Q. What is the effect of deforestation on river soil quality?
-
A.
Improves soil quality
-
B.
No effect
-
C.
Decreases soil quality
-
D.
Increases soil moisture
Solution
Deforestation decreases soil quality by increasing erosion and reducing the organic matter content in the soil.
Correct Answer:
C
— Decreases soil quality
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Q. What is the electron configuration of a chlorine atom (atomic number 17)? (2020)
-
A.
1s² 2s² 2p⁶ 3s² 3p⁵
-
B.
1s² 2s² 2p⁶ 3s² 3p⁶
-
C.
1s² 2s² 2p⁶ 3s² 3p⁴
-
D.
1s² 2s² 2p⁶ 3s² 3d⁵
Solution
The electron configuration of chlorine is 1s² 2s² 2p⁶ 3s² 3p⁵, filling up to the 3p subshell.
Correct Answer:
A
— 1s² 2s² 2p⁶ 3s² 3p⁵
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Q. What is the electron configuration of a neutral carbon atom? (2022)
-
A.
1s² 2s² 2p²
-
B.
1s² 2s² 2p⁶
-
C.
1s² 2s² 2p⁴
-
D.
1s² 2s² 2p³
Solution
Carbon has an atomic number of 6, and its electron configuration is 1s² 2s² 2p².
Correct Answer:
A
— 1s² 2s² 2p²
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Q. What is the electron configuration of an oxygen atom? (2021)
-
A.
1s² 2s² 2p⁴
-
B.
1s² 2s² 2p²
-
C.
1s² 2s² 2p⁶
-
D.
1s² 2s² 2p³
Solution
Oxygen has 8 electrons, and its electron configuration is 1s² 2s² 2p⁴.
Correct Answer:
A
— 1s² 2s² 2p⁴
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Q. What is the empirical formula of a compound with a molecular formula C6H12? (2021)
-
A.
CH
-
B.
C2H4
-
C.
C3H6
-
D.
C6H12
Solution
The empirical formula is obtained by dividing the subscripts by the greatest common divisor, which is 2. Thus, C6H12 becomes C3H6.
Correct Answer:
B
— C2H4
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Q. What is the empirical formula of a compound with the molecular formula C6H12? (2021)
-
A.
CH
-
B.
C2H4
-
C.
C3H6
-
D.
C6H12
Solution
The empirical formula is obtained by dividing the subscripts by the greatest common divisor, which is 2. Thus, C6H12 becomes C3H6.
Correct Answer:
B
— C2H4
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Q. What is the energy of a photon with a frequency of 5 x 10^14 Hz? (Planck's constant h = 6.626 x 10^-34 J·s) (2021)
-
A.
3.31 x 10^-19 J
-
B.
1.32 x 10^-19 J
-
C.
2.48 x 10^-19 J
-
D.
4.97 x 10^-19 J
Solution
Energy (E) = h * frequency = 6.626 x 10^-34 J·s * 5 x 10^14 Hz = 3.31 x 10^-19 J.
Correct Answer:
A
— 3.31 x 10^-19 J
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Q. What is the equation of a circle with center at (2, -3) and radius 4? (2022)
-
A.
(x-2)² + (y+3)² = 16
-
B.
(x+2)² + (y-3)² = 16
-
C.
(x-2)² + (y-3)² = 16
-
D.
(x+2)² + (y+3)² = 16
Solution
The standard form of a circle's equation is (x-h)² + (y-k)² = r². Here, h=2, k=-3, r=4. Thus, (x-2)² + (y+3)² = 16.
Correct Answer:
A
— (x-2)² + (y+3)² = 16
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Q. What is the equation of a circle with center at (3, -2) and radius 4? (2023)
-
A.
(x-3)² + (y+2)² = 16
-
B.
(x+3)² + (y-2)² = 16
-
C.
(x-3)² + (y-2)² = 16
-
D.
(x+3)² + (y+2)² = 16
Solution
The standard equation of a circle is (x-h)² + (y-k)² = r². Here, h=3, k=-2, r=4. Thus, (x-3)² + (y+2)² = 16.
