Q. What is the general formula for cycloalkanes?
A.
CnH2n
B.
CnH2n+2
C.
CnH2n-2
D.
CnH2n-4
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Solution
The general formula for cycloalkanes is CnH2n.
Correct Answer:
A
— CnH2n
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Q. What is the general formula for ketones?
A.
CnH2nO
B.
CnH2n+2O
C.
CnH2n-2O
D.
CnH2nO2
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Solution
The general formula for ketones is CnH2nO, where n is the number of carbon atoms.
Correct Answer:
A
— CnH2nO
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Q. What is the general formula for secondary amines? (2021) 2021
A.
RNH2
B.
R2NH
C.
R3N
D.
RNH
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Solution
The general formula for secondary amines is R2NH, where R represents an alkyl or aryl group.
Correct Answer:
B
— R2NH
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Q. What is the general formula for secondary amines? (2023)
A.
RNH2
B.
R2NH
C.
R3N
D.
RNH
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Solution
The general formula for secondary amines is R2NH, where R represents an alkyl group.
Correct Answer:
B
— R2NH
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Q. What is the general solution of the differential equation dy/dx = 3x^2?
A.
y = x^3 + C
B.
y = 3x^3 + C
C.
y = x^2 + C
D.
y = 3x^2 + C
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Solution
Integrating both sides gives y = ∫3x^2 dx = x^3 + C.
Correct Answer:
A
— y = x^3 + C
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Q. What is the general solution of the differential equation dy/dx = 3y?
A.
y = Ce^(3x)
B.
y = Ce^(-3x)
C.
y = 3x + C
D.
y = Cx^3
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Solution
The differential equation is separable. Integrating both sides gives ln|y| = 3x + C, hence y = Ce^(3x).
Correct Answer:
A
— y = Ce^(3x)
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Q. What is the general solution of the differential equation dy/dx = 4y? (2019)
A.
y = Ce^(4x)
B.
y = Ce^(x/4)
C.
y = 4Ce^x
D.
y = 4Ce^(4x)
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Solution
The differential equation dy/dx = 4y can be solved using separation of variables, leading to y = Ce^(4x).
Correct Answer:
A
— y = Ce^(4x)
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Q. What is the general solution of the equation y' + 4y = 0?
A.
y = Ce^(-4x)
B.
y = Ce^(4x)
C.
y = 4x + C
D.
y = Cx^4
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Solution
This is a separable equation, and integrating gives y = Ce^(-4x).
Correct Answer:
A
— y = Ce^(-4x)
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Q. What is the general solution of the equation y' = 4y + 3?
A.
y = Ce^(4x) - 3/4
B.
y = Ce^(4x) + 3/4
C.
y = 3e^(4x)
D.
y = Ce^(3x) + 4
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Solution
The integrating factor is e^(-4x). The solution is y = Ce^(4x) + 3/4.
Correct Answer:
B
— y = Ce^(4x) + 3/4
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Q. What is the general solution of the equation y'' - 3y' + 2y = 0?
A.
y = C1 e^(x) + C2 e^(2x)
B.
y = C1 e^(2x) + C2 e^(x)
C.
y = C1 e^(3x) + C2 e^(0)
D.
y = C1 e^(0) + C2 e^(3x)
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Solution
The characteristic equation is r^2 - 3r + 2 = 0, which factors to (r - 1)(r - 2) = 0. Thus, the general solution is y = C1 e^(2x) + C2 e^(x).
Correct Answer:
B
— y = C1 e^(2x) + C2 e^(x)
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Q. What is the general solution of the equation y'' - 4y' + 4y = 0?
A.
y = (C1 + C2x)e^(2x)
B.
y = C1 e^(2x) + C2 e^(-2x)
C.
y = C1 e^(4x) + C2 e^(-4x)
D.
y = C1 cos(2x) + C2 sin(2x)
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Solution
The characteristic equation has a repeated root r = 2. The general solution is y = (C1 + C2x)e^(2x).
Correct Answer:
A
— y = (C1 + C2x)e^(2x)
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Q. What is the general term in the expansion of (x + y)^n?
A.
C(n, k)x^k y^(n-k)
B.
C(n, k)x^(n-k) y^k
C.
C(n, k)x^n y^k
D.
C(n, k)x^k y^n
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Solution
The general term in the expansion of (x + y)^n is given by C(n, k)x^k y^(n-k).
Correct Answer:
A
— C(n, k)x^k y^(n-k)
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Q. What is the general trend in the melting points of alkali metals as you move down the group?
A.
They increase
B.
They decrease
C.
They remain constant
D.
They fluctuate
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Solution
The melting points of alkali metals generally decrease as you move down the group due to the increase in atomic size and decrease in metallic bonding strength.
Correct Answer:
B
— They decrease
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Q. What is the general trend of ionization energy across a period?
A.
Increases
B.
Decreases
C.
Remains constant
D.
Increases then decreases
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Solution
Ionization energy generally increases across a period due to increasing nuclear charge.
