Q. What is the equation of the line parallel to y = 3x + 4 that passes through the point (2, 5)? (2022)
A.
y = 3x - 1
B.
y = 3x + 1
C.
y = 3x + 2
D.
y = 3x + 3
Show solution
Solution
Since parallel lines have the same slope, the equation is y - 5 = 3(x - 2) which simplifies to y = 3x + 1.
Correct Answer:
B
— y = 3x + 1
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Q. What is the equation of the line parallel to y = 3x - 5 and passing through (2, 1)?
A.
y = 3x - 8
B.
y = 3x + 5
C.
y = 3x - 1
D.
y = 3x + 1
Show solution
Solution
Parallel lines have the same slope. The slope is 3. Using point-slope form: y - 1 = 3(x - 2) gives y = 3x - 8.
Correct Answer:
A
— y = 3x - 8
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Q. What is the equation of the line parallel to y = 3x - 5 that passes through the point (2, 1)?
A.
y = 3x - 8
B.
y = 3x + 5
C.
y = 3x - 1
D.
y = 3x + 1
Show solution
Solution
Since the lines are parallel, they have the same slope. Using point-slope form: y - 1 = 3(x - 2) gives y = 3x - 8.
Correct Answer:
A
— y = 3x - 8
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Q. What is the equation of the line passing through (0, 0) and (2, 4)? (2019)
A.
y = 2x
B.
y = x
C.
y = 4x
D.
y = 3x
Show solution
Solution
Slope = (4-0)/(2-0) = 2, so the equation is y = 2x.
Correct Answer:
A
— y = 2x
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Q. What is the equation of the line passing through (0, 0) with a slope of 3? (2021)
A.
y = 3x
B.
y = x/3
C.
y = 3/x
D.
y = 1/3x
Show solution
Solution
Equation of line: y = mx + c; here m = 3, c = 0 => y = 3x
Correct Answer:
A
— y = 3x
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Q. What is the equation of the line passing through (2, 3) with a slope of 2? (2021)
A.
y = 2x - 1
B.
y = 2x + 1
C.
y = 2x + 3
D.
y = 2x - 3
Show solution
Solution
Using point-slope form: y - 3 = 2(x - 2) => y = 2x - 4 + 3 => y = 2x - 1.
Correct Answer:
B
— y = 2x + 1
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Q. What is the equation of the line passing through the points (1, 2) and (3, 4)?
A.
y = x + 1
B.
y = 2x
C.
y = x + 2
D.
y = 2x - 2
Show solution
Solution
The slope m = (4 - 2) / (3 - 1) = 1. Using point-slope form, y - 2 = 1(x - 1) gives y = x + 1.
Correct Answer:
A
— y = x + 1
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Q. What is the equation of the line passing through the points (1, 2) and (3, 6)?
A.
y = 2x
B.
y = 3x - 1
C.
y = x + 1
D.
y = 4x - 2
Show solution
Solution
The slope m = (6 - 2) / (3 - 1) = 2. Using point-slope form, y - 2 = 2(x - 1) gives y = 2x.
Correct Answer:
A
— y = 2x
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Q. What is the equation of the line perpendicular to y = 3x + 1 that passes through (2, 3)?
A.
y = -1/3x + 4
B.
y = 3x - 3
C.
y = -3x + 9
D.
y = 1/3x + 2
Show solution
Solution
The slope of the perpendicular line is -1/3. Using point-slope form, we find y - 3 = -1/3(x - 2) which simplifies to y = -1/3x + 4.
Correct Answer:
A
— y = -1/3x + 4
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Q. What is the equation of the line that passes through the origin and has a slope of -1?
A.
y = -x
B.
y = x
C.
y = -2x
D.
y = 2x
Show solution
Solution
The equation of a line through the origin with slope m is y = mx. Thus, y = -1x or y = -x.
Correct Answer:
A
— y = -x
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Q. What is the equation of the line that passes through the origin and has a slope of -5?
