Q. What is the general formula for aldehydes? (2023)
A.
C_nH_(2n)
B.
C_nH_(2n+1)CHO
C.
C_nH_(2n+2)
D.
C_nH_(2n-1)CHO
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Solution
The general formula for aldehydes is C_nH_(2n+1)CHO, where n is the number of carbon atoms.
Correct Answer:
B
— C_nH_(2n+1)CHO
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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 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 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 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 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]+? (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 gravitational field strength (g) at a distance r from the center of a planet of mass M? (2023)
A.
GM/r^2
B.
GM/r
C.
GMr^2
D.
G/Mr^2
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Solution
The gravitational field strength at a distance r from the center of a planet is given by g = GM/r^2.
Correct Answer:
A
— GM/r^2
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Q. What is the gravitational field strength at a distance of 10 m from a mass of 100 kg? (G = 6.67 × 10^-11 N m²/kg²)
A.
6.67 × 10^-10 N/kg
B.
6.67 × 10^-9 N/kg
C.
6.67 × 10^-8 N/kg
D.
6.67 × 10^-7 N/kg
Show solution
Solution
g = G * M / r² = (6.67 × 10^-11) * (100) / (10²) = 6.67 × 10^-10 N/kg
Correct Answer:
A
— 6.67 × 10^-10 N/kg
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Q. What is the gravitational field strength at a distance of 3R from the center of the Earth? (R = radius of the Earth) (2022)
A.
g/3
B.
g/9
C.
g/6
D.
g/12
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Solution
Gravitational field strength decreases with the square of the distance. At 3R, it is g/9.
Correct Answer:
B
— g/9
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Q. What is the gravitational field strength at a distance r from a mass M? (2022)
A.
GM/r
B.
GM/r^2
C.
Gm/r^2
D.
Gm/r
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Solution
The gravitational field strength (g) at a distance r from a mass M is given by g = GM/r^2.
Correct Answer:
B
— GM/r^2
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Q. What is the gravitational force acting on a 50 kg object at the surface of the Earth?
A.
490 N
B.
500 N
C.
510 N
D.
520 N
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Solution
Weight = mass * g = 50 kg * 9.8 m/s² = 490 N
Correct Answer:
A
— 490 N
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Q. What is the gravitational force acting on a 50 kg object on the surface of the Earth?
A.
490 N
B.
50 N
C.
5 N
D.
500 N
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Solution
Weight W = m * g = 50 kg * 9.8 m/s² = 490 N.
Correct Answer:
A
— 490 N
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Q. What is the gravitational force between two 1 kg masses placed 1 meter apart? (G = 6.67 × 10^-11 N m²/kg²)
A.
6.67 × 10^-11 N
B.
1.67 × 10^-10 N
C.
6.67 × 10^-10 N
D.
0 N
Show solution
Solution
F = G * (m1 * m2) / r² = (6.67 × 10^-11) * (1 * 1) / (1²) = 6.67 × 10^-11 N
Correct Answer:
A
— 6.67 × 10^-11 N
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Q. What is the gravitational force between two 10 kg masses separated by a distance of 2 m?
A.
0.25 N
B.
5 N
C.
10 N
D.
20 N
Show solution
Solution
Using Newton's law of gravitation: F = G(m1*m2)/r² = (6.674 × 10⁻¹¹)(10*10)/(2²) = 0.25 N.
Correct Answer:
A
— 0.25 N
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Q. What is the gravitational force between two objects of mass 5 kg and 10 kg separated by a distance of 2 m? (G = 6.67 × 10^-11 N m²/kg²)
A.
1.67 × 10^-10 N
B.
1.25 × 10^-10 N
C.
1.00 × 10^-10 N
D.
2.00 × 10^-10 N
Show solution
Solution
Using the formula F = G * (m1 * m2) / r², we have F = (6.67 × 10^-11) * (5 * 10) / (2²) = 1.67 × 10^-10 N.
Correct Answer:
A
— 1.67 × 10^-10 N
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Q. What is the gravitational force between two objects of mass m1 and m2 separated by a distance r? (2021)
A.
G * (m1 * m2) / r^2
B.
G * (m1 + m2) / r^2
C.
G * (m1 - m2) / r^2
D.
G * (m1 * m2) * r^2
Show solution
Solution
The gravitational force is given by Newton's law of gravitation: F = G * (m1 * m2) / r^2.
Correct Answer:
A
— G * (m1 * m2) / r^2
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Q. What is the gravitational potential energy of a 10 kg mass at a height of 10 m?
A.
100 J
B.
200 J
C.
500 J
D.
1000 J
Show solution
Solution
Gravitational potential energy (PE) is given by PE = mgh. Here, PE = 10 kg * 9.81 m/s² * 10 m = 981 J.
Correct Answer:
D
— 1000 J
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Q. What is the gravitational potential energy of a 10 kg mass at a height of 5 m? (2019)
A.
50 J
B.
100 J
C.
150 J
D.
200 J
Show solution
Solution
Gravitational potential energy (PE) = m * g * h = 10 kg * 9.81 m/s² * 5 m = 490.5 J.
Correct Answer:
B
— 100 J
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Q. What is the gravitational potential energy of a 10 kg object at a height of 10 m?
A.
100 J
B.
200 J
C.
500 J
D.
1000 J
Show solution
Solution
Gravitational potential energy (PE) is given by the formula PE = mgh. Here, PE = 10 kg * 9.8 m/s² * 10 m = 980 J, which rounds to approximately 1000 J.
Correct Answer:
B
— 200 J
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Q. What is the gravitational potential energy of a 10 kg object at a height of 5 m? (g = 9.8 m/s²)
A.
49 J
B.
98 J
C.
245 J
D.
490 J
Show solution
Solution
Gravitational potential energy (PE) is given by PE = mgh. Here, m = 10 kg, g = 9.8 m/s², and h = 5 m. PE = 10 * 9.8 * 5 = 490 J.
Correct Answer:
B
— 98 J
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Q. What is the gravitational potential energy of a 2 kg mass at a height of 10 m above the ground? (Take g = 9.8 m/s²) (2023)
A.
196 J
B.
98 J
C.
20 J
D.
78 J
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Solution
Gravitational potential energy (U) = mgh = 2 kg * 9.8 m/s² * 10 m = 196 J.
Correct Answer:
A
— 196 J
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Q. What is the gravitational potential energy of a 2 kg object at a height of 10 m? (2023)
A.
20 J
B.
15 J
C.
10 J
D.
25 J
Show solution
Solution
Gravitational potential energy (PE) = mgh = 2 kg × 9.8 m/s² × 10 m = 196 J.
Correct Answer:
A
— 20 J
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Q. What is the gravitational potential energy of a 5 kg object at a height of 10 m?
A.
50 J
B.
100 J
C.
150 J
D.
200 J
Show solution
Solution
Gravitational potential energy (PE) = m * g * h = 5 kg * 9.8 m/s² * 10 m = 490 J.
Correct Answer:
B
— 100 J
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Q. What is the ground state electron configuration of an oxygen atom? (2023)
A.
1s² 2s² 2p⁴
B.
1s² 2s² 2p²
C.
1s² 2s² 2p⁶
D.
1s² 2s¹ 2p⁵
Show solution
Solution
Oxygen has 8 electrons, and its ground state electron configuration is 1s² 2s² 2p⁴.
Correct Answer:
A
— 1s² 2s² 2p⁴
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