Q. What is the integrating factor for the equation dy/dx + 2y = 6?
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A.
e^(2x)
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B.
e^(-2x)
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C.
e^(6x)
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D.
e^(-6x)
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 + 3y = 6?
-
A.
e^(3x)
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B.
e^(-3x)
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C.
3e^(3x)
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D.
3e^(-3x)
Solution
The integrating factor is e^(∫3dx) = e^(3x).
Correct Answer: A — e^(3x)
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Q. What is the integrating factor for the equation dy/dx + 3y = 6x?
-
A.
e^(3x)
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B.
e^(-3x)
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C.
e^(6x)
-
D.
e^(-6x)
Solution
The integrating factor is e^(∫3dx) = e^(3x).
Correct Answer: A — e^(3x)
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Q. What is the interquartile range (IQR) of the data set {1, 3, 5, 7, 9, 11, 13, 15}?
Solution
Q1 = 4, Q3 = 10. IQR = Q3 - Q1 = 10 - 4 = 6.
Correct Answer: B — 6
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Q. What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9, 10}?
Solution
IQR = Q3 - Q1; Q1 = 3, Q3 = 8; IQR = 8 - 3 = 5.
Correct Answer: A — 5
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Q. What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9}?
Solution
Q1 = 3, Q3 = 8. IQR = Q3 - Q1 = 8 - 3 = 5.
Correct Answer: A — 6
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Q. What is the interquartile range (IQR) of the data set: 1, 2, 3, 4, 5, 6, 7, 8, 9?
Solution
Q1 = 3, Q3 = 7; IQR = Q3 - Q1 = 7 - 3 = 4.
Correct Answer: A — 4
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Q. What is the interquartile range (IQR) of the data set: 1, 3, 5, 7, 9, 11, 13?
Solution
Q1 = 3, Q3 = 9. IQR = Q3 - Q1 = 9 - 3 = 6.
Correct Answer: B — 6
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Q. What is the intersection of the sets A = {1, 2, 3} and B = {2, 3, 4}?
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A.
{1, 2, 3}
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B.
{2, 3}
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C.
{4}
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D.
{1, 4}
Solution
The intersection of two sets includes only the elements that are present in both sets. Here, the intersection is {2, 3}.
Correct Answer: B — {2, 3}
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Q. What is the inverse of the function f(x) = 2x + 3?
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A.
(x - 3)/2
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B.
(x + 3)/2
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C.
2x - 3
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D.
2(x - 3)
Solution
To find the inverse, set y = 2x + 3, solve for x: x = (y - 3)/2.
Correct Answer: A — (x - 3)/2
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Q. What is the inverse of the function f(x) = 2x + 5?
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A.
f^-1(x) = (x - 5)/2
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B.
f^-1(x) = 2x - 5
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C.
f^-1(x) = (x + 5)/2
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D.
f^-1(x) = 5 - 2x
Solution
To find the inverse, set y = 2x + 5, solve for x: x = (y - 5)/2, thus f^-1(x) = (x - 5)/2.
Correct Answer: A — f^-1(x) = (x - 5)/2
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Q. What is the inverse of the function f(x) = 3x + 1?
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A.
(x-1)/3
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B.
(x-1)/3
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C.
(x-3)/1
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D.
3(x-1)
Solution
To find the inverse, set y = 3x + 1, solve for x: x = (y - 1)/3.
Correct Answer: A — (x-1)/3
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Q. What is the inverse of the function f(x) = 3x + 4?
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A.
(x - 4)/3
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B.
(x + 4)/3
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C.
3/x - 4
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D.
3/x + 4
Solution
To find the inverse, set y = 3x + 4, solve for x: x = (y - 4)/3, hence the inverse is (x - 4)/3.
Correct Answer: A — (x - 4)/3
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Q. What is the inverse of the function f(x) = 3x - 5?
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A.
(x + 5)/3
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B.
(x - 5)/3
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C.
3(x + 5)
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D.
3(x - 5)
Solution
To find the inverse, set y = 3x - 5, solve for x: x = (y + 5)/3, hence f^(-1)(x) = (x + 5)/3.
Correct Answer: A — (x + 5)/3
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Q. What is the inverse of the matrix A = [[0, 1], [1, 0]]?
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A.
[[0, 1], [1, 0]]
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B.
[[1, 0], [0, 1]]
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C.
[[0, 0], [0, 0]]
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D.
[[1, 1], [1, 1]]
Solution
The inverse of A is A itself since A is an involutory matrix.
Correct Answer: A — [[0, 1], [1, 0]]
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Q. What is the inverse of the matrix A = [[1, 2], [3, 4]]?
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A.
[[4, -2], [-3, 1]]
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B.
[[-2, 1], [1.5, -0.5]]
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C.
[[-2, 1], [1.5, -0.5]]
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D.
