Q. What is the probability of rolling an even number on a single die?
-
A.
1/2
-
B.
1/3
-
C.
1/6
-
D.
2/3
Solution
Even numbers on a die = 2, 4, 6. Probability = 3/6 = 1/2.
Correct Answer: A — 1/2
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Q. What is the probability of rolling an even number on a single six-sided die?
-
A.
1/2
-
B.
1/3
-
C.
1/6
-
D.
2/3
Solution
The even numbers on a die are 2, 4, and 6. There are 3 even numbers out of 6 total numbers, so the probability is 3/6 = 1/2.
Correct Answer: A — 1/2
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Q. What is the probability of selecting a vowel from the English alphabet?
-
A.
1/5
-
B.
1/10
-
C.
1/26
-
D.
1/13
Solution
There are 5 vowels (A, E, I, O, U) in the English alphabet of 26 letters. Therefore, P(vowel) = 5/26.
Correct Answer: A — 1/5
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Q. What is the product of (1 + i) and (1 - i)?
Solution
(1 + i)(1 - i) = 1 - i^2 = 1 - (-1) = 2.
Correct Answer: A — 2
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Q. What is the product of the complex numbers (1 + i) and (1 - i)?
Solution
(1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 2.
Correct Answer: A — 2
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Q. What is the product of the complex numbers z1 = 1 + i and z2 = 1 - i?
Solution
z1 * z2 = (1 + i)(1 - i) = 1 - i^2 = 1 + 1 = 2.
Correct Answer: A — 2
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Q. What is the product of the roots of the equation 2x^2 + 3x - 5 = 0?
-
A.
-5/2
-
B.
5/2
-
C.
2/5
-
D.
-2/5
Solution
The product of the roots is c/a = -5/2.
Correct Answer: A — -5/2
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Q. What is the product of the roots of the equation 2x^2 - 3x + 1 = 0?
Solution
Using Vieta's formulas, the product of the roots is 1/2 (c/a = 1/2).
Correct Answer: A — 1/2
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Q. What is the product of the roots of the equation 3x^2 + 6x + 2 = 0?
-
A.
2/3
-
B.
1/3
-
C.
1/2
-
D.
1/6
Solution
The product of the roots is given by c/a = 2/3.
Correct Answer: B — 1/3
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Q. What is the product of the roots of the equation 3x^2 - 12x + 9 = 0?
Solution
The product of the roots is given by c/a = 9/3 = 3.
Correct Answer: C — 4
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Q. What is the product of the roots of the equation x^2 - 6x + 8 = 0?
Solution
The product of the roots is given by c/a = 8/1 = 8.
Correct Answer: B — 8
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Q. What is the product of the roots of the equation x^2 - 8x + 15 = 0?
Solution
The product of the roots is given by c/a = 15/1 = 15.
Correct Answer: A — 15
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Q. What is the projection of vector a = (3, 4) onto vector b = (1, 0)?
Solution
Projection = (a · b / |b|^2) * b = (3*1 + 4*0) / 1^2 * (1, 0) = 3 * (1, 0) = (3, 0).
Correct Answer: A — 3
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Q. What is the projection of vector A = (3, 4) onto vector B = (1, 2)?
Solution
Projection = (A . B / |B|^2) * B = (3*1 + 4*2) / (1^2 + 2^2) * (1, 2) = 11/5 * (1, 2) = (2.2, 4.4).
Correct Answer: B — 3
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Q. What is the radius of the circle given by the equation (x - 1)² + (y + 4)² = 16?
Solution
The radius is the square root of 16, which is 4.
Correct Answer: A — 4
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Q. What is the range of sin^(-1)(x)?
-
A.
[-π/2, π/2]
-
B.
[-1, 1]
-
C.
[0, π]
-
D.
[-π, π]
Solution
The range of sin^(-1)(x) is [-π/2, π/2].
Correct Answer: A — [-π/2, π/2]
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Q. What is the range of the data set {15, 22, 18, 30, 25}?
Solution
Range = Maximum value - Minimum value = 30 - 15 = 15.
Correct Answer: A — 15
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Q. What is the range of the data set {15, 22, 30, 18, 25}?
Solution
Range = Maximum - Minimum = 30 - 15 = 15.
Correct Answer: A — 15
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Q. What is the range of the data set {4, 8, 6, 5, 3}?
Solution
Range = Maximum value - Minimum value = 8 - 3 = 5.
Correct Answer: A — 5
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Q. What is the range of the data set {5, 8, 12, 15, 20}?
Solution
Range = Maximum value - Minimum value = 20 - 5 = 15.
Correct Answer: A — 15
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Q. What is the range of the data set: 12, 15, 22, 30, 5?
Solution
Range = max - min = 30 - 5 = 25.
Correct Answer: A — 25
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Q. What is the range of the data set: 5, 10, 15, 20, 25?
Solution
Range = Maximum - Minimum = 25 - 5 = 20.
Correct Answer: A — 15
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Q. What is the range of the data set: 5, 7, 9, 12, 15?
Solution
Range = Maximum - Minimum = 15 - 5 = 10.
Correct Answer: A — 10
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Q. What is the range of the following data set: 10, 20, 30, 40, 50?
Solution
Range = Maximum - Minimum = 50 - 10 = 40.
Correct Answer: A — 30
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Q. What is the range of the following data set: 5, 10, 15, 20, 25?
Solution
Range = Maximum - Minimum = 25 - 5 = 20.
Correct Answer: A — 15
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Q. What is the range of the function f(x) = -x^2 + 4?
-
A.
(-∞, 4]
-
B.
[0, 4]
-
C.
[4, ∞)
-
D.
(-∞, 0)
Solution
The function is a downward-opening parabola with a maximum value of 4, so the range is (-∞, 4].
Correct Answer: A — (-∞, 4]
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Q. What is the range of the function f(x) = x^2?
-
A.
(-∞, ∞)
-
B.
[0, ∞)
-
C.
(-∞, 0)
-
D.
[0, 1]
Solution
The function f(x) = x^2 has a minimum value of 0, so its range is [0, ∞).
Correct Answer: B — [0, ∞)
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Q. What is the range of the function sin^(-1)(x)?
-
A.
(-π/2, π/2)
-
B.
(-1, 1)
-
C.
(0, π)
-
D.
(0, 1)
Solution
The range of sin^(-1)(x) is (-π/2, π/2).
Correct Answer: A — (-π/2, π/2)
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Q. What is the range of the function y = cos^(-1)(x)?
-
A.
[0, π]
-
B.
[0, 2π]
-
C.
[−π/2, π/2]
-
D.
[−1, 1]
Solution
The range of y = cos^(-1)(x) is [0, π].
Correct Answer: A — [0, π]
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Q. What is the range of the function y = sin^(-1)(x)?
-
A.
[-π/2, π/2]
-
B.
[0, π]
-
C.
[-1, 1]
-
D.
[0, 1]
Solution
The range of y = sin^(-1)(x) is [-π/2, π/2].
Correct Answer: A — [-π/2, π/2]
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