Q. Which of the following is true for all angles A?
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A.
sin^2 A + cos^2 A = 1
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B.
tan A = sin A/cos A
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C.
sec A = 1/cos A
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D.
All of the above
Solution
All the given identities are true for all angles A.
Correct Answer: D — All of the above
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Q. Which of the following lines is parallel to the line 4x - 5y + 10 = 0?
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A.
y = (4/5)x + 2
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B.
y = (5/4)x - 1
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C.
y = (4/5)x - 3
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D.
y = (-5/4)x + 1
Solution
The slope of the given line is 4/5. A line parallel to it must have the same slope, hence y = (4/5)x - 3.
Correct Answer: C — y = (4/5)x - 3
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Q. Which of the following measures is NOT a measure of dispersion?
-
A.
Range
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B.
Variance
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C.
Mean
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D.
Standard Deviation
Solution
Mean is a measure of central tendency, not dispersion.
Correct Answer: C — Mean
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Q. Which of the following measures of dispersion is affected by extreme values?
-
A.
Range
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B.
Interquartile Range
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C.
Variance
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D.
Standard Deviation
Solution
Range is affected by extreme values as it is calculated as the difference between the maximum and minimum values.
Correct Answer: A — Range
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Q. Which of the following relations is an equivalence relation on the set of integers?
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A.
x ~ y if x + y is even
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B.
x ~ y if x - y is prime
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C.
x ~ y if x > y
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D.
x ~ y if x = y
Solution
The relation x ~ y if x + y is even is reflexive, symmetric, and transitive, thus it is an equivalence relation.
Correct Answer: A — x ~ y if x + y is even
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Q. Which of the following relations is not a function?
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A.
R = {(1, 2), (2, 3), (3, 4)}
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B.
R = {(1, 2), (1, 3)}
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C.
R = {(2, 3), (3, 4)}
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D.
R = {(4, 5), (5, 6)}
Solution
R = {(1, 2), (1, 3)} is not a function because the input 1 maps to two different outputs.
Correct Answer: B — R = {(1, 2), (1, 3)}
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Q. Which of the following relations on the set of integers is not a function?
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A.
R1 = {(1, 2), (1, 3)}
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B.
R2 = {(2, 3), (3, 4)}
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C.
R3 = {(4, 5)}
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D.
R4 = {(5, 6), (6, 7)}
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?
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A.
(x - h)^2 + (y - k)^2 = r^2
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B.
(x - h)^2 + (y - k) = r
-
C.
x^2 + y^2 = r
-
D.
x^2 + y^2 = kx
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)?
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A.
Linear functions
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B.
Exponential functions
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C.
Sine waves with varying amplitudes and frequencies
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D.
Quadratic functions
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?
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A.
Linear functions
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B.
Quadratic functions
-
C.
Cubic functions
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D.
Exponential functions
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)
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B.
y = ax^2 + bx + c
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C.
y = a sin(bx)
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D.
y = a log(bx)
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?
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A.
y = mx + c
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B.
y = ax^2 + bx + c
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C.
y = e^x
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D.
y = sin(x)
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 hyperbola with transverse axis along the x-axis?
-
A.
x^2/a^2 - y^2/b^2 = 1
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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
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 the solution to the inequality 4 - x < 1?
-
A.
x > 3
-
B.
x < 3
-
C.
x > 4
-
D.
x < 4
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
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
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
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
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
Solution
x/3 - 2 < 1 => x/3 < 3 => x < 9.
Correct Answer: A — x < 9
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Q. Which of the following sets is a power set of F = {1, 2}?
-
A.
{{1}, {2}}
-
B.
{{}, {1}, {2}, {1, 2}}
-
C.
{{1, 2}}
-
D.
{{1, 2}, {1}}
Solution
The power set of F = {1, 2} is {{}, {1}, {2}, {1, 2}}.
Correct Answer: B — {{}, {1}, {2}, {1, 2}}
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Q. Which of the following sets is a power set of F = {a, b}?
-
A.
{∅, {a}, {b}}
-
B.
{∅, {a}, {b}, {a, b}}
-
C.
{a, b}
-
D.
{a, b, ∅}
Solution
The power set of F = {a, b} is {∅, {a}, {b}, {a, b}}.
Correct Answer: B — {∅, {a}, {b}, {a, b}}
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Q. Which of the following sets is a universal set for the sets A = {1, 2} and B = {2, 3}?
-
A.
{1, 2, 3}
-
B.
{2, 3, 4}
-
C.
{1, 2, 4}
-
D.
{1, 3}
Solution
A universal set contains all elements under consideration. Here, {1, 2, 3} contains all elements from both A and B.
Correct Answer: A — {1, 2, 3}
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Q. Which of the following sets is equal to the power set of G = {x, y}?
-
A.
{∅, {x}, {y}, {x, y}}
-
B.
{x, y}
-
C.
{∅, {x, y}}
-
D.
{x, y, ∅}
Solution
The power set of a set with n elements has 2^n subsets. For G, n=2, so the power set is {∅, {x}, {y}, {x, y}}.
Correct Answer: A — {∅, {x}, {y}, {x, y}}
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Q. Which of the following sets is equal to the set of all subsets of {1, 2}?
-
A.
{{1}, {2}}
-
B.
{{}, {1}, {2}, {1, 2}}
-
C.
{{1, 2}}
-
D.
{{1, 2}, {1}, {2}}
Solution
The power set of {1, 2} is {{}, {1}, {2}, {1, 2}}.
Correct Answer: B — {{}, {1}, {2}, {1, 2}}
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Q. Which of the following sets is not a subset of {1, 2, 3, 4}?
-
A.
{1, 2}
-
B.
{2, 3, 4}
-
C.
{5}
-
D.
{1, 2, 3}
Solution
A subset can only contain elements from the original set. {5} is not a subset of {1, 2, 3, 4}.
Correct Answer: C — {5}
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Q. Which of the following sets is not a subset of {x | x is a natural number}?
-
A.
{1, 2}
-
B.
{0}
-
C.
{3, 4}
-
D.
{5, 6}
Solution
The set {0} is not a subset of the natural numbers, as natural numbers start from 1.
Correct Answer: B — {0}
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Q. Which of the following statements is true about continuous functions?
-
A.
They can be differentiated everywhere
-
B.
They are always bounded
-
C.
They can be integrated
-
D.
They can have jump discontinuities
Solution
Continuous functions can be integrated over an interval, but they are not necessarily differentiable or bounded.
Correct Answer: C — They can be integrated
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