Q. Which of the following relations on the set of integers is not a function?
A.
R1 = {(1, 2), (1, 3)}
B.
R2 = {(2, 3), (3, 4)}
C.
R3 = {(4, 5)}
D.
R4 = {(5, 6), (6, 7)}
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Solution
R1 is not a function because the input 1 maps to two different outputs (2 and 3).
Correct Answer: A — R1 = {(1, 2), (1, 3)}
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Q. Which of the following represents a family of circles with varying radii?
A.
(x - h)^2 + (y - k)^2 = r^2
B.
(x - h)^2 + (y - k) = r
C.
x^2 + y^2 = r
D.
x^2 + y^2 = kx
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Solution
The equation (x - h)^2 + (y - k)^2 = r^2 represents a circle centered at (h, k) with radius r.
Correct Answer: A — (x - h)^2 + (y - k)^2 = r^2
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Q. Which of the following represents a family of curves for the equation y = a sin(bx)?
A.
Linear functions
B.
Exponential functions
C.
Sine waves with varying amplitudes and frequencies
D.
Quadratic functions
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Solution
The equation y = a sin(bx) represents sine waves where 'a' is the amplitude and 'b' is the frequency.
Correct Answer: C — Sine waves with varying amplitudes and frequencies
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Q. Which of the following represents a family of curves for the equation y = ax^2 + bx + c?
A.
Linear functions
B.
Quadratic functions
C.
Cubic functions
D.
Exponential functions
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Solution
The equation y = ax^2 + bx + c represents a family of quadratic functions where 'a', 'b', and 'c' are constants.
Correct Answer: B — Quadratic functions
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Q. Which of the following represents a family of exponential curves?
A.
y = ae^(bx)
B.
y = ax^2 + bx + c
C.
y = a sin(bx)
D.
y = a log(bx)
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Solution
The equation y = ae^(bx) represents a family of exponential curves where a and b are constants.
Correct Answer: A — y = ae^(bx)
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Q. Which of the following represents a family of straight lines?
A.
y = mx + c
B.
y = ax^2 + bx + c
C.
y = e^x
D.
y = sin(x)
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Solution
The equation y = mx + c represents a family of straight lines for different values of m and c.
Correct Answer: A — y = mx + c
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Q. Which of the following represents a homozygous dominant genotype? (2021)
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Solution
The genotype 'AA' represents a homozygous dominant individual.
Correct Answer: A — AA
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Q. Which of the following represents a hyperbola with transverse axis along the x-axis?
A.
x^2/a^2 - y^2/b^2 = 1
B.
y^2/a^2 - x^2/b^2 = 1
C.
x^2/b^2 - y^2/a^2 = 1
D.
y^2/b^2 - x^2/a^2 = 1
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Solution
The equation x^2/a^2 - y^2/b^2 = 1 represents a hyperbola with transverse axis along the x-axis.
Correct Answer: A — x^2/a^2 - y^2/b^2 = 1
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Q. Which of the following represents a phenotype? (2021)
A.
BB
B.
Bb
C.
bb
D.
Brown eyes
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Solution
A phenotype is the observable characteristic, such as brown eyes.
Correct Answer: D — Brown eyes
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Q. Which of the following represents a physical change?
A.
Burning wood
B.
Dissolving sugar in water
C.
Rusting of iron
D.
Cooking an egg
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Solution
Dissolving sugar in water is a physical change as it does not alter the chemical composition of sugar.
Correct Answer: B — Dissolving sugar in water
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Q. Which of the following represents a systematic error? (2020)
A.
Calibration error
B.
Random fluctuations
C.
Environmental changes
D.
Human error
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Solution
Systematic errors are consistent and repeatable inaccuracies, often due to calibration errors.
Correct Answer: A — Calibration error
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Q. Which of the following represents a test cross? (2020)
A.
AA x aa
B.
Aa x Aa
C.
AA x Aa
D.
aa x aa
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Solution
A test cross is performed by crossing an individual with a homozygous recessive individual (AA x aa) to determine the genotype of the former.
Correct Answer: A — AA x aa
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Q. Which of the following represents an endothermic reaction?
A.
Combustion of gasoline
B.
Dissolving ammonium nitrate in water
C.
Respiration
D.
Rusting of iron
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Solution
Dissolving ammonium nitrate in water absorbs heat, making it an endothermic reaction.
Correct Answer: B — Dissolving ammonium nitrate in water
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Q. Which of the following represents the concept of significant figures? (2023)
A.
All digits in a number
B.
Only the non-zero digits
C.
All digits except leading zeros
D.
All digits except trailing zeros
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Solution
Significant figures include all non-zero digits and any zeros between them or trailing after a decimal point.
Correct Answer: C — All digits except leading zeros
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Q. Which of the following represents the correct relationship between moles and mass?
A.
Moles = Mass / Molar Mass
B.
