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Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of the value 40?

A. 0
B. 1
C. 2
D. 3

Solution

Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1

Correct Answer: C — 2

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Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of a value 40?

A. 1
B. 0
C. 2
D. -1

Solution

Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1.

Correct Answer: C — 2

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Q. If the data set has a mean of 30 and a variance of 16, what is the standard deviation?

A. 4
B. 5
C. 6
D. 7

Solution

Standard Deviation = √Variance = √16 = 4.

Correct Answer: A — 4

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Q. If the data set has a mean of 50 and a median of 45, what can be said about the data distribution?

A. Symmetric
B. Positively skewed
C. Negatively skewed
D. Uniform

Solution

Since the mean is greater than the median, the distribution is positively skewed.

Correct Answer: B — Positively skewed

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Q. If the data set has a mean of 50 and a standard deviation of 10, what is the z-score of the value 70?

A. 1
B. 2
C. 3
D. 4

Solution

Z-score = (X - Mean) / Standard Deviation = (70 - 50) / 10 = 2.

Correct Answer: B — 2

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Q. If the data set has a mean of 50 and a variance of 16, what is the standard deviation?

A. 2
B. 4
C. 8
D. 16

Solution

Standard Deviation = √Variance = √16 = 4.

Correct Answer: B — 4

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Q. If the data set is 1, 2, 2, 3, 4, 4, 4, 5, what is the mode?

A. 2
B. 3
C. 4
D. 5

Solution

Mode = 4 (most frequent value).

Correct Answer: C — 4

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Q. If the data set is 4, 4, 4, 5, 5, 6, what is the mode?

A. 4
B. 5
C. 6
D. None

Solution

Mode = 4 (most frequent value).

Correct Answer: A — 4

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Q. If the data set is {5, 7, 7, 8, 10}, what is the mode?

A. 5
B. 7
C. 8
D. 10

Solution

Mode = 7 (most frequently occurring value).

Correct Answer: B — 7

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Q. If the data set is {5, 7, 8, 9, 10}, what is the interquartile range?

A. 2
B. 3
C. 4
D. 5

Solution

Q1 = 7, Q3 = 9; Interquartile Range = Q3 - Q1 = 9 - 7 = 2.

Correct Answer: B — 3

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Q. If the data set is {5, 7, 8, 9, 10}, what is the standard deviation?

A. 1.58
B. 2.58
C. 3.58
D. 4.58

Solution

Mean = 7.8. Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²]/5 = 2.5. Standard Deviation = √2.5 ≈ 1.58.

Correct Answer: A — 1.58

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Q. If the data set is: 3, 7, 7, 19, what is the median?

A. 7
B. 10
C. 11
D. 12

Solution

Median = (7 + 7) / 2 = 7.

Correct Answer: A — 7

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Q. If the data set is: 5, 7, 8, 9, 10, what is the median?

A. 7
B. 8
C. 9
D. 10

Solution

Median is the middle value. Here, the middle values are 7 and 8, so Median = (7+8)/2 = 7.5.

Correct Answer: B — 8

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Q. If the data set {1, 2, 3, 4, 5} is transformed to {2, 3, 4, 5, 6}, what happens to the standard deviation?

A. Increases
B. Decreases
C. Remains the same
D. Cannot be determined

Solution

The standard deviation remains the same because the transformation is a shift.

Correct Answer: C — Remains the same

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Q. If the data set {10, 20, 30, 40, 50} is transformed to {x + 5}, what happens to the standard deviation?

A. Increases
B. Decreases
C. Remains the same
D. Cannot be determined

Solution

Standard deviation remains the same as adding a constant does not affect dispersion.

Correct Answer: C — Remains the same

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Q. If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?

A. 3
B. 7
C. 8
D. 12

Solution

Q1 is the median of the first half of the data set {3, 7}, which is 7.

Correct Answer: B — 7

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Q. If the data set {3, 7, 8, 12, 14} is given, what is the median?