Correct Answer:
A
— (x-3)² + (y+2)² = 16
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Q. What is the equation of a circle with center at (3, -2) and radius 5? (2022)
-
A.
(x-3)² + (y+2)² = 25
-
B.
(x+3)² + (y-2)² = 25
-
C.
(x-3)² + (y-2)² = 25
-
D.
(x+3)² + (y+2)² = 25
Solution
The standard form of a circle's equation is (x-h)² + (y-k)² = r². Here, h=3, k=-2, r=5, so (x-3)² + (y+2)² = 25.
Correct Answer:
A
— (x-3)² + (y+2)² = 25
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Q. What is the equation of the circle with center at (2, -3) and radius 5?
-
A.
(x-2)² + (y+3)² = 25
-
B.
(x+2)² + (y-3)² = 25
-
C.
(x-2)² + (y-3)² = 25
-
D.
(x+2)² + (y+3)² = 25
Solution
Standard form of a circle: (x-h)² + (y-k)² = r². Here, h=2, k=-3, r=5.
Correct Answer:
A
— (x-2)² + (y+3)² = 25
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Q. What is the equation of the directrix of the parabola x^2 = 12y?
-
A.
y = 3
-
B.
y = -3
-
C.
y = 6
-
D.
y = -6
Solution
The directrix of the parabola x^2 = 4py is given by y = -p. Here, p = 3, so the directrix is y = -3.
Correct Answer:
B
— y = -3
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Q. What is the equation of the line parallel to y = 3x + 2 that passes through the point (4, 1)? (2020)
-
A.
y = 3x - 11
-
B.
y = 3x + 1
-
C.
y = 3x + 2
-
D.
y = 3x - 2
Solution
Since parallel lines have the same slope, the equation is y - 1 = 3(x - 4) which simplifies to y = 3x - 11.
Correct Answer:
A
— y = 3x - 11
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Q. What is the equation of the line parallel to y = 3x + 4 that passes through the point (1, 2)? (2020)
-
A.
y = 3x - 1
-
B.
y = 3x + 1
-
C.
y = 3x + 2
-
D.
y = 3x - 2
Solution
Parallel lines have the same slope. Using point-slope form: y - 2 = 3(x - 1) gives y = 3x - 1.
Correct Answer:
A
— y = 3x - 1
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Q. What is the equation of the line parallel to y = 3x - 4 that passes through the point (2, 1)? (2020)
-
A.
y = 3x - 5
-
B.
y = 3x + 1
-
C.
y = 3x - 1
-
D.
y = 3x + 4
Solution
Since parallel lines have the same slope, the equation is y - 1 = 3(x - 2) which simplifies to y = 3x - 5.
Correct Answer:
C
— y = 3x - 1
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Q. What is the equation of the line that is perpendicular to y = 3x + 2 and passes through the point (1, 1)? (2022)
-
A.
y = -1/3x + 4/3
-
B.
y = 3x - 2
-
C.
y = -3x + 4
-
D.
y = 1/3x + 2/3
Solution
The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1) gives y = -1/3x + 4/3.
Correct Answer:
A
— y = -1/3x + 4/3
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Q. What is the equation of the line that is perpendicular to y = 3x + 4 and passes through the point (1, 1)? (2022)
-
A.
y - 1 = -1/3(x - 1)
-
B.
y - 1 = 3(x - 1)
-
C.
y - 1 = 3/1(x - 1)
-
D.
y - 1 = -3(x - 1)
Solution
The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1).
Correct Answer:
A
— y - 1 = -1/3(x - 1)
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Q. What is the equation of the line that passes through the origin and has a slope of -3? (2022)
-
A.
y = -3x
-
B.
y = 3x
-
C.
y = -x/3
-
D.
y = 1/3x
Solution
The equation of a line through the origin with slope m is y = mx. Thus, y = -3x.
Correct Answer:
A
— y = -3x
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Q. What is the equation of the line that passes through the origin and has a slope of -4? (2023)
-
A.
y = -4x
-
B.
y = 4x
-
C.
y = -x/4
-
D.
y = 1/4x
Solution
Using the slope-intercept form y = mx + b, with m = -4 and b = 0, the equation is y = -4x.