A.
y = -5x
B.
y = 5x
C.
y = -x/5
D.
y = 5/x
Show solution
Solution
The equation of a line through the origin with slope m is y = mx. Thus, y = -5x.
Correct Answer:
A
— y = -5x
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Q. What is the equation of the plane passing through the point (1, 2, 3) with normal vector (1, -1, 1)? (2023)
A.
x - y + z = 0
B.
x + y + z = 6
C.
x - y + z = 1
D.
x + y - z = 0
Show solution
Solution
Equation of the plane: 1(x-1) - 1(y-2) + 1(z-3) = 0 => x - y + z = 1.
Correct Answer:
C
— x - y + z = 1
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Q. What is the equation of the plane passing through the points (1, 2, 3), (4, 5, 6), and (7, 8, 9)? (2021)
A.
0 = 0
B.
x + y + z = 12
C.
x + y + z = 10
D.
x + y + z = 9
Show solution
Solution
The points are collinear, hence the equation of the plane is 0 = 0.
Correct Answer:
A
— 0 = 0
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Q. What is the equilibrium constant (K) for the dissociation of acetic acid (CH3COOH) in water? (2023)
A.
1.8 x 10^-5
B.
1.0
C.
10
D.
100
Show solution
Solution
The dissociation constant (K) for acetic acid is approximately 1.8 x 10^-5, indicating it is a weak acid.
Correct Answer:
A
— 1.8 x 10^-5
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Q. What is the equilibrium constant (Kc) expression for the reaction: 2A + B ⇌ C?
A.
Kc = [C] / ([A]^2[B])
B.
Kc = [A]^2[B] / [C]
C.
Kc = [C] / [A]^2
D.
Kc = [A]^2 / ([B][C])
Show solution
Solution
The equilibrium constant Kc is defined as the ratio of the concentration of products to the concentration of reactants, each raised to the power of their coefficients in the balanced equation. For the reaction 2A + B ⇌ C, Kc = [C] / ([A]^2[B]).
Correct Answer:
A
— Kc = [C] / ([A]^2[B])
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Q. What is the equilibrium constant (Kc) for the reaction 2A + B ⇌ C? (2022)
A.
Kc = [C] / ([A]^2[B])
B.
Kc = [A]^2[B] / [C]
C.
Kc = [B] / ([A]^2[C])
D.
Kc = [C] / ([B][A])
Show solution
Solution
The equilibrium constant Kc is defined as the concentration of the products raised to the power of their coefficients divided by the concentration of the reactants raised to the power of their coefficients. For the reaction 2A + B ⇌ C, Kc = [C] / ([A]^2[B]).
Correct Answer:
A
— Kc = [C] / ([A]^2[B])
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Q. What is the equilibrium constant (Kc) for the reaction: A + B ⇌ C + D? (2022)
A.
Kc = [C][D]/[A][B]
B.
Kc = [A][B]/[C][D]
C.
Kc = [C][D][A][B]
D.
Kc = [A][B][C][D]
Show solution
Solution
The equilibrium constant Kc is defined as the ratio of the concentrations of the products to the reactants, each raised to the power of their coefficients in the balanced equation.
Correct Answer:
A
— Kc = [C][D]/[A][B]
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Q. What is the equilibrium constant (Kc) for the reaction: N2(g) + 3H2(g) ⇌ 2NH3(g)? (2022) 2022
A.
1.0 × 10^-5
B.
1.0 × 10^-2
C.
1.0 × 10^2
D.
1.0 × 10^5
Show solution
Solution
The equilibrium constant Kc for the formation of ammonia from nitrogen and hydrogen is typically around 1.0 × 10^5 at standard conditions.
Correct Answer:
D
— 1.0 × 10^5
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Q. What is the equivalent resistance of three resistors of 2 ohms each connected in series? (2020)
A.
2 ohms
B.
