Undergraduate
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
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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
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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
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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 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 for CH3-CH2-CH2-COOH? (2020)
A.
Butanoic acid
B.
Propanoic acid
C.
Pentanoic acid
D.
Hexanoic acid
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Solution
The IUPAC name for CH3-CH2-CH2-COOH is Butanoic acid, as it has four carbon atoms.
Correct Answer: A — Butanoic acid
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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 carboxylic acid with the formula C3H6O2? (2023)
A.
Propanoic acid
B.
Butanoic acid
C.
Acetic acid
D.
Formic acid
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Solution
The IUPAC name of C3H6O2 is Propanoic acid, which has a three-carbon chain.
Correct Answer: A — Propanoic acid
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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 jelly-like substance inside the cell called? (2018)
A.
Nucleoplasm
B.
Cytoplasm
C.
Protoplasm
D.
Chloroplast
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Solution
Cytoplasm is the jelly-like substance that fills the cell and contains organelles.
Correct Answer: B — Cytoplasm
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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
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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 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
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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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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021) 2021
A.
10.47 cm
B.
15.71 cm
C.
20.94 cm
D.
25.13 cm
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Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Correct Answer: A — 10.47 cm
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Q. What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)
A.
2π cm
B.
4π cm
C.
π cm
D.
8 cm
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Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π * 4 = 2π cm.
Correct Answer: A — 2π cm
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Q. What is the length of an arc of a circle with a radius of 5 cm and a central angle of 60 degrees? (2020)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
10.47 cm
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Solution
Arc length = (θ/360) * 2πr = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.
Correct Answer: A — 5.24 cm
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Q. What is the length of an arc of a circle with radius 5 cm and angle 60 degrees? (2020)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
6.00 cm
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Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * π * 5 = 5.24 cm.
Correct Answer: A — 5.24 cm
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Q. What is the length of the diagonal of a rectangle with vertices at (0, 0), (4, 0), (4, 3), and (0, 3)? (2021)
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Solution
Length of diagonal = √[(4-0)² + (3-0)²] = √[16 + 9] = √25 = 5.
Correct Answer: A — 5
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Q. What is the length of the diagonal of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4)? (2021)
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Solution
Diagonal length = √[(5-1)² + (4-1)²] = √[16 + 9] = √25 = 5.
Correct Answer: B — 5
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Q. What is the magnetic field inside a long solenoid? (2023)
A.
Zero
B.
Uniform and parallel
C.
Concentric circles
D.
Decreasing
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Solution
The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid.
Correct Answer: B — Uniform and parallel
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