38.5 cm²
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Q. What is the area of a triangle with base 10 cm and height 5 cm? (2021)
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A.
25 cm²
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B.
50 cm²
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C.
15 cm²
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D.
30 cm²
Solution
Area = 1/2 * base * height = 1/2 * 10 * 5 = 25 cm².
Correct Answer: A — 25 cm²
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Q. What is the area of the base of a cone with radius 3? (2023)
Solution
Area of base = πr² = π(3²) = 9π square units.
Correct Answer: A — 9π
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Q. What is the area of the base of a cylinder with radius 4 units? (2020)
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A.
16π
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B.
8π
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C.
12π
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D.
20π
Solution
Area of base = πr² = π(4)² = 16π square units.
Correct Answer: A — 16π
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Q. What is the argument of the complex number -1 + 0i? (2021)
Solution
The argument of -1 + 0i is π (180 degrees) since it lies on the negative x-axis.
Correct Answer: A — π
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Q. What is the atomic mass of Oxygen approximately? (2019)
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A.
16 u
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B.
18 u
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C.
14 u
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D.
12 u
Solution
The atomic mass of Oxygen is approximately 16 u.
Correct Answer: A — 16 u
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Q. What is the atomic mass of Sodium (Na)? (2021)
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A.
22.99
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B.
23.00
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C.
24.00
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D.
25.00
Solution
The atomic mass of Sodium (Na) is approximately 22.99 u.
Correct Answer: A — 22.99
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Q. What is the atomic number of Carbon? (2021)
Solution
The atomic number of Carbon is 6, which is the number of protons in its nucleus.
Correct Answer: A — 6
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Q. What is the atomic number of Oxygen?
Solution
The atomic number of Oxygen is 8.
Correct Answer: B — 8
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Q. What is the average duration of a human menstrual cycle? (2023)
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A.
21 days
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B.
28 days
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C.
35 days
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D.
14 days
Solution
The average duration of a human menstrual cycle is approximately 28 days.
Correct Answer: B — 28 days
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