Correct Answer:
A
— y = -4x
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Q. What is the equivalent resistance of two resistors of 4 ohms and 6 ohms connected in series?
-
A.
10 ohms
-
B.
24 ohms
-
C.
2.4 ohms
-
D.
0.67 ohms
Solution
In series, the equivalent resistance is the sum: R_eq = R1 + R2 = 4 Ω + 6 Ω = 10 Ω.
Correct Answer:
A
— 10 ohms
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Q. What is the equivalent resistance of two resistors of 4 ohms and 6 ohms in series?
-
A.
10 ohms
-
B.
24 ohms
-
C.
2.4 ohms
-
D.
0.67 ohms
Solution
In series, the equivalent resistance is the sum: R_eq = R1 + R2 = 4 Ω + 6 Ω = 10 Ω.
Correct Answer:
A
— 10 ohms
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Q. What is the equivalent resistance of two resistors, R1 = 4Ω and R2 = 6Ω, in parallel? (2022)
-
A.
2.4Ω
-
B.
10Ω
-
C.
24Ω
-
D.
1.5Ω
Solution
The formula for equivalent resistance in parallel is 1/R_eq = 1/R1 + 1/R2. Thus, 1/R_eq = 1/4 + 1/6 = 5/12, so R_eq = 12/5 = 2.4Ω.
Correct Answer:
A
— 2.4Ω
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Q. What is the equivalent resistance of two resistors, R1 and R2, in parallel? (2022)
-
A.
R1 + R2
-
B.
R1 * R2 / (R1 + R2)
-
C.
1 / (1/R1 + 1/R2)
-
D.
R1 - R2
Solution
The formula for equivalent resistance (R_eq) of two resistors in parallel is given by 1 / (1/R1 + 1/R2).
Correct Answer:
C
— 1 / (1/R1 + 1/R2)
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Q. What is the estimated temperature at the Earth's inner core?
-
A.
4000°C
-
B.
5000°C
-
C.
6000°C
-
D.
7000°C
Solution
The temperature at the Earth's inner core is estimated to be around 6000°C.
Correct Answer:
C
— 6000°C
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Q. What is the expansion of (2x - 3)²? (2022)
-
A.
4x² - 9
-
B.
4x² - 12x + 9
-
C.
4x² + 12x + 9
-
D.
4x² - 6x
Solution
(2x - 3)² = 4x² - 12x + 9 by the square of a binomial.
Correct Answer:
B
— 4x² - 12x + 9
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Q. What is the expansion of (2x - 3y)²?
-
A.
4x² - 9y²
-
B.
4x² - 12xy + 9y²
-
C.
4x² + 9y²
-
D.
4x² + 12xy + 9y²
Solution
(2x - 3y)² = 4x² - 12xy + 9y² by applying the square of a binomial.
Correct Answer:
B
— 4x² - 12xy + 9y²
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Q. What is the expansion of (x + 2)(x - 2)?
-
A.
x² - 4
-
B.
x² + 4
-
C.
2x² - 4
-
D.
x² - 2
Solution
(x + 2)(x - 2) = x² - 2² = x² - 4 by the difference of squares.
Correct Answer:
A
— x² - 4
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Q. What is the first derivative of f(x) = ln(x)? (2019)
-
A.
1/x
-
B.
x
-
C.
ln(x)
-
D.
e^x
Solution
The derivative f'(x) = 1/x.
Correct Answer:
A
— 1/x
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Q. What is the first derivative of f(x) = tan(x)? (2021)
-
A.
sec^2(x)
-
B.
cos^2(x)
-
C.
sin^2(x)
-
D.
csc^2(x)
Solution
The derivative of f(x) = tan(x) is f'(x) = sec^2(x).
Correct Answer:
A
— sec^2(x)
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Q. What is the focal length of a diverging lens if the image distance is -15 cm and the object distance is -10 cm? (2023)
-
A.
-30 cm
-
B.
-20 cm
-
C.
-15 cm
-
D.
-10 cm
Solution
Using the lens formula 1/f = 1/v - 1/u, we find f = -20 cm.
Correct Answer:
B
— -20 cm
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