Mass = Moles x Molar Mass
C.
Molar Mass = Mass / Moles
D.
All of the above
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Solution
All the given relationships are correct and represent the conversion between moles, mass, and molar mass.
Correct Answer: D — All of the above
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Q. Which of the following represents the correct relationship between moles, mass, and molar mass?
A.
moles = mass × molar mass
B.
mass = moles × molar mass
C.
molar mass = mass / moles
D.
mass = moles / molar mass
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Solution
The correct relationship is mass = moles × molar mass.
Correct Answer: B — mass = moles × molar mass
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Q. Which of the following represents the enthalpy change for a reaction at constant pressure?
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Solution
The enthalpy change for a reaction at constant pressure is represented by ΔH.
Correct Answer: B — ΔH
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Q. Which of the following represents the ideal gas constant? (2022)
A.
R = 0.0821 L·atm/(K·mol)
B.
R = 8.314 J/(K·mol)
C.
Both A and B
D.
None of the above
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Solution
The ideal gas constant can be represented as R = 0.0821 L·atm/(K·mol) or R = 8.314 J/(K·mol).
Correct Answer: C — Both A and B
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Q. Which of the following represents the number of particles in one mole of a substance?
A.
6.022 x 10^23
B.
3.14 x 10^22
C.
1.6 x 10^19
D.
9.11 x 10^28
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Solution
Avogadro's number is 6.022 x 10^23, which represents the number of particles in one mole.
Correct Answer: A — 6.022 x 10^23
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Q. Which of the following represents the slope of the line represented by the equation y = mx + b?
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Solution
In the equation y = mx + b, 'm' represents the slope of the line.
Correct Answer: A — m
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Q. Which of the following represents the solution to the inequality 4 - x < 1?
A.
x > 3
B.
x < 3
C.
x > 4
D.
x < 4
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Solution
4 - x < 1 => -x < -3 => x > 3
Correct Answer: A — x > 3
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Q. Which of the following represents the solution to the inequality 4 - x < 2?
A.
x < 2
B.
x > 2
C.
x < 4
D.
x > 4
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Solution
4 - x < 2 => -x < -2 => x > 2.
Correct Answer: B — x > 2
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Q. Which of the following represents the solution to the inequality 6x - 4 ≤ 2x + 8?
A.
x ≤ 3
B.
x ≥ 3
C.
x < 3
D.
x > 3
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Solution
6x - 4 ≤ 2x + 8 => 4x ≤ 12 => x ≤ 3.
Correct Answer: B — x ≥ 3
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Q. Which of the following represents the solution to the inequality 7x - 4 < 10?
A.
x < 2
B.
x > 2
C.
x < 3
D.
x > 3
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Solution
7x - 4 < 10 => 7x < 14 => x < 2.
Correct Answer: C — x < 3
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Q. Which of the following represents the solution to the inequality x/3 + 2 < 5?
A.
x < 9
B.
x > 9
C.
x < 6
D.
x > 6
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Solution
x/3 + 2 < 5 => x/3 < 3 => x < 9.
Correct Answer: A — x < 9
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Q. Which of the following represents the solution to the inequality x/3 - 2 < 1?
A.
x < 9
B.
x > 9
C.
x ≤ 9
D.
x ≥ 9
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Solution
x/3 - 2 < 1 => x/3 < 3 => x < 9.
Correct Answer: A — x < 9
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Q. Which of the following revolutions is associated with the establishment of constitutional governance in England?
A.
Glorious Revolution
B.
American Revolution
C.
French Revolution
D.
Industrial Revolution
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Solution
The Glorious Revolution of 1688 is associated with the establishment of constitutional governance in England, limiting the powers of the monarchy.
Correct Answer: A — Glorious Revolution
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Q. Which of the following revolutions is associated with the phrase 'Liberty, Equality, Fraternity'?
A.
American Revolution
B.
French Revolution
C.
Russian Revolution
D.
Industrial Revolution
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Solution
The phrase 'Liberty, Equality, Fraternity' is associated with the French Revolution, which emphasized these ideals as fundamental rights.
Correct Answer: B — French Revolution
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Q. Which of the following revolutions is associated with the rise of industrial capitalism in the 18th century?
A.
American Revolution
B.
French Revolution
C.
Industrial Revolution
D.
Russian Revolution
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Solution
The Industrial Revolution, which began in the late 18th century, marked the transition to industrial capitalism, characterized by the growth of factories, mechanization, and urbanization.
Correct Answer: C — Industrial Revolution
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Q. Which of the following revolutions is known for the phrase 'Liberty, Equality, Fraternity'?
A.
The American Revolution.
B.
The French Revolution.
C.
The Russian Revolution.
D.
The Industrial Revolution.
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Solution
The phrase 'Liberty, Equality, Fraternity' is famously associated with the French Revolution, encapsulating its core ideals.
Correct Answer: B — The French Revolution.
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