Q. If 50 mL of a 2 M HCl solution is diluted to 200 mL, what is the new molarity?
-
A.
0.25 M
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B.
0.5 M
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C.
1 M
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D.
2 M
Solution
Using the dilution formula M1V1 = M2V2, (2 M)(50 mL) = M2(200 mL) => M2 = 0.5 M.
Correct Answer: B — 0.5 M
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Q. If 500 J of heat is added to a system and 200 J of work is done by the system, what is the change in internal energy?
-
A.
300 J
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B.
500 J
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C.
700 J
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D.
200 J
Solution
According to the first law of thermodynamics, ΔU = Q - W. Here, ΔU = 500 J - 200 J = 300 J.
Correct Answer: A — 300 J
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Q. If 5x - 7 < 3, what is the range of x?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 1
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D.
x > 1
Solution
5x - 7 < 3 => 5x < 10 => x < 2
Correct Answer: A — x < 2
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Q. If 5x - 7 < 3, what is the value of x?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 1
-
D.
x > 1
Solution
5x - 7 < 3 => 5x < 10 => x < 2
Correct Answer: A — x < 2
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Q. If 5x - 7 < 3x + 1, what is the range of x?
-
A.
x < 4
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B.
x > 4
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C.
x < 2
-
D.
x > 2
Solution
5x - 7 < 3x + 1 => 2x < 8 => x < 4.
Correct Answer: A — x < 4
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Q. If 5^(x+1) = 125, what is the value of x?
Solution
125 = 5^3, so x + 1 = 3, hence x = 2.
Correct Answer: B — 2
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Q. If 5^(x-1) = 25, what is the value of x?
Solution
Since 25 = 5^2, we have 5^(x-1) = 5^2, thus x - 1 = 2, giving x = 3.
Correct Answer: A — 2
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Q. If 5^x = 125, what is the value of x?
Solution
125 = 5^3 => x = 3
Correct Answer: C — 3
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Q. If 5^x = 25, what is the value of x?
Solution
Since 25 = 5^2, we have 5^x = 5^2, thus x = 2.
Correct Answer: B — 2
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Q. If 6x + 4 > 10, what is the value of x?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
6x + 4 > 10 => 6x > 6 => x > 1.
Correct Answer: B — x > 1
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Q. If 7 - 2x > 3, what is the value of x?
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A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
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D.
x ≥ 2
Solution
7 - 2x > 3 => -2x > -4 => x < 2.
Correct Answer: B — x > 2
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Q. If 7 - 2x ≥ 1, what is the range of x?
-
A.
x ≤ 3
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B.
x ≥ 3
-
C.
x < 3
-
D.
x > 3
Solution
7 - 2x ≥ 1 => -2x ≥ -6 => x ≤ 3
Correct Answer: B — x ≥ 3
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Q. If 7 - 2x ≥ 3, what is the value of x?
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x < 2
-
D.
x > 2
Solution
7 - 2x ≥ 3 => -2x ≥ -4 => x ≤ 2.
Correct Answer: B — x ≥ 2
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Q. If 7 - 3x ≤ 1, what is the value of x?
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x < 2
-
D.
x > 2
Solution
7 - 3x ≤ 1 => -3x ≤ -6 => x ≥ 2.
Correct Answer: B — x ≥ 2
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Q. If 7 - 3x ≥ 1, what is the solution for x?
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
7 - 3x ≥ 1 => -3x ≥ -6 => x ≤ 2.
Correct Answer: B — x ≥ 2
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Q. If 7x + 1 ≥ 15, what is the value of x?
-
A.
x ≥ 2
-
B.
x < 2
-
C.
x > 2
-
D.
x ≤ 2
Solution
7x + 1 ≥ 15 => 7x ≥ 14 => x ≥ 2
Correct Answer: A — x ≥ 2
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Q. If 7x - 3 = 4x + 6, what is the value of x?
