Q. What is the integral of 1/x with respect to x? (2022)
A.
ln
B.
x
C.
+ C
D.
1/x + C
.
x + C
.
e^x + C
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Solution
The integral of 1/x is ln|x| + C.
Correct Answer: A — ln
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Q. What is the integral of 1/x? (2022)
A.
ln
B.
x
C.
+ C
D.
1/x + C
.
x + C
.
x^2 + C
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Solution
The integral of 1/x is ln|x| + C.
Correct Answer: A — ln
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Q. What is the integral of cos(2x) dx? (2021)
A.
(1/2)sin(2x) + C
B.
sin(2x) + C
C.
(1/2)cos(2x) + C
D.
2sin(2x) + C
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Solution
The integral of cos(2x) is (1/2)sin(2x) + C.
Correct Answer: A — (1/2)sin(2x) + C
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Q. What is the integral of e^x with respect to x? (2023)
A.
e^x + C
B.
xe^x + C
C.
e^x/x + C
D.
x^2e^x + C
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Solution
The integral of e^x is e^x + C.
Correct Answer: A — e^x + C
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Q. What is the integral of e^x? (2023)
A.
e^x + C
B.
xe^x + C
C.
e^x/x + C
D.
x^2e^x + C
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Solution
The integral of e^x is e^x + C.
Correct Answer: A — e^x + C
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Q. What is the integral of sin(x) dx? (2021)
A.
-cos(x) + C
B.
cos(x) + C
C.
sin(x) + C
D.
-sin(x) + C
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Solution
The integral of sin(x) is -cos(x) + C.
Correct Answer: A — -cos(x) + C
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Q. What is the integral of tan(x) dx? (2023)
A.
-ln
B.
cos(x)
C.
+ C
D.
ln
.
sin(x)
.
+ C
.
ln
.
tan(x)
.
+ C
.
-ln
.
sin(x)
.
+ C
Show solution
Solution
The integral of tan(x) is -ln|cos(x)| + C.
Correct Answer: A — -ln
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Q. What is the integral of tan(x) with respect to x? (2021)
A.
-ln
B.
cos(x)
C.
+ C
D.
ln
.
sin(x)
.
+ C
.
ln
.
tan(x)
.
+ C
.
-ln
.
sin(x)
.
+ C
Show solution
Solution
The integral of tan(x) is -ln|cos(x)| + C.
Correct Answer: A — -ln
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Q. What is the integral of tan(x)? (2021)
A.
-ln
B.
cos(x)
C.
+ C
D.
ln
.
sin(x)
.
+ C
.
ln
.
tan(x)
.
+ C
.
-ln
.
sin(x)
.
+ C
Show solution
Solution
The integral of tan(x) is -ln|cos(x)| + C.
Correct Answer: A — -ln
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Q. What is the integral of x^2 with respect to x? (2021)
A.
(1/3)x^3 + C
B.
(1/2)x^2 + C
C.
(1/4)x^4 + C
D.
(1/5)x^5 + C
Show solution
Solution
The integral of x^n is (1/(n+1))x^(n+1) + C. Here, n=2, so the integral is (1/3)x^3 + C.
Correct Answer: A — (1/3)x^3 + C
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Q. What is the integral of x^3 + 2x? (2021)
A.
(1/4)x^4 + x^2 + C
B.
(1/3)x^3 + x^2 + C
C.
(1/4)x^4 + (1/2)x^2 + C
D.
(1/5)x^5 + (1/2)x^2 + C
Show solution
Solution
Integrating term by term, ∫x^3dx = (1/4)x^4 and ∫2xdx = x^2. Thus, ∫(x^3 + 2x)dx = (1/4)x^4 + (1/2)x^2 + C.
Correct Answer: C — (1/4)x^4 + (1/2)x^2 + C
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Q. What is the integral of x^n where n ≠ -1? (2021)
A.
(1/n)x^(n+1) + C
B.
(1/(n+1))x^n + C
C.
(1/(n+1))x^(n+1) + C
D.
nx^(n-1) + C
Show solution
Solution
The integral of x^n is (1/(n+1))x^(n+1) + C, provided n ≠ -1.
Correct Answer: C — (1/(n+1))x^(n+1) + C
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Q. What is the integrating factor for the equation dy/dx + (1/x)y = 2?
A.
x
B.
e^(ln(x))
C.
e^(ln(x^2))
D.
1/x
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Solution
The integrating factor is e^(∫(1/x)dx) = e^(ln(x)) = x.
Correct Answer: C — e^(ln(x^2))
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Q. What is the integrating factor for the equation dy/dx + 2y = 3?
A.
e^(2x)
B.
e^(-2x)
C.
e^(3x)
D.
e^(-3x)
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Solution
The integrating factor is e^(∫2dx) = e^(2x).
Correct Answer: A — e^(2x)
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Q. What is the integrating factor for the equation dy/dx + 2y = 6?
A.
e^(2x)
B.
e^(-2x)
C.
e^(6x)
D.
e^(-6x)
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Solution
The integrating factor is e^(∫2dx) = e^(2x).
Correct Answer: A — e^(2x)
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Q. What is the IUPAC name of CH3CH2Cl?
A.
Chloroethane
B.
Ethyl chloride
C.
Ethane chloride
D.
Chloromethane
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Solution
The IUPAC name of CH3CH2Cl is Chloroethane, as it is a two-carbon alkane with a chlorine substituent.
