Q. Solve the inequality 6 - 3x ≥ 0. What is the solution?
A.
x ≤ 2
B.
x ≥ 2
C.
x < 2
D.
x > 2
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Solution
6 - 3x ≥ 0 => -3x ≥ -6 => x ≤ 2.
Correct Answer: B — x ≥ 2
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Q. Solve the inequality 6x + 2 < 14.
A.
x < 2
B.
x < 3
C.
x > 2
D.
x > 3
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Solution
6x + 2 < 14 => 6x < 12 => x < 2.
Correct Answer: B — x < 3
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Q. Solve the inequality 7 - 3x > 1.
A.
x < 2
B.
x > 2
C.
x < 3
D.
x > 3
Show solution
Solution
7 - 3x > 1 => -3x > -6 => x < 2.
Correct Answer: B — x > 2
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Q. Solve the inequality 7 - 3x > 1. What is the solution?
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
7 - 3x > 1 => -3x > -6 => x > 2.
Correct Answer: B — x > 2
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Q. Solve the inequality 7 - 3x < 1. What is the solution?
A.
x < 2
B.
x > 2
C.
x < 3
D.
x > 3
Show solution
Solution
7 - 3x < 1 => -3x < -6 => x > 2.
Correct Answer: B — x > 2
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Q. Solve the inequality 7 - x < 2.
A.
x > 5
B.
x < 5
C.
x > 7
D.
x < 7
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Solution
7 - x < 2 => -x < -5 => x > 5.
Correct Answer: A — x > 5
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Q. Solve the inequality 7x + 2 < 3x + 10.
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
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Solution
7x + 2 < 3x + 10 => 4x < 8 => x < 2.
Correct Answer: B — x > 2
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Q. Solve the inequality 7x - 4 < 2x + 11. What is the solution?
A.
x < 3
B.
x > 3
C.
x ≤ 3
D.
x ≥ 3
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Solution
7x - 4 < 2x + 11 => 5x < 15 => x < 3.
Correct Answer: B — x > 3
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Q. Solve the inequality 7x - 5 < 2x + 10. What is the solution?
A.
x < 1
B.
x > 1
C.
x < 2
D.
x > 2
Show solution
Solution
7x - 5 < 2x + 10 => 5x < 15 => x < 3.
Correct Answer: B — x > 1
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Q. Solve the inequality 8 - x > 3.
A.
x < 5
B.
x > 5
C.
x < 3
D.
x > 3
Show solution
Solution
8 - x > 3 => -x > -5 => x < 5.
Correct Answer: A — x < 5
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Q. Solve the inequality x/3 + 2 > 1. What is the solution?
A.
x > -3
B.
x < -3
C.
x > 3
D.
x < 3
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Solution
x/3 + 2 > 1 => x/3 > -1 => x > -3.
Correct Answer: C — x > 3
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Q. Solve the inequality x/3 - 2 > 1. What is the solution set?
A.
x < 9
B.
x > 9
C.
x < 3
D.
x > 3
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Solution
x/3 - 2 > 1 => x/3 > 3 => x > 9.
Correct Answer: B — x > 9
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Q. Solve the inequality x/3 - 2 ≤ 1. What is the solution?
A.
x ≤ 9
B.
x ≥ 9
C.
x ≤ 3
D.
x ≥ 3
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Solution
x/3 - 2 ≤ 1 => x/3 ≤ 3 => x ≤ 9.
Correct Answer: A — x ≤ 9
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Q. Solve the inequality x/4 - 1 < 0.
A.
x < 4
B.
x > 4
C.
x ≤ 4
D.
x ≥ 4
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Solution
x/4 - 1 < 0 => x/4 < 1 => x < 4.
Correct Answer: A — x < 4
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Q. Solve the inequality: 4x + 1 ≥ 3.
A.
x ≥ 0.5
B.
x ≤ 0.5
C.
x ≥ 1
D.
x ≤ 1
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Solution
4x + 1 ≥ 3 => 4x ≥ 2 => x ≥ 0.5.
Correct Answer: A — x ≥ 0.5
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Q. Solve the inequality: 6 - x ≤ 2.