[[2, -1], [-1.5, 0.5]]
Solution
The inverse of A is (1/det(A)) * adj(A) = (1/-2) * [[4, -2], [-3, 1]] = [[-2, 1], [1.5, -0.5]].
Correct Answer: A — [[4, -2], [-3, 1]]
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Q. What is the ionization energy of an atom? (2023)
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A.
Energy required to remove an electron
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B.
Energy released when an electron is added
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C.
Energy required to excite an electron
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D.
Energy required to split the nucleus
Solution
Ionization energy is defined as the energy required to remove an electron from an atom in its gaseous state.
Correct Answer: A — Energy required to remove an electron
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Q. What is the ionization energy of hydrogen in eV? (2019)
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A.
1.51 eV
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B.
13.6 eV
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C.
3.4 eV
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D.
10.2 eV
Solution
The ionization energy of hydrogen is 13.6 eV, which is the energy required to remove the electron from the ground state.
Correct Answer: B — 13.6 eV
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Q. What is the isoelectric point (pI) of a protein?
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A.
The pH at which the protein is positively charged
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B.
The pH at which the protein is negatively charged
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C.
The pH at which the protein has no net charge
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D.
The pH at which the protein is denatured
Solution
The isoelectric point (pI) of a protein is the pH at which the protein has no net charge, leading to minimal solubility.
Correct Answer: C — The pH at which the protein has no net charge
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Q. What is the isoelectric point of a protein?
-
A.
The pH at which the protein is positively charged
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B.
The pH at which the protein is negatively charged
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C.
The pH at which the protein has no net charge
-
D.
The pH at which the protein denatures
Solution
The isoelectric point of a protein is the pH at which the protein has no net charge, leading to minimal solubility.
Correct Answer: C — The pH at which the protein has no net charge
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Q. What is the IUPAC name for CH3-CH2-CH2-CHO? (2020)
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A.
Butanal
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B.
Propanal
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C.
Pentanal
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D.
Hexanal
Solution
The IUPAC name for CH3-CH2-CH2-CHO is Butanal, as it has a four-carbon chain with an aldehyde functional group.
Correct Answer: A — Butanal
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Q. What is the IUPAC name for CH3-CH2-CH2-COOH? (2020)
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A.
Butanoic acid
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B.
Propanoic acid
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C.
Pentanoic acid
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D.
Hexanoic acid
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 for CH3-CH2-CH=CH2?
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A.
Butene
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B.
Propene
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C.
Butyne
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D.
Pentene
Solution
The IUPAC name for CH3-CH2-CH=CH2 is butene.
Correct Answer: A — Butene
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Q. What is the IUPAC name for CH3-CH2-CHO?
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A.
Ethyl alcohol
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B.
Propionaldehyde
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C.
Acetaldehyde
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D.
Butyraldehyde
Solution
The IUPAC name for CH3-CH2-CHO is acetaldehyde.
Correct Answer: C — Acetaldehyde
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Q. What is the IUPAC name for CH3-CH2-COOH?
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A.
Propanoic acid
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B.
Butanoic acid
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C.
Acetic acid
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D.
Methanoic acid
Solution
The IUPAC name for CH3-CH2-COOH is propanoic acid, as it has three carbon atoms in the longest chain.
Correct Answer: A — Propanoic acid
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Q. What is the IUPAC name for CH3CH2COOH? (2021)
-
A.
Propanoic acid
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B.
Butanoic acid
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C.
Acetic acid
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D.
Formic acid
Solution
CH3CH2COOH is propanoic acid, which has a three-carbon chain with a carboxylic acid functional group.
Correct Answer: A — Propanoic acid
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Q. What is the IUPAC name for CH3COOH?
-
A.
Methanol
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B.
Ethanol
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C.
Acetic acid
-
D.
Butanoic acid
Solution
The IUPAC name for CH3COOH is acetic acid.
Correct Answer: C — Acetic acid
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Q. What is the IUPAC name for the compound C2H5-CHO?
-
A.
Ethanal
-
B.
Propanoic acid
-
C.
Acetaldehyde
-
D.
Butanal
Solution
The compound is an aldehyde with two carbons, hence the name is Ethanal.
Correct Answer: A — Ethanal
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Q. What is the IUPAC name for the compound C2H5-CO-CH3?
-
A.
2-Pentanone
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B.
3-Pentanone
-
C.
Butan-2-one
-
D.
Butan-3-one
Solution
The compound is a ketone with four carbons, and the carbonyl group is on the second carbon, hence Butan-2-one.
Correct Answer: C — Butan-2-one
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Q. What is the IUPAC name for the compound C2H5OH?
-
A.
Ethanol
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B.
Ethylene
-
C.
Ethane
-
D.
Acetaldehyde
Solution
C2H5OH is ethanol, which is an alcohol with two carbon atoms.
Correct Answer: A — Ethanol
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