Solution
Subtracting 4x from both sides gives 3x - 3 = 6, then adding 3 gives 3x = 9, leading to x = 3.
Correct Answer: B — 2
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Q. If 7x = 21, what is the value of x?
Solution
Dividing both sides by 7 gives x = 3.
Correct Answer: C — 3
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Q. If 7^(x) = 49, what is the value of x?
Solution
49 = 7^2, so x = 2.
Correct Answer: B — 2
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Q. If 8^(x) = 64, what is the value of x?
Solution
64 = 8^2, so x = 2.
Correct Answer: B — 2
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Q. If a + b = 10 and ab = 21, what are the values of a and b?
-
A.
3 and 7
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B.
4 and 6
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C.
5 and 5
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D.
2 and 8
Solution
The roots of the equation x^2 - 10x + 21 = 0 are found using the quadratic formula, yielding a = 3 and b = 7.
Correct Answer: A — 3 and 7
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Q. If a + b = 10 and ab = 21, what is the value of a^2 + b^2?
Solution
Using the identity a^2 + b^2 = (a + b)^2 - 2ab, we get a^2 + b^2 = 10^2 - 2*21 = 100 - 42 = 58.
Correct Answer: A — 49
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Q. If a 10 kg object is dropped from a height of 20 m, what is its potential energy at the top? (1960)
-
A.
200 J
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B.
1000 J
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C.
500 J
-
D.
1500 J
Solution
Potential Energy (PE) = m * g * h = 10 kg * 9.8 m/s^2 * 20 m = 1960 J
Correct Answer: B — 1000 J
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Q. If a 10 kg object is dropped from a height of 5 m, what is the potential energy at that height?
-
A.
50 J
-
B.
100 J
-
C.
150 J
-
D.
200 J
Solution
Potential energy = mgh = 10 kg × 9.8 m/s² × 5 m = 490 J.
Correct Answer: B — 100 J
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Q. If a 10 kg object is in free fall, what is the force acting on it due to gravity?
-
A.
10 N
-
B.
20 N
-
C.
30 N
-
D.
40 N
Solution
The force due to gravity is F = mg = 10 kg * 9.8 m/s² = 98 N, which rounds to 100 N.
Correct Answer: B — 20 N
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Q. If a 10 kg object is moving with a velocity of 4 m/s, what is its kinetic energy?
-
A.
80 J
-
B.
40 J
-
C.
20 J
-
D.
160 J
Solution
Kinetic Energy (KE) = 1/2 * m * v^2 = 1/2 * 10 * (4^2) = 80 J
Correct Answer: A — 80 J
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Q. If a 10 kg object is pulled with a force of 30 N, what is its acceleration?
-
A.
1 m/s²
-
B.
2 m/s²
-
C.
3 m/s²
-
D.
4 m/s²
Solution
Using F = ma, acceleration a = F/m = 30 N / 10 kg = 3 m/s².
Correct Answer: C — 3 m/s²
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Q. If a 10 kg object is pulled with a force of 50 N, what is its acceleration?
-
A.
2 m/s²
-
B.
5 m/s²
-
C.
10 m/s²
-
D.
20 m/s²
Solution
Using F = ma, a = F/m = 50 N / 10 kg = 5 m/s².
Correct Answer: B — 5 m/s²
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Q. If a 10 kg object is subjected to a net force of 30 N, what is the object's acceleration?
-
A.
3 m/s²
-
B.
2 m/s²
-
C.
1.5 m/s²
-
D.
4 m/s²
Solution
Using F = ma, a = F/m = 30 N / 10 kg = 3 m/s².
Correct Answer: A — 3 m/s²
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Q. If a 10 kg object is subjected to a net force of 30 N, what will be its acceleration?
-
A.
3 m/s²
-
B.
0.3 m/s²
-
C.
30 m/s²
-
D.
300 m/s²
Solution
Using F = ma, acceleration a = F/m = 30 N / 10 kg = 3 m/s².
Correct Answer: A — 3 m/s²
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