4 ohms
C.
6 ohms
D.
8 ohms
Show solution
Solution
In series, the equivalent resistance is the sum of the individual resistances: R_eq = R1 + R2 + R3 = 2 + 2 + 2 = 6 ohms.
Correct Answer:
C
— 6 ohms
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Q. What is the equivalent resistance of two 10Ω resistors connected in series? (2022)
A.
5Ω
B.
10Ω
C.
20Ω
D.
15Ω
Show solution
Solution
In series, R_eq = R1 + R2 = 10 + 10 = 20Ω.
Correct Answer:
C
— 20Ω
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Q. What is the equivalent resistance of two 12Ω resistors connected in series? (2019)
A.
6Ω
B.
12Ω
C.
24Ω
D.
18Ω
Show solution
Solution
In series, R_eq = R1 + R2 = 12Ω + 12Ω = 24Ω.
Correct Answer:
C
— 24Ω
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Q. What is the equivalent resistance of two 4Ω resistors in parallel? (2019)
Show solution
Solution
Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/4 + 1/4 = 1/2, thus R_eq = 2Ω.
Correct Answer:
A
— 2Ω
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Q. What is the equivalent resistance of two resistors of 4Ω and 12Ω in parallel? (2022)
Show solution
Solution
Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/4 + 1/12 = 1/3, so R_eq = 3Ω.
Correct Answer:
A
— 3Ω
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Q. What is the equivalent resistance of two resistors of 8Ω and 12Ω connected in series? (2019)
A.
20Ω
B.
24Ω
C.
16Ω
D.
10Ω
Show solution
Solution
In series, R_eq = R1 + R2 = 8Ω + 12Ω = 20Ω.
Correct Answer:
A
— 20Ω
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Q. What is the equivalent resistance of two resistors of 8Ω and 4Ω connected in series? (2022)
A.
12Ω
B.
32Ω
C.
2Ω
D.
8Ω
Show solution
Solution
In series, R_eq = R1 + R2 = 8Ω + 4Ω = 12Ω.
Correct Answer:
A
— 12Ω
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Q. What is the error called that occurs due to the limitations of the measuring instrument? (2023)
A.
Random error
B.
Systematic error
C.
Instrumental error
D.
Human error
Show solution
Solution
Instrumental error occurs due to the limitations of the measuring instrument.
Correct Answer:
C
— Instrumental error
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Q. What is the error in a measurement of 20.0 cm if the true value is 19.5 cm? (2023)
A.
0.5 cm
B.
0.5%
C.
2.5 cm
D.
2.5%
Show solution
Solution
The error is the absolute difference between the measured value and the true value, which is |20.0 - 19.5| = 0.5 cm.
Correct Answer:
A
— 0.5 cm
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Q. What is the error in measurement if the true value is 100 and the measured value is 95? (2023)
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Solution
The error in measurement is the difference between the true value and the measured value, which is 100 - 95 = 5.
Correct Answer:
A
— 5
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Q. What is the escape velocity from the surface of a planet with a radius of 4,000 km and a mass of 6 × 10^24 kg? (G = 6.67 × 10^-11 N m²/kg²)
A.
10,000 m/s
B.
11,200 m/s
C.
12,000 m/s
D.
13,000 m/s
Show solution
Solution
Escape velocity = √(2GM/R) = √(2 * 6.67 × 10^-11 * 6 × 10^24 / 4 × 10^6) = 11,200 m/s
Correct Answer:
B
— 11,200 m/s
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Q. What is the escape velocity from the surface of the Earth? (g = 9.8 m/s², R = 6.4 × 10^6 m)
A.
11.2 km/s
B.
9.8 km/s
C.
7.9 km/s
D.
15 km/s
Show solution
Solution
Escape velocity (v) = √(2gR) = √(2 * 9.8 * 6.4 × 10^6) ≈ 11.2 km/s
Correct Answer:
A
— 11.2 km/s
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