Correct Answer:
A
— Increases
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Q. What is the genetic material in most living organisms? (2023)
A.
RNA
B.
DNA
C.
Protein
D.
Carbohydrate
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Solution
DNA (deoxyribonucleic acid) is the genetic material that carries the instructions for life.
Correct Answer:
B
— DNA
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Q. What is the geometric interpretation of the solution to a system of linear equations?
A.
The area enclosed by the lines
B.
The point of intersection of the lines
C.
The distance between the lines
D.
The angle between the lines
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Solution
The solution represents the point where the lines intersect, if they do.
Correct Answer:
B
— The point of intersection of the lines
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Q. What is the geometric interpretation of the solution to a system of linear equations in two variables?
A.
The point where the two lines intersect.
B.
The area enclosed by the lines.
C.
The distance between the lines.
D.
The slope of the lines.
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Solution
The solution to a system of linear equations in two variables is represented by the point where the two lines intersect.
Correct Answer:
A
— The point where the two lines intersect.
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Q. What is the geometric interpretation of the solution to a system of two linear equations?
A.
The area between the lines.
B.
The point of intersection of the lines.
C.
The distance between the lines.
D.
The slope of the lines.
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Solution
The solution to a system of two linear equations is represented by the point where the two lines intersect.
Correct Answer:
B
— The point of intersection of the lines.
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Q. What is the geometric representation of the equation 3x - 4y = 12?
A.
A point
B.
A line
C.
A plane
D.
A curve
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Solution
Linear equations represent straight lines in a two-dimensional space.
Correct Answer:
B
— A line
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Q. What is the geometric representation of the equation 5x + 2y = 10?
A.
A point
B.
A line
C.
A plane
D.
A curve
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Solution
The equation represents a straight line in a two-dimensional space.
Correct Answer:
B
— A line
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Q. What is the geometric representation of the equation x + 2y = 4?
A.
A point
B.
A line
C.
A plane
D.
A curve
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Solution
The equation x + 2y = 4 represents a straight line in a two-dimensional space.
Correct Answer:
B
— A line
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Q. What is the geometry of a molecule with four bonding pairs and no lone pairs around the central atom? (2023)
A.
Linear
B.
Trigonal planar
C.
Tetrahedral
D.
Octahedral
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Solution
The geometry is tetrahedral when there are four bonding pairs and no lone pairs around the central atom.
Correct Answer:
C
— Tetrahedral
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Q. What is the geometry of a molecule with four bonding pairs and no lone pairs? (2023)
A.
Linear
B.
Trigonal planar
C.
Tetrahedral
D.
Octahedral
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Solution
A molecule with four bonding pairs and no lone pairs has a tetrahedral geometry.
Correct Answer:
C
— Tetrahedral
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Q. What is the geometry of a molecule with sp3d hybridization?
A.
Linear
B.
Trigonal planar
C.
Tetrahedral
D.
Trigonal bipyramidal
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Solution
Molecules with sp3d hybridization have a trigonal bipyramidal geometry.
Correct Answer:
D
— Trigonal bipyramidal
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Q. What is the geometry of a molecule with two bonding pairs and no lone pairs on the central atom? (2023)
A.
Linear
B.
Trigonal planar
C.
Tetrahedral
D.
Bent
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Solution
The geometry is linear when there are two bonding pairs and no lone pairs on the central atom.
Correct Answer:
A
— Linear
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Q. What is the geometry of the complex ion [Ag(NH3)2]+?
A.
Linear
B.
Tetrahedral
C.
Octahedral
D.
Square planar
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Solution
The geometry of [Ag(NH3)2]+ is linear due to the presence of two ligands.
Correct Answer:
A
— Linear
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Q. What is the geometry of the complex ion [Ag(NH3)2]+? (2019) 2019
A.
Tetrahedral
B.
Square planar
C.
Octahedral
D.
Linear
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Solution
The complex [Ag(NH3)2]+ has a linear geometry due to the presence of two ligands around the silver ion.
Correct Answer:
D
— Linear
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Q. What is the geometry of the complex ion [Cu(NH3)4]2+?
A.
Tetrahedral
B.
Square planar
C.
Octahedral
D.
Trigonal bipyramidal
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Solution
The geometry of the complex ion [Cu(NH3)4]2+ is square planar.
Correct Answer:
B
— Square planar
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Q. What is the geometry of the complex ion [Ni(CN)4]2-?
A.
Tetrahedral
B.
Square planar
C.
Octahedral
D.
Trigonal bipyramidal
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Solution
[Ni(CN)4]2- has a square planar geometry due to the presence of 4 ligands around the nickel ion.
Correct Answer:
B
— Square planar
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Q. What is the geometry of the complex [Ag(NH3)2]+?
A.
Linear
B.
Tetrahedral
C.
Square Planar
D.
Octahedral
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Solution
The geometry of [Ag(NH3)2]+ is linear due to the coordination number of 2.
Correct Answer:
A
— Linear
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