Correct Answer: A — Chloroethane
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Q. What is the IUPAC name of CH3CH2OH? (2021) 2021
A.
Ethanol
B.
Methanol
C.
Propanol
D.
Butanol
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Solution
The compound CH3CH2OH is an alcohol with two carbon atoms, which is named Ethanol.
Correct Answer: A — Ethanol
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Q. What is the IUPAC name of CH3CHO? (2023) 2023
A.
Acetaldehyde
B.
Ethanal
C.
Ethyl aldehyde
D.
Methyl ketone
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Solution
The IUPAC name of CH3CHO is ethanal, which is the simplest aldehyde.
Correct Answer: B — Ethanal
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Q. What is the IUPAC name of the compound CH3CH2NH2? (2021)
A.
Ethylamine
B.
Dimethylamine
C.
Propylamine
D.
Methylamine
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Solution
The IUPAC name of CH3CH2NH2 is Ethylamine, as it consists of an ethyl group attached to an amine.
Correct Answer: A — Ethylamine
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Q. What is the kinetic energy of a 3 kg object moving at a speed of 4 m/s? (2022)
A.
24 J
B.
12 J
C.
6 J
D.
48 J
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Solution
Kinetic Energy (KE) = 0.5 × m × v² = 0.5 × 3 kg × (4 m/s)² = 24 J.
Correct Answer: B — 12 J
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Q. What is the kinetic energy of a 4 kg object moving at a speed of 3 m/s? (2015)
A.
18 J
B.
12 J
C.
24 J
D.
36 J
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Solution
Kinetic Energy (KE) = 0.5 × mass × velocity² = 0.5 × 4 kg × (3 m/s)² = 18 J.
Correct Answer: B — 12 J
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Q. What is the Ksp expression for the salt AgCl? (2023)
A.
[Ag+][Cl-]
B.
[AgCl]
C.
[Ag+][Cl-]^2
D.
[AgCl]^2
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Solution
The solubility product constant (Ksp) for AgCl is expressed as Ksp = [Ag+][Cl-], where [Ag+] and [Cl-] are the molar concentrations of the ions in a saturated solution.
Correct Answer: A — [Ag+][Cl-]
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Q. What is the Ksp of AgCl if the solubility of AgCl in water is 1.33 x 10^-5 M? (2023)
A.
1.78 x 10^-10
B.
1.33 x 10^-5
C.
1.33 x 10^-10
D.
1.78 x 10^-5
Show solution
Solution
Ksp = [Ag+][Cl-] = (1.33 x 10^-5)(1.33 x 10^-5) = 1.78 x 10^-10.
Correct Answer: A — 1.78 x 10^-10
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Q. What is the latent heat of fusion if 2000 J of energy is required to melt 0.5 kg of ice? (2021)
A.
2000 J/kg
B.
4000 J/kg
C.
1000 J/kg
D.
500 J/kg
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Solution
Latent heat of fusion (L) = Q / m = 2000 J / 0.5 kg = 4000 J/kg.
Correct Answer: A — 2000 J/kg
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Q. What is the latent heat of fusion of ice if 80 calories are required to melt 20 grams of ice? (2020)
A.
40 cal/g
B.
60 cal/g
C.
80 cal/g
D.
100 cal/g
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Solution
Latent heat of fusion (L_f) = Q / m = 80 cal / 20 g = 4 cal/g.
Correct Answer: C — 80 cal/g
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Q. What is the latent heat of fusion of ice if 80 g of ice at 0°C melts to water at 0°C, absorbing 3360 J of heat? (2022)
A.
40 J/g
B.
60 J/g
C.
80 J/g
D.
100 J/g
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Solution
Latent heat of fusion (L) = Q/m = 3360 J / 80 g = 42 J/g.
Correct Answer: C — 80 J/g
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Q. What is the latent heat of vaporization if 500 g of water at 100°C is converted to steam at the same temperature, absorbing 2260 kJ of heat? (2023)
A.
2260 J/g
B.
450 J/g
C.
334 J/g
D.
1000 J/g
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Solution
Latent heat of vaporization (L) = Q / m = 2260 kJ / 500 g = 4.52 kJ/g = 2260 J/g.
Correct Answer: A — 2260 J/g
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Q. What is the latent heat of vaporization of water if 540 J of energy is required to convert 100 g of water at 100°C to steam? (2021)
A.
540 J/g
B.
54 J/g
C.
5.4 J/g
D.
0.54 J/g
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Solution
Latent heat of vaporization (L) = Q/m = 540 J / 100 g = 5.4 J/g.
Correct Answer: A — 540 J/g
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Q. What is the length of a chord that is 6 cm away from the center of a circle with a radius of 10 cm? (2015)
A.
8 cm
B.
12 cm
C.
10 cm
D.
6 cm
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Solution
Using Pythagoras: (radius)² = (distance from center)² + (half chord)²; 10² = 6² + (half chord)²; half chord = 8 cm, so full chord = 16 cm.
Correct Answer: A — 8 cm
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Q. What is the length of a chord that is 6 cm from the center of a circle with a radius of 10 cm? (2019)
A.
8 cm
B.
12 cm
C.
10 cm
D.
6 cm
Show solution
Solution
Using Pythagoras: chord length = 2√(r² - d²) = 2√(10² - 6²) = 2√(100 - 36) = 2√64 = 16 cm.
Correct Answer: A — 8 cm
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