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 product when propan-2-one reacts with iodine in the presence of a base?
-
A.
Iodoform
-
B.
Bromoform
-
C.
Chloroform
-
D.
No reaction
Solution
Propan-2-one reacts with iodine in the presence of a base to form iodoform (CHI3).
Correct Answer: A — Iodoform
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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 purpose of a demodulator in a communication system?
-
A.
To encode the signal for transmission
-
B.
To convert the modulated signal back to its original form
-
C.
To amplify the received signal
-
D.
To filter out unwanted frequencies
Solution
A demodulator's purpose is to convert the modulated signal back to its original baseband form for further processing.
Correct Answer: B — To convert the modulated signal back to its original form
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Q. What is the purpose of a galvanometer in a Wheatstone bridge?
-
A.
To measure voltage
-
B.
To measure current
-
C.
To detect the balance condition
-
D.
To provide power
Solution
A galvanometer is used to detect the balance condition in a Wheatstone bridge by indicating zero current when balanced.
Correct Answer: C — To detect the balance condition
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Q. What is the purpose of the galvanometer in a Wheatstone bridge?
-
A.
To measure voltage
-
B.
To measure current
-
C.
To detect the balance condition
-
D.
To provide power
Solution
The galvanometer is used to detect the balance condition by indicating the current flow.
Correct Answer: C — To detect the balance condition
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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 human hearing in Hertz?
-
A.
20 Hz to 20 kHz
-
B.
20 kHz to 20 MHz
-
C.
1 Hz to 100 kHz
-
D.
10 Hz to 10 kHz
Solution
The typical range of human hearing is from 20 Hz to 20 kHz.
Correct Answer: A — 20 Hz to 20 kHz
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Q. What is the range of human hearing in terms of frequency?
-
A.
20 Hz to 20 kHz
-
B.
20 kHz to 20 MHz
-
C.
1 Hz to 100 kHz
-
D.
100 Hz to 10 kHz
Solution
The typical range of human hearing is from 20 Hz to 20 kHz.
Correct Answer: A — 20 Hz to 20 kHz
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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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Q. What is the range of the function y = tan^(-1)(x)?
-
A.
(-π/2, π/2)
-
B.
(0, π)
-
C.
(0, 1)
-
D.
(-1, 1)
Solution
The range of the function y = tan^(-1)(x) is (-π/2, π/2).
Correct Answer: A — (-π/2, π/2)
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Q. What is the rank of the matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Solution
The rows of A are linearly dependent, hence the rank is 2.
Correct Answer: B — 2
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Q. What is the rank of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
Solution
The rank of the matrix is 2, as the rows are linearly dependent.
Correct Answer: B — 2
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