A.
x ≥ 4
B.
x ≤ 4
C.
x ≥ 6
D.
x ≤ 6
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Solution
6 - x ≤ 2 => -x ≤ -4 => x ≥ 4.
Correct Answer: B — x ≤ 4
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Q. The angle between the lines represented by the equation 2x^2 + 3xy + y^2 = 0 is:
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
60 degrees
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Solution
Using the angle formula, we find the angle between the lines is 60 degrees.
Correct Answer: D — 60 degrees
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Q. The angle between the lines represented by the equation 3x^2 - 4xy + 2y^2 = 0 is:
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
90 degrees
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Solution
Using the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)|, we find that the angle is 60 degrees.
Correct Answer: C — 60 degrees
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Q. The area of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4) is:
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Solution
Length = 5 - 1 = 4, Width = 4 - 1 = 3. Area = Length * Width = 4 * 3 = 12.
Correct Answer: B — 16
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Q. The area of a triangle with vertices at (0,0), (4,0), and (0,3) is:
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Solution
Area = 0.5 * base * height = 0.5 * 4 * 3 = 6.
Correct Answer: A — 6
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Q. The area of triangle ABC is 24 cm², and the base BC = 8 cm. What is the height from A to BC?
A.
6 cm
B.
8 cm
C.
4 cm
D.
3 cm
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Solution
Area = 1/2 * base * height => 24 = 1/2 * 8 * height => height = 6 cm.
Correct Answer: A — 6 cm
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Q. The area of triangle ABC is 30 square units, and the base BC is 10 units. What is the height from A to BC?
A.
3 units
B.
6 units
C.
5 units
D.
4 units
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Solution
Area = 1/2 * base * height => 30 = 1/2 * 10 * height => height = 6 units.
Correct Answer: B — 6 units
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Q. The argument of the complex number z = -1 - i is?
A.
-3π/4
B.
3π/4
C.
π/4
D.
-π/4
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Solution
The argument of z = -1 - i is θ = tan^(-1)(-1/-1) = -3π/4.
Correct Answer: A — -3π/4
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Q. The Arrhenius equation relates the rate constant to which of the following?
A.
Temperature and concentration
B.
Temperature and activation energy
C.
Concentration and pressure
D.
Temperature and volume
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Solution
The Arrhenius equation relates the rate constant to temperature and activation energy.
Correct Answer: B — Temperature and activation energy
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Q. The average kinetic energy of gas molecules is proportional to which of the following?
A.
Pressure
B.
Volume
C.
Temperature
D.
Density
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Solution
The average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas.
Correct Answer: C — Temperature
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Q. The average of five numbers is 18. If one number is excluded, the average becomes 16. What is the excluded number?
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Solution
Total sum = 5 * 18 = 90. New sum = 4 * 16 = 64. Excluded number = 90 - 64 = 26.
Correct Answer: C — 24
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Q. The average of five numbers is 18. If one number is removed, the average becomes 16. What was the removed number?
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Solution
Total of five numbers = 5 * 18 = 90. Total of four numbers = 4 * 16 = 64. Removed number = 90 - 64 = 26.
Correct Answer: C — 24
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Q. The concept of an ideal gas is based on which of the following assumptions?
A.
Molecules have no volume
B.
Molecules do not attract or repel each other
C.
Collisions are perfectly elastic
D.
All of the above
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Solution
The concept of an ideal gas is based on the assumptions that molecules have no volume, do not attract or repel each other, and that collisions are perfectly elastic.
Correct Answer: D — All of the above
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Q. The concept of mean free path is associated with which of the following?
A.
Distance traveled by a gas molecule between collisions
B.
Average speed of gas molecules
C.
Pressure of the gas
D.
Volume of the gas
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Solution
Mean free path is defined as the average distance traveled by a gas molecule between successive collisions.
Correct Answer: A — Distance traveled by a gas molecule between collisions
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Q. The condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel is:
A.
h^2 = ab
B.
h^2 > ab
C.
h^2 < ab
D.
a + b = 0
Show solution
Solution
The lines are parallel if h^2 = ab.
Correct Answer: A — h^2 = ab
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