A. 8
B. 7
C. 12
D. 10

Solution

Median is the middle value, which is 8.

Correct Answer: A — 8

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Q. If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the deviations from the mean?

A. 0
B. 1
C. 2
D. 3

Solution

The sum of deviations from the mean is always 0.

Correct Answer: A — 0

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Q. If the density of a substance is calculated as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the relative uncertainty?

A. 0.025
B. 0.02
C. 0.005
D. 0.01

Solution

Relative uncertainty = (absolute uncertainty / density) = 0.2 / 8.0 = 0.025.

Correct Answer: B — 0.02

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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the relative uncertainty in the density?

A. 0.0125
B. 0.01
C. 0.005
D. 0.02

Solution

Relative uncertainty = (absolute uncertainty / measured value) = 0.1 / 8.0 = 0.0125.

Correct Answer: B — 0.01

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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.5 g/cm³, what is the range of possible values for the density?

A. 7.5 to 8.5 g/cm³
B. 8.0 to 8.5 g/cm³
C. 8.0 to 9.0 g/cm³
D. 7.0 to 9.0 g/cm³

Solution

Range = (8.0 - 0.5) to (8.0 + 0.5) = 7.5 to 8.5 g/cm³.

Correct Answer: A — 7.5 to 8.5 g/cm³

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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the relative uncertainty in the density?

A. 0.025
B. 0.02
C. 0.005
D. 0.1

Solution

Relative uncertainty = (absolute uncertainty / measured value) = 0.2 / 8.0 = 0.025.

Correct Answer: B — 0.02

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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the range of possible densities?

A. 7.8 to 8.2 g/cm³
B. 7.5 to 8.5 g/cm³
C. 8.0 to 8.4 g/cm³
D. 8.0 to 8.2 g/cm³

Solution

Range = 8.0 ± 0.2 gives 7.8 to 8.2 g/cm³.

Correct Answer: A — 7.8 to 8.2 g/cm³

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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the absolute error in the density?

A. 0.1 g/cm³
B. 0.01 g/cm³
C. 0.5 g/cm³
D. 0.2 g/cm³

Solution

The absolute error is given directly as ±0.1 g/cm³.

Correct Answer: A — 0.1 g/cm³

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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the fractional error in the density?

A. 0.0125
B. 0.01
C. 0.005
D. 0.02

Solution

Fractional error = (absolute error / measured value) = 0.1 / 8.0 = 0.0125.

Correct Answer: B — 0.01

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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the absolute error in the volume calculated from this density?

A. 0.025 cm³
B. 0.1 cm³
C. 0.2 cm³
D. 0.5 cm³

Solution

Volume = mass/density; if mass is constant, the absolute error in volume = (mass * absolute error in density) / (density²).

Correct Answer: A — 0.025 cm³

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Q. If the determinant | x 2 | | 3 4 | = 0, find x.

A. 1
B. 2
C. 3
D. 4

Solution

Setting the determinant to zero gives x*4 - 2*3 = 0, thus x = 1.5.

Correct Answer: B — 2

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Q. If the directrix of a parabola is given by the equation y = -p, what is the equation of the parabola?

A. y^2 = 4px
B. x^2 = 4py
C. y^2 = -4px
D. x^2 = -4py

Solution

The equation of a parabola with directrix y = -p is y^2 = -4px.

Correct Answer: C — y^2 = -4px

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Q. If the distance between the object and the image formed by a lens is 70 cm, and the object distance is 30 cm, what is the image distance?

A. 40 cm
B. 50 cm
C. 60 cm
D. 70 cm

Solution

Image distance (v) = Object distance (u) + Distance between object and image = 30 cm + 70 cm = 40 cm.

Correct Answer: A — 40 cm

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Q. If the distance between the plates of a capacitor is doubled, what happens to its capacitance?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

Capacitance is inversely proportional to the distance between the plates. If the distance d is doubled, the capacitance C becomes C/2.

Correct Answer